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Abergavenny

Abergavenny (Y Fenni, archaically Abergafenni meaning "mouth of the River Gavenny") is a market town and community in Monmouthshire, Wales. Abergavenny is promoted as a Gateway to Wales; it is approximately 6 mi from the border with England and is located where the A40 trunk road and the recently upgraded A465 Heads of the Valleys road meet.

Originally the site of a Roman fort, Gobannium, it became a medieval walled town within the Welsh Marches. The town contains the remains of a medieval stone castle built soon after the Norman conquest of Wales.

Abergavenny is situated at the confluence of the River Usk and a tributary stream, the Gavenny. It is almost entirely surrounded by mountains and hills: the Blorenge (559 m), the Sugar Loaf (596 m), Ysgyryd Fawr (Great Skirrid), Ysgyryd Fach (Little Skirrid), Deri, Rholben and Mynydd Llanwenarth, known locally as "Llanwenarth Breast". Abergavenny provides access to the nearby Black Mountains and the Brecon Beacons National Park. The Marches Way and Beacons Way pass through Abergavenny whilst the Offa's Dyke Path passes through Pandy five miles to the north and the Usk Valley Walk passes through nearby Llanfoist.

In the UK 2011 census, the six relevant wards (Lansdown, Grofield, Castle, Croesonen, Cantref and Priory) collectively listed Abergavenny's population as 12,515. The town hosted the 2016 National Eisteddfod of Wales.

Etymology
The town derives its name from a Brythonic word Gobannia meaning "river of the blacksmiths", and relates to the town's pre-Roman importance in iron smelting. The name is related to the modern Welsh word gof (blacksmith), and so is also associated with the Welsh smith Gofannon from folklore. The river later became, in Welsh, Gafenni, and the town's name became Abergafenni, meaning "mouth of (Welsh: Aber) the Gavenny (Gafenni)". In Welsh, the shortened form Y Fenni may have come into use after about the 15th century, and is now used as the Welsh name. Abergavenny, the English spelling, is in general use.

Geography
The town originally developed on the high ground to the north of the floodplain of the River Usk and to the west of the valley of the much smaller Gavenny River though has since extended to the east of the latter. It has merged with the originally separate settlement of Mardy to the north but remains separate from that of Llanfoist to the south due to the presence of the river and its floodplain; nevertheless Llanfoist is in many ways a suburb of the town. The ground rises gradually in the north of the town before steepening to form the Deri and Rholben spurs of Sugar Loaf. The A4143 crossing of the Usk by means of the historic Usk Bridge is sited at the narrowest point of the floodplain, a site also chosen for the former crossing of a tramroad and the later mainline railway. The high ground at either side is formed by a legacy of the last ice age, the recessional Llanfoist moraine which underlies both the village which gives it its name, the town centre and the Nevill Hall area. The older parts of the town north of its centre are built upon a relatively flat-lying alluvial fan extending west from the area of St Mary's Priory to Cantref and of similar age to the moraine.

In the UK 2011 census, the six relevant wards (Lansdown, Grofield, Castle, Croesonen, Cantref and Priory) collectively listed Abergavenny's population as 12,515.

Roman period
Gobannium was a Roman fort guarding the road along the valley of the River Usk, which linked the legionary fortress of Burrium (Usk) and later Isca Augusta or Isca Silurum (Caerleon) in the south with Y Gaer, Brecon and Mid Wales. It was also built to keep the peace among the local British Iron Age tribe, the Silures. Cadw considers that the fort was occupied from around CE50 to CE150. Remains of the walls of this fort were discovered west of the castle when excavating the foundations for a new post office and telephone exchange building in the late 1960s.

11th century
Abergavenny grew as a town in early Norman times under the protection of the Baron Bergavenny (or Abergavenny). The first Baron was Hamelin de Balun, from Ballon, a small town with a castle in Maine-Anjou near Le Mans. Today it is in the Sarthe département of France. He founded the Benedictine priory, now the Priory Church of St Mary, in the late 11th century. The Priory belonged originally to the Benedictine foundation of St. Vincent Abbaye at Le Mans. It was subsequently endowed by William de Braose, with a tithe of the profits of the castle and town. The church contains some unique alabaster effigies, church monuments and unique medieval wood carving, such as the Tree of Jesse.

12th and 13th centuries
Owing to its geographical location, the town was frequently embroiled in the border warfare and power play of the 12th and 13th centuries in the Welsh Marches. In 1175, Abergavenny Castle was the site of a massacre of Seisyll ap Dyfnwal and his associates by William de Braose, 4th Lord of Bramber. Reference to a market at Abergavenny is found in a charter granted to the Prior by William de Braose.

15th to 17th centuries
Owain Glyndŵr attacked Abergavenny in 1404. According to popular legend, his raiders gained access to the walled town with the aid of a local woman who sympathised with the rebellion, letting a small party in via the Market Street gate at midnight. They were able to open the gate and allow a much larger party who set fire to the town and plundered its churches and homes leaving Abergavenny Castle intact. Market Street has been referred to as "Traitors' Lane" thereafter. In 1404 Abergavenny was declared its own nation by Ieuan ab Owain Glyndŵr, illegitimate son of Owain Glyndŵr. The arrangement lasted approximately two weeks.

At the Dissolution of the Monasteries in 1541, the priory's endowment went towards the foundation of a free grammar school, King Henry VIII Grammar School, the site itself passing to the Gunter family. During the Civil War, prior to the siege of Raglan Castle in 1645, King Charles I visited Abergavenny and presided in person over the trial of Sir Trefor Williams, 1st Baronet of Llangibby, a Royalist who changed sides, and other Parliamentarians. In 1639, Abergavenny received a charter of incorporation under the title of bailiff and burgesses. A charter with extended privileges was drafted in 1657, but appears never to have been enrolled or to have come into effect. Owing to the refusal of the chief officers of the corporation to take the oath of allegiance to William III in 1688, the charter was annulled, and the town subsequently declined in prosperity. Chapter 28 of the 1535 Act of Henry VIII, which provided that Monmouth, as county town, should return one burgess to Parliament, further stated that other ancient Monmouthshire boroughs were to contribute towards the payment of the member. In consequence of this clause Abergavenny on various occasions shared in the election, the last instance being in 1685.

The right to hold two weekly markets and three yearly fairs, beginning in the 13th century, was held ever since as confirmed in 1657. Abergavenny was celebrated for the production of Welsh flannel, and also for the manufacture, whilst the fashion prevailed, of goats' hair periwigs.

19th and 20th centuries

Abergavenny railway station, situated south-east of the town centre, opened on 2 January 1854 as part of the Newport, Abergavenny and Hereford Railway. The London North Western Railway sponsored the construction of the railway linking Newport station to Hereford station. The line was taken over by the West Midland Railway in 1860 before becoming part of the Great Western Railway in 1863. A railway line also ran up the valley towards Brynmawr and to Merthyr Tydfil; this was closed during the Beeching cuts in the 1960s and the line to Clydach Gorge is now a cycle track and footpath. The Baker Street drill hall was completed in 1896. Adolf Hitler's deputy, Rudolf Hess, was kept under escort at Maindiff Court Hospital during the Second World War, after his flight to Britain. In 1964, the Royal Observer Corps opened a small monitoring bunker to be used in the event of a nuclear attack. It was closed in 1968 but reopened in 1973 due to the closure of a bunker near Brynmawr. It closed in 1991 on the stand down of the ROC. It remains mostly intact.

Baron of Abergavenny
The title of Baron Abergavenny, in the Nevill family, dates from the 15th century with Edward Nevill, 3rd Baron Bergavenny. From him it has descended continuously, the title being increased to an earldom in 1784; and in 1876 William Nevill [sic] 5th Earl, an indefatigable and powerful supporter of the Tory Party, was created 1st Marquess of Abergavenny.

Coldbrook Park was a country house in an estate some 2 km southeast of the town. The house was originally built in the 14th century and belonged to the Herbert family for many generations until purchased by John Hanbury for his son, the diplomat Sir Charles Hanbury Williams. Sir Charles reconstructed the house in 1746 with the addition of a nine-bay two-storey Georgian façade with a Doric portico. It subsequently passed down in the Hanbury Williams family until it was demolished in 1954.

Events
Held during the first week of August every year, the National Eisteddfod is a celebration of the culture and language in Wales. The festival travels from place to place, alternating between north and south Wales, attracting around 150,000 visitors and over 250 tradestands and stalls. In 2016 it was held in Abergavenny for the first time since 1913. The Chair and Crown for 2016 were presented to the festival's Executive Committee at a ceremony held in Monmouth on 14 June 2016.

The Abergavenny Food Festival is held in the second week of September each year. The Steam, Veteran and Vintage Rally takes place in May every year. The event expands year on year with the 2016 rally including a rock choir, shire horses, motorcycling stunts, vintage cars and steam engines. The Country and Western Music Festival is attended by enthusiasts of country music. It marked its third year in 2016 and was attended by acts including Ben Thompson, LA Country and many more. The event was last held in 2017. The Abergavenny Writing Festival began in April 2016 and is a celebration of writing and the written word. The Abergavenny Arts Festival, first held in 2018, celebrates arts in their broadest sense and showcases amateur and professional artists from the vibrant local arts scene together with some from further afield.

Welsh language
In recent decades the number of Welsh speakers in the town has increased dramatically. The 2001 census recorded 10% of the local population spoke the language, a five-fold increase over ten years from the figure of 2% recorded in 1991. The town has one of the two Welsh-medium primary schools in Monmouthshire, Ysgol Gymraeg y Fenni, which was founded in the early 1990s. It is also home to the Abergavenny Welsh society, Cymreigyddion y Fenni, and the local Abergavenny Eisteddfod.

Sport
Abergavenny was the home of Abergavenny Thursdays F.C., formed in 1927 and merged with Govilon, the local village side in 2013. The new club, Abergavenny Town F.C., plays at the Pen-y-pound Stadium, maintained and run by Thursday’s football trust, as members of the Ardal South East league (tier 3) for the 2021–22 season. It is also the home of Abergavenny RFC, a rugby union club founded in 1875 who play at Bailey Park, Abergavenny. In the 2018–19 season, they play in the Welsh Rugby Union Division Three East A league. Abergavenny Hockey Club, formed in 1897, currently play at the Abergavenny Leisure Centre on Old Hereford Road.

Abergavenny Cricket Club play at Pen-y-Pound, Avenue Road and Glamorgan CCC also play some of their games here. Abergavenny Cricket Club was founded in 1834 and celebrated the 175th anniversary of its foundation in 2009. Abergavenny Tennis Club also play at Pen-y-Pound and plays in the South Wales Doubles League and Aegon Team Tennis. The club engages the services of a head tennis professional to run a coaching programme for the town and was crowned Tennis Wales' Club of the Year in 2010. Abergavenny hosted the British National Cycling Championships in 2007, 2009 and 2014, as part of the town's Festival of Cycling.

Cattle market
A cattle market was held in Abergavenny from 1863 to December 2013. During the period 1825–1863 a sheep market was held at a site in Castle Street, to stop the sale of sheep on the streets of the town. At the time of its closure the market was leased and operated by Abergavenny Market Auctioneers Ltd, who held regular livestock auctions on the site. Market days were held on Tuesdays for the auction sale of finished sheep, cull ewe/store and fodder (hay and straw), and some Fridays for the auction sale of cattle. Following the closure of Newport's cattle market in 2009 for redevelopment, Newport’s sales were held at Abergavenny every Wednesday.

In 2011 doubts about the future of Abergavenny Cattle Market were raised following the granting of planning permission by Monmouthshire County Council for its demolition and replacement with a supermarket, car park, and library. In January 2012 the Welsh Government announced the repeal the Abergavenny Improvement Acts of 1854 to 1871 which obliged the holding of a livestock market within the boundaries of Abergavenny town; that repeal being effective from 26 March 2012. Monmouthshire County Council, which requested that the Abergavenny Improvement Acts be repealed, supported plans for a new cattle market to be established about 10 mi from Abergavenny in countryside at Bryngwyn, some 3 mi from Raglan. There was local opposition to this site. The new Monmouthshire Livestock Centre, a 27-acre site at Bryngwyn, opened in November 2013.

Cultural history
Abergavenny has hosted the National Eisteddfod of Wales in 1838, 1913 and most recently in 2016. In 2017 the town was named one of the best places to live in Wales. The town's local radio stations are currently Sunshine Radio 107.8 FM and NH Sound 1287 AM. Abergavenny is home to an award-winning brass band. Formed in Abergavenny prior to 1884 the band became joint National Welsh League Champions in 2006 and joint National Welsh League Champions in 2011. The band also operate a Junior Band training local young musicians.

The Borough Theatre in Abergavenny town centre hosts live events covering drama, opera, ballet, music, children's events, dance, comedy, storytelling, tribute bands and talks. The Melville Centre is close to the town centre and includes the Melville Theatre that hosts a range of live events. The town held its first Abergavenny Arts Festival in 2018 and also hosts the Abergavenny Food Festival in September each year.

In popular culture
William Shakespeare's play Henry VIII features the character Lord Abergavenny. In 1968 "Abergavenny" was the title of a UK single by Marty Wilde. In 1969, it was also released in the US, under a Marty Wilde pseudonym Shannon, where it was also a minor hit. In The Adventure of the Priory School Sherlock Holmes refers to a case he is working on in Abergavenny. Abergavenny is mentioned by Stan Shunpike, the conductor of the Knight Bus when the bus takes a detour there to drop off a passenger in J. K. Rowling's Harry Potter and the Prisoner of Azkaban. The TV series Upstairs, Downstairs, features a character in the second season, Thomas Watkins, the devious Bellamy family chauffeur, who comes from Abergavenny. In the 1979 spinoff of Upstairs, Downstairs titled Thomas & Sarah, Watkins and Sarah Moffat, another major character, marry and return briefly to Abergavenny. * Much of the 1996 film, Intimate Relations starring Julie Walters, Rupert Graves, Les Dennis and Amanda Holden, was filmed at many locations in and around Abergavenny.

Railway
Abergavenny railway station lies on the Welsh Marches Line from Newport to Hereford. The weekday daytime service pattern typically sees one train per hour in each direction between Manchester Piccadilly and Cardiff Central, with most trains continuing beyond Cardiff to Swansea and west Wales. There is also a two-hourly service between Cardiff and the North Wales Coast Line to Holyhead, via Wrexham General. These services are all operated by Transport for Wales.

Roads
The town is located where the A40 trunk road and the A465 Heads of the Valleys road meet. The latter used to meet the A40 in the town centre but the A465 now runs to the east of the town centre.

Buses
A network of services link the town with local villages. In addition Stagecoach South Wales operate service 23 to Hereford and Newport approximately every two hours while Newport Bus operate service 83 to Monmouth.

Notable buildings
Abergavenny Castle is located strategically just south of the town centre overlooking the River Usk. It was built in about 1067 by the Norman baron Hamelin de Ballon to guard against incursions by the Welsh from the hills to the north and west. All that remains is defensive ditches and the ruins of the stone keep, towers, and part of the curtain wall. It is a Grade I listed building.

Various markets are held in the Market Hall, for example: Tuesdays, Fridays and Saturdays – retail market; Wednesdays – flea market; fourth Thursday of each month – farmers' market; third Sunday of each month – antique fair; second Saturday of each month – craft fair.

The Church in Wales church of the Holy Trinity is in the Diocese of Monmouth. Holy Trinity Church was consecrated by the Bishop of Llandaff on 6 November 1840. It was originally built as a chapel to serve the adjacent almshouses and the nearby school. It has been Grade II listed since January 1974.

Other listed buildings in the town include the parish Priory Church of St Mary, a medieval and Victorian building that was originally the church of the Benedictine priory founded in Abergavenny before 1100; the sixteenth century Tithe Barn near St Mary's; the Victorian Church of the Holy Trinity; the Grade II* listed St John's Masonic Lodge; Abergavenny Museum; the Public Library; the Town Hall; and the remains of Abergavenny town walls behind Neville Street.

From 1851, the Monmouthshire lunatic asylum, later Pen-y-Fal Hospital, a psychiatric hospital, stood on the outskirts of Abergavenny. Between 1851 and 1950, over 3,000 patients died at the hospital. A memorial plaque for the deceased has now been placed at the site. After closure in the 1990s, its buildings and grounds were redeveloped as housing. Some psychiatric services are now administered from Maindiff Court Hospital on the outskirts of the town, close to the foot of the Skirrid mountain.

Parks and gardens
Abergavenny has three public urban parks which are listed on the Register of Parks and Gardens of Special Historic Interest in Wales: the grounds of Abergavenny Castle, Linda Vista Gardens and Bailey Park. A fourth registered garden, at The Hill to the north of the town, forms part of the grounds of a residential development.

Twinning

 * 🇩🇪 Östringen, Germany
 * 🇫🇷 Beaupréau, France
 * 🇮🇹 Sarno, Italy

Military
One of the eleven Victoria Cross medals won at Rorke's Drift was awarded to John Fielding from Abergavenny. He had enlisted under the false name of Williams. One was also awarded for the same action to Robert Jones, born at Clytha between Abergavenny and Raglan. Another Abergavenny-born soldier, Thomas Monaghan received his VC for defending his colonel during the Indian Rebellion. In 1908 following the formation of the Territorial Force the Abergavenny Cadet Corps was formed and affiliated with the 3rd Battalion, The Monmouthshire Regiment. In 1912 the regiment was affiliated with the new formed 1st Cadet Battalion, The Monmouthshire Regiment.

Notable people
See also Category:People from Abergavenny
 * Augustine Baker (1575–1641), well-known Benedictine mystic and an ascetic writer. He was one of the earliest members of the English Benedictine Congregation which was newly restored to England after the Reformation.
 * John Williams VC (1857–1932) soldier, recipient of the Victoria Cross for actions at Rorke’s Drift.
 * Scott Ellaway (born 1981), conductor, was born and brought up locally.
 * Becky James (born 1991), racing cyclist, double gold medallist at the 2013 UCI Track Cycling World Championships and double silver medallist at the 2016 Summer Olympics, was born and grew up in Abergavenny.
 * Matthew Jay (1978–2003), singer-songwriter, spent much of his life in the town.
 * Peter Law (1948–2006), politician and Independent MP, notable for defeating the Labour candidate in the safest Welsh seat during the 2005 general election was born in Abergavenny.
 * Saint David Lewis (1616–1679), Catholic priest and martyr, was born in Abergavenny and prayed in the local Gunter Mansion.
 * Malcolm Nash (1945–2019), cricketer, famous for bowling to Gary Sobers who hit six sixes in one Nash over, was born in Abergavenny.
 * Mary Penry (1735–1804), Moravian sister in 18th-century Pennsylvania was born in Abergavenny.
 * Owen Sheers (born 1974), poet, grew up in Abergavenny.
 * Oliver Thornton (born 1979), West End actor, starred of Priscilla, Queen of the Desert, was born and grew up in Abergavenny.
 * Vulcana (Miriam Kate Williams, 1874–1946), world-famous strongwoman, was born in Abergavenny.
 * Ethel Lina White (1876–1944), crime writer best known for her novel The Wheel Spins (1936), on which the Alfred Hitchcock film The Lady Vanishes (1938) was based.
 * Jules Williams (born 1968), writer, director, and producer of The Weigh Forward.
 * Raymond Williams, (1921–1988) academic, critic and writer was born and brought up locally.
 * Dave Richards, (1993) professional footballer for Crewe Alexandra was born and raised in the town.
 * Marina Diamandis (1985) Professional singer and songwriter

title: Abergavenny


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Abersychan

Abersychan is a town and community north of Pontypool in Torfaen, Wales, and lies within the boundaries of the historic county of Monmouthshire and the preserved county of Gwent.

Abersychan lies in the narrow northern section of the Afon Lwyd valley.

The town includes two schools; Abersychan Comprehensive School and Victoria Primary School; together with various shops and other amenities including Abersychan Rugby Club.

Abersychan was the birthplace of the politicians Roy Jenkins, Don Touhig and Paul Murphy (member of parliament for Torfaen); and of the rugby footballers Wilfred Hodder, Candy Evans and Bryn Meredith.

History
Like many of the 17th century isolated agricultural hamlets in the forested South Wales Valleys, Abersychan became a thriving industrial centre in the 19th and early 20th centuries, particularly for iron production. After the discovery of iron stone locally, the principal ironworks were built by the British Iron Company in 1825, served mainly by the London and North Western Railway's Brynmawr and Blaenavon Railway. The ironwork's main office building and quadrangle were designed by architect Decimus Burton, best known for his design of London Zoo. The works passed to the New British Iron Company in 1843 and to the Ebbw Vale Company in 1852, before closing in 1889. On 6 February 1890, an underground explosion at Llanerch Colliery killed 176.

The site of the former ironworks today is a core site of 71 hectare, and a total land area of 526 hectare, includes a number of listed buildings:
 * Abersychan Limestone Railway: built c. 1830 to carry limestone from Cwm Lascarn quarry to the British Ironworks.
 * Air Furnace at British Ironworks
 * British Colliery Pumping Engine House: a Cornish beam pumping engine house built by the British Iron Company. Built of sandstone with a slate roof, and retains several fixtures
 * Cwmbyrgwm Colliery: Site of former colliery including remains of a water-balance headgear, chimney, oval shafts, water power dams, tramroad routes, and waste tips.

Various proposals have been made over the years to redevelop the site, currently under the ownership of HSBC, but none have so far passed the requirements of Torfaen county council.

Local government
Abersychan constitutes a community and electoral ward of the county borough of Torfaen. The area was part of the ancient parish of Trevethin, in Monmouthshire. On 3 June 1864 Abersychan was constituted a local government district, governed by a local board. In 1894 Abersychan became an urban district and civil parish. The urban district was abolished in 1935, with most of its area passing to Pontypool urban district, and a small area going to Abercarn UD.

In 1974 the area became part of the borough of Torfaen, in the new local government county of Gwent. The community of Abersychan was formed in 1985, but no community council has yet been formed. Abersychan and Cwmavon is now a ward for the Pontypool Community Council. In 1996 Torfaen became a unitary authority.

The Abersychan community includes Abersychan, Cwmavon, Garndiffaith, Pentwyn, Talywain, Varteg, and Victoria Village.

Local Transport
The nearest railway stations to Abersychan are Pontypool & New Inn (3 miles), Llanhilleth (3.5 miles) and Abergavenny (7 miles). Abersychan was served by the following (disused) stations:
 * Abersychan and Talywain railway station
 * Abersychan Low Level railway station

Pentwyn
Pentwyn, Torfaen is a small village located in the district of Abersychan. It contains a post office, several houses and a small play park. The village has a cricket team (Pontnewynydd CC) and is located right next to the old railway line. The cricket club celebrated its 100-year anniversary in 2006 with a successful tour to Cork, Ireland. The village has superb views over the River Severn and Newport to the south.

Victoria Village
Victoria Village is a small hamlet located in the district of Abersychan. It comprises a small village school and a number of houses. A small group of houses on Incline Road mark the beginning of the village and the village boundary is near Cwmavon. Victoria Primary School is also in this area, housed in large grounds. Many homes are built around the school's boundaries. Victoria Village primary school was opened in 1903 and closed by the council in 2018. The last head of the school was Miss Joy Dando. And caretaker Miss Debbie Williams.

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title: Abersychan


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Abertillery

Abertillery (Abertyleri) is a town and a community of the Ebbw Fach valley in the historic county of Monmouthshire, Wales. Following local government reorganisation it became part of the Blaenau Gwent County Borough administrative area.

The surrounding landscape borders the Brecon Beacons National Park and the Blaenavon World heritage Site. Formerly a major coal mining centre the Abertillery area was transformed in the 1990s using EU and other funding to return to a greener environment.

Situated on the A467 the town is 15 mi north of the M4 and 5 mi south of the A465 "Heads of the Valleys" trunk road. It is about 25 mi by road from Cardiff and 47 mi from Bristol.

According to the 2011 Census, 4.8% of the ward's 4,416 (212 residents) resident-population can speak, read, and write Welsh. This is below the county's figure of 5.5% of 67,348 (3,705 residents) who can speak, read, and write Welsh.

Etymology
The name of the community means "the mouth of the River Tyleri", which flows into the town. The name Tyleri is probably derived from a personal name.

Town centre
Abertillery's traditional-style town centre mainly developed in the late 19th century and as such has some interesting Victorian architecture. Spread over 4 main streets the town in its heyday had two department stores and a covered Victorian arcade linking two of the main shopping areas. These were all included in a Blaenau Gwent Borough Council remodelling and modernisation project using European Union funding in a £13 million programme spread over a 5-year period ending in 2015.

The project included a new multi-storey car park, a revamp of public areas and the town's Metropole Theatre. This building provides production, exhibition, conference and meeting facilities as well as housing Abertillery museum. In March 2014 Prince Edward, Earl of Wessex, officiated at the launch of Jubilee Square, a public facility in the town centre next to St Michael's Church.

Coal mining
Major industry came to the area in 1843 when the locality's first deep coal mine was sunk at Tir Nicholas Farm, Cwmtillery. The town developed rapidly thereafter and played a major part in the South Wales coalfield. Its population rose steeply, being 10,846 in the 1891 census and 21,945 ten years later. The population peaked just short of 40,000 around the beginning of the 1930s. Eventually there were six deep coal mines, numerous small coal levels, a tin works, brick works, iron foundry and light engineering businesses in the area. Just one of the coal mines, Cwmtillery, produced over 32 million tons of coal in its lifetime and at its height employed 2760 men and boys.

In 1960 an underground explosion at Six Bells Colliery resulted in the loss of life of 45 local miners. Fifty years later the archbishop of Canterbury Rowan Williams officiated at the launch of the Guardian mining memorial. This artistically acclaimed monument standing at 20m tall overlooks Parc Arael Griffin, the now reclaimed and landscaped former colliery site. The adjoining Ty Ebbw Fach visitor centre provides conference facilities, a restaurant and a "mining valley" experience room. Not long after the disaster the renowned artist L. S. Lowry visited the area and recorded the scene. The resultant landscape painting now hangs in National Museum Cardiff.

The coal mines remained the predominant economic emphasis until the general run down of the industry in the 1980s.

Abertillery Conurbation
Away from the town centre, the often steep sided nature of the landscape, imposes its own demands on development. Whilst this sounds limiting it has helped provide the almost amphitheatre nature of Abertillery Park, often described as one of the most attractive rugby grounds in world rugby.

The street plan and housing stock flow uninterrupted from Cwmtillery in the north to Six Bells in the south, forming the town that is Abertillery. Prior to 1974 local government was provided by Abertillery Urban District Council (AUDC). Its area included the small neighbouring villages of Aberbeeg, Llanhilleth and Brynithel. Historical data relating to Abertillery occasionally refers to this AUDC area meaning that it can be difficult to compare like with like. For example, the 2014 population for the wider conurbation area is around 20,000 rather than the 11,000 often quoted for Abertillery itself.

Whilst in the main the area has an older housing stock there are several developments of modern, often large homes, generally found on the outskirts of the town with views out over the surrounding area. These apart, terraced council tax band A and B properties predominate, meaning that average house prices are among the most affordable in the UK.

Early history
There are very few written historical records relating to the area before the town developed in the middle of the 19th century. Nevertheless, there are facts that you can use to outline important events.

 * Abertillery museum has locally discovered artefacts dating as far back as the Bronze Age.
 * St Illtyd's Church overlooking the town dates to the 13th century – probably with 6th century origins.
 * St Illtyd's Motte lies just to the south west of the church. A Norman castle mound, it was probably destroyed in 1233.
 * The ruins of two more recent, probably 14th century, castles lie on private land to the northeast of St Illtyd's Church.
 * There are several ruined mediaeval farmhouses in the Abertillery area.
 * The Local Blaenau Gwent Baptist church can trace its roots back to Tŷ Nest Llewellyn, a ruined 17th-century dwelling place often used by non-conformists to escape from the religious persecution of the times.

Before the coming of major industry, Abertillery was little more than an area of scattered farms in the ancient parish of Aberystruth. In 1779 the parish minister Edmund Jones described the area thus: "The valley of Tyleri ... is the most delightful. The trees ... especially the beech trees, abounding about rivers great and small, the hedges and lanes make these places exceeding pleasant and the passing by them delightful and affecting ... in these warm valleys, with the prospect of the grand high mountains about them would make very delightful habitations." In 1799 clergyman and historian Archdeacon William Coxe toured the area and in writing a diary of his travels described it as "... richly wooded, and highly cultivated...we looked down with delight upon numerous valleys ... with romantic scenery". The entire population of Aberystruth parish at the turn of the 19th century was just a little over 800. It is not known what the population of Abertillery was at the time but it was probably in the very low hundreds, all of whom would have spoken Welsh only.

Industrialisation
The area's first deep coal mine was sunk in 1843.

Collieries in Abertillery

 * Six Bells Colliery

Abertillery Institute
The first reading rooms were set up in Abertillery in 1856. However, when Thomas Powell took over the Tillery Colliery in 1882 he made a commitment to establish educational facilities for his workers.

Local government
Formed in 1877, Abertillery Urban District Council incorporated the adjoining smaller communities of Six Bells, Cwmtillery, Brynithel, Aberbeeg and Llanhilleth. The population of this conurbation climbed to almost 40,000 in 1931 making it the second largest town in Monmouthshire. The council was abolished in 1974 as part of major UK wide local government reorganisation.

Transport
The reopening of Abertillery railway station has been identified as a future development of the Ebbw Valley Railway.

Education
Abertillery Learning Community provides all-through education for the town and neighbouring areas. Until the 1970s the town had its own local authority-run Grammar school providing education up to the age of eighteen. Tertiary education is now provided by Coleg Gwent at Ebbw Vale – opened in 2013.

Industry
There are several small and medium-sized business parks in the area offering a range of business premises. In 2014 the largest employer was Tyleri Valley Foods. Many local people commute outside the area to work.

Sport, leisure and tourism
Abertillery Town cricket club and Abertillery Blaenau Gwent RFC formed in the 1880s. Both have their playing headquarters at "the Park" one of the most picturesque sporting complexes in the UK.

The town supports two local Saturday football teams: Abertillery Bluebirds and Abertillery Excelsiors. There are numerous other sports activities running on an organized basis such as bowls, badminton, squash etc.

The surrounding landscape provides hill walking opportunities and walker led groups are thriving in the area. One example is Ebbw Fach Trekkers walking group.

The local museum has displays showing what life was like in the area in its heyday. It also has its own "valleys" Italian café complete with original furnishings.

The Metropole theatre holds musical and drama events – from Blues to amateur dramatics and dance.

The 20 m Guardian memorial is a destination for visitors to South Wales and amateur photographers. The visitor centre Tŷ Ebbw Fach stands nearby and provides cafe and visitor "mining valley" experience facilities.

Notable people

 * See also Category:People from Abertillery.

Local people of note in the fields of civil engineering, sport, science, medicine, religion and art:

 * Beatrice Green, labour activist and orator
 * Chris Hill, professional tennis player
 * Harold Jones (murderer), the 15-year old killer committed 2 murders in 1921.
 * Jack Shore (MMA fighter), competes in the UFC
 * Thora Silverthorne, leading activist within the Communist Party of Great Britain, Labour Party MP for Reading, veteran of the Spanish Civil War, founder of the Association of Nurses, and former president of the Socialist Medical Association
 * Jake Blackmore, international rugby forward who played rugby union for Abertillery and represented his country in the rugby union and in the rugby league.

International relations
Abertillery is twinned with:

 * Flag of France.svg Royat, France

title: Abertillery


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Abeyance

Abeyance (from the Old French abeance meaning "gaping") is a state of expectancy in respect of property, titles or office, when the right to them is not vested in any one person, but awaits the appearance or determination of the true owner. In law, the term abeyance can be applied only to such future estates as have not yet vested or possibly may not vest. For example, an estate is granted to A for life, with remainder to the heir of B. Following A's death, if B is still alive, the remainder is in abeyance, for B has no heirs until B's death. Similarly, the freehold of a benefice, on the death of the incumbent, is said to be in abeyance until the next incumbent takes possession.

The term hold in abeyance is used in lawsuits and court cases when a case is temporarily put on hold.

History
The most common use of the term is in the case of English peerage dignities. Most such peerages pass to heirs-male, but the ancient baronies created by writ, as well as some very old earldoms, pass instead to heirs-general (by cognatic primogeniture). In this system, sons are preferred from eldest to youngest, the heirs of a son over the next son, and any son over daughters, but there is no preference among daughters: they or their heirs inherit equally.

If the daughter is an only child or her sisters are deceased and have no living issue, she (or her heir) is vested with the title; otherwise, since a peerage cannot be shared nor divided, the dignity goes into abeyance between the sisters or their heirs, and is held by no one. If through lack of issue, marriage, or both, eventually only one person represents the claims of all the sisters, they can claim the dignity as a matter of right, and the abeyance is said to be terminated. On the other hand, the number of prospective heirs can grow quite large, since each share potentially can be divided between daughters, where the owner of a share dies without leaving a son.

A co-heir may petition the Crown for a termination of the abeyance. The Crown may choose to grant the petition, but if there is any doubt whatsoever as to the pedigree of the petitioner, the claim is normally referred to the Committee for Privileges. If the claim is unopposed, the committee will generally award the claim, unless there is evidence of collusion, the peerage has been in abeyance for more than a century, or the petitioner holds less than one-third of the claim.

This doctrine is a 17th-century innovation, although it is now applied retrospectively for centuries. It cannot be applied perfectly; for example, the eighth Baron De La Warr had three surviving sons; the first died without children, the second left two daughters, and the third left a son. In modern law, the title would have fallen into abeyance between the two daughters of the second son, and nobody else would have been able to claim it even if the abeyance were settled; however, in 1597, the grandson of the third son (whose father had been re-created Baron De La Warr in 1570) claimed the title and its precedence.

In 1604, the Baron le Despencer case was the first peerage abeyance ever settled; the second was at the Restoration in 1660. Most subsequent abeyances (only a few dozen cases) were settled after a few years, in favour of the holder of the family properties; there were two periods in which long-abeyant peerages (in some cases peerages of doubtful reality) were brought back: between 1838 and 1841 and between 1909 and 1921. The Complete Peerage reports that only baronies have been called out of abeyance, although the Earldom of Cromartie was called out of a two-year abeyance in 1895.

It is entirely possible for a peerage to remain in abeyance for centuries. For example, the Barony of Grey of Codnor was in abeyance for over 490 years between 1496 and 1989, and the Barony of Hastings was similarly in abeyance for over 299 years from 1542 to 1841. Some other baronies became abeyant in the 13th century, and the abeyance has yet to be terminated. The only modern examples of titles other than a barony that have yet gone into abeyance are the earldom of Arlington and the viscountcy of Thetford, which are united, and (as noted above) the earldom of Cromartie.

It is no longer straightforward to claim English peerages after long abeyances. In 1927, a parliamentary Select Committee on Peerages in Abeyance recommended that no claim should be considered where the abeyance has lasted more than 100 years, nor where the claimant lays claim to less than one third of the dignity. The Barony of Grey of Codnor was treated as an exception to this principle, as a claim to it had been submitted prior to these recommendations being made to the Sovereign.

It is common, but incorrect, to speak of peerage dignities which are dormant (i.e. unclaimed) as being in abeyance.

Settling litigation
Abeyance can be used in cases where parties are interested in temporarily settling litigation while still holding the right to seek relief later if necessary. This may be considered a desirable outcome in cases where the party to the lawsuit is an organization with a transient membership and political perspective. The use of abeyance in such instances can allow such an organization to 'settle' with the party without officially binding its actions in the future, should a new group of decision makers within the organization choose to pursue taking the dispute to court.

For example, abeyance was used as a settlement method in a Canadian lawsuit involving the University of Victoria Students' Society (UVSS), the British Columbia Civil Liberties Association, and a campus anti-abortion club to whom the UVSS denied funding. The parties agreed to settle the lawsuit by holding the case in abeyance in return for the UVSS temporarily giving resources back to the club. With this arrangement, the anti-abortion club held on to its right to immediately reopen the case again should the UVSS deny resources to the club in the future, and the UVSS was able to avoid an expensive legal battle it did not have the will to pursue at the time. Thus, the use of abeyance provided the security of a settlement for the anti-abortion campus club, while preserving the student society's voting membership's ability to take the matter back to court should they choose in the future to deny resources to the club.

Other court cases may be held in abeyance when the issue may be resolved by another court or another event. This saves time and effort trying to resolve a dispute that may be made moot by the other events. During lawsuits related to the Patient Protection and Affordable Care Act after the Supreme Court of the United States granted certiorari in King v. Burwell, attorneys in Halbig v. Burwell requested abeyance of that case as the matter would be resolved in King and it would be a waste of time and effort to try to resolve it in the Halbig case.

Scottish peerage law
Titles in the Peerage of Scotland cannot go into abeyance, because in Scottish law the eldest sister is preferred over younger sisters; sisters are not considered equal co-heirs.

title: Abeyance


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Anders Celsius

Anders Celsius (27 November 1701 – 25 April 1744) was a Swedish astronomer, physicist and mathematician. He was professor of astronomy at Uppsala University from 1730 to 1744, but traveled from 1732 to 1735 visiting notable observatories in Germany, Italy and France. He founded the Uppsala Astronomical Observatory in 1741, and in 1742 proposed (an inverted form of) the Centigrade temperature scale which was later renamed Celsius in his honour.

Early life and education
Anders Celsius was born in Uppsala, Sweden, on 27 November 1701. His family originated from Ovanåker in the province of Hälsingland. Their family estate was at Doma, also known as Höjen or Högen (locally as Högen 2). The name Celsius is a latinization of the estate's name (Latin celsus 'mound').

As the son of an astronomy professor, Nils Celsius, nephew of botanist Olof Celsius and the grandson of the mathematician Magnus Celsius and the astronomer Anders Spole, Celsius chose a career in science. He was a talented mathematician from an early age. Anders Celsius studied at Uppsala University, where his father was a teacher, and in 1730 he, too, became a professor of astronomy there. Noted Swedish dramatic poet and actor Johan Celsius was also his uncle.

Career
In 1730, Celsius published the Nova Methodus distantiam solis a terra determinandi (New Method for Determining the Distance from the Earth to the Sun). His research also involved the study of auroral phenomena, which he conducted with his assistant Olof Hiorter, and he was the first to suggest a connection between the aurora borealis and changes in the magnetic field of the Earth. He observed the variations of a compass needle and found that larger deflections correlated with stronger auroral activity. At Nuremberg in 1733, he published a collection of 316 observations of the aurora borealis made by himself and others over the period 1716–1732.

Celsius traveled frequently in the early 1730s, including to Germany, Italy and France, when he visited most of the major European observatories. In Paris he advocated the measurement of an arc of the meridian in Lapland. In 1736, he participated in the expedition organized for that purpose by the French Academy of Sciences, led by the French mathematician Pierre Louis Maupertuis (1698–1759) to measure a degree of latitude. The aim of the expedition was to measure the length of a degree along a meridian, close to the pole, and compare the result with a similar expedition to Peru, today in Ecuador, near the equator. The expeditions confirmed Isaac Newton's belief that the shape of the Earth is an ellipsoid flattened at the poles.

In 1738, he published the De observationibus pro figura telluris determinanda (Observations on Determining the Shape of the Earth). Celsius's participation in the Lapland expedition won him much respect in Sweden with the government and his peers, and played a key role in generating interest from the Swedish authorities in donating the resources required to construct a new modern observatory in Uppsala. He was successful in the request, and Celsius founded the Uppsala Astronomical Observatory in 1741. The observatory was equipped with instruments purchased during his long voyage abroad, comprising the most modern instrumental technology of the period.

He made observations of eclipses and various astronomical objects and published catalogues of carefully determined magnitudes for some 300 stars using his own photometric system (mean error=0.4 mag). In 1742 he proposed the Celsius temperature scale in a paper to the Royal Society of Sciences in Uppsala, the oldest Swedish scientific society, founded in 1710. His thermometer was calibrated with a value of 0 for the boiling point of water and 100 for the freezing point. In 1745, a year after Celsius's death, the scale was reversed by Carl Linnaeus to facilitate more practical measurement.

Celsius conducted many geographical measurements for the Swedish General map, and was one of earliest to note that much of Scandinavia is slowly rising above sea level, a continuous process which has been occurring since the melting of the ice from the latest ice age. However, he wrongly posed the notion that the water was evaporating.

In 1725 he became secretary of the Royal Society of Sciences in Uppsala, and served at this post until his death from tuberculosis in 1744. He supported the formation of the Royal Swedish Academy of Sciences in Stockholm in 1739 by Linnaeus and five others, and was elected a member at the first meeting of this academy. It was in fact Celsius who proposed the new academy's name.

title: Anders Celsius


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Adam Carolla

Adam Carolla (born May 27, 1964) is an American radio personality, comedian, actor and podcaster. He hosts The Adam Carolla Show, a talk show distributed as a podcast which set the record as the "most downloaded podcast" as judged by Guinness World Records in 2011.

Carolla co-hosted the syndicated radio call-in program Loveline with Drew Pinsky from 1995 to 2005 as well as the show's television incarnation on MTV from 1996 to 2000. He was the co-host and co-creator of the television program The Man Show (1999–2004), and the co-creator and a regular performer on the television show Crank Yankers (2002–2007, 2019–present). He hosted The Adam Carolla Project, a home improvement television program which aired on TLC in 2005 and The Car Show on Speed in 2011.

Carolla has also appeared on the network reality television programs Dancing with the Stars and The Celebrity Apprentice. His book In Fifty Years We'll All Be Chicks debuted on The New York Times Best Seller list in 2010, and his second book, Not Taco Bell Material, also reached The New York Times bestseller status.

Carolla has made numerous guest appearances on political talk shows as a commentator. He hosted a weekly segment, "Rollin' with Carolla", on Bill O'Reilly's The O'Reilly Factor.

Early life
Adam Carolla was born on May 27, 1964, to Jim and Kris (née McCall) Carolla. Some sources list his birthplace as Los Angeles County, California, while others list it as Philadelphia, Pennsylvania. He grew up in the Los Angeles San Fernando Valley, and his parents separated when he was young. Carolla was not given a middle name by his parents; on his driver's license application he listed his middle name as "Lakers" as a joke. The application was processed without notice. His maternal step-grandfather was screenwriter László Görög.

Carolla was raised in the North Hollywood neighborhood of Los Angeles. He attended Colfax Elementary School, Walter Reed Junior High, and North Hollywood High School. Carolla did not receive his high school diploma until years later as it was held by the school until a library fine was paid. Carolla can be seen paying off the book and receiving his diploma in an episode of his 2005 television show, The Adam Carolla Project.

During his youth, Carolla played Pop Warner football for seven years; he later suggested that being involved in sports saved him from a chaotic home life. During his senior year at North Hollywood High School, Carolla distinguished himself in football. In December 1981, he was named to the First Team Offensive Line, Central Valley League, one of 8 leagues at the time in the LA City Section of the California Interscholastic Federation. In October 2020 he spoke of being recruited by "7 or 8" schools including UC-Davis, Cal Poly Pomona, and Cal Poly San Luis Obispo.

He began living on his own at the age of 18. He briefly attended Los Angeles Valley College, a community college, where he was placed on academic probation before dropping out to work in a series of jobs, including carpet cleaner, carpenter, boxing instructor, and traffic school instructor. Although broke, Carolla, his friends, and roommates owned a 1963 Cadillac limousine.

In the early 1990s, Carolla studied improvisational comedy with The Groundlings and was a member of the ACME Comedy Theatre troupe.

Radio
In 1994, Carolla volunteered his services as a boxing trainer to prepare Jimmy Kimmel for a bout being staged by KROQ-FM's morning radio program Kevin and Bean. Kimmel was a regular on the show as "Jimmy the Sports Guy" and he was set to fight another KROQ personality in a boxing exhibition which was being billed as the "Bleeda in Reseda". Carolla parlayed this opportunity into a long-running friendship and business partnership with Kimmel as well as a recurring role on Kevin and Bean as cranky woodshop teacher, Mr. Birchum.

Loveline
In October 1995, after being signed to the William Morris Agency by Mark Itkin, Carolla was offered the job of co-hosting the evening radio call-in show Loveline. His co-hosts were the physician Drew Pinsky ("Dr. Drew") and metal DJ Riki Rachtman. Carolla received the offer after Pinsky heard him on Kevin and Bean (Rachtman left the show the following year.) Loveline was broadcast on KROQ-FM in Los Angeles and was syndicated nationwide on the former Westwood One radio network.

While the format of the program was primarily that of a call-in show wherein listeners would ask questions about sex and relationships, Carolla would often spend much of the show ranting about various topics from fart jokes to extended parodies of radio morning shows, including mocking the format's penchant for useless and repetitive weather and traffic reports. In contrast to the reserved, thoughtful Pinsky, Carolla served as the loud, funny side of the show. Carolla's character was described by one reviewer as "a toned-down version of Howard Stern minus the huge ego".

In a late-2003 Loveline episode, Carolla said that Hawaiians are "dumb", "in-bred", "retarded" people who are among the "dumbest people we have". The comments were met with anger in Hawaii and resulted in Loveline's cancellation on Hawaiian affiliate KPOI.

The Adam Carolla Show
In October 2005, Carolla was announced as the host of a new morning radio show on the Infinity Broadcasting network. His new show would replace the popular syndicated Howard Stern Show (which was moving to satellite radio) in twelve of the 27 markets in which Stern had been broadcast including Los Angeles, Las Vegas, San Francisco, San Diego, Phoenix, and Portland, Oregon. The Adam Carolla Show debuted in January 2006.

In early 2008, actor Gerard Butler sat in and observed Adam Carolla on The Adam Carolla Show in order to prepare for his role in The Ugly Truth as a cynical and crass talk-radio host allegedly based on Carolla.

On February 18, 2009, The Adam Carolla Show was canceled as part of a format switch at KLSX to AMP FM, a new top 40 station. The final show was Friday, February 20, 2009.

The Adam Carolla Podcast
Carolla started a daily podcast on February 23, 2009, at his personal website, which would evolve into the ACE Broadcasting Network. The first Adam Carolla podcast was downloaded more than 250,000 times in the initial 24 hours, and by the third podcast, it was the number one podcast on iTunes in both the U.S. and Canada. During the debut week, the Adam Carolla podcast recorded 1.6 million downloads. In the second week it recorded 2.4 million downloads. By the fourth episode of the second week, featuring former Adam Carolla Show sidekick Dave Dameshek, the show was downloaded more than 500,000 times. Adam stated that bandwidth cost more than $9,000 a month as of May 2009.

At the end of 2009, The Adam Carolla Podcast was selected by iTunes for its end-of-the-year awards as the Best Audio Podcast of 2009.

On the April 4, 2010, episode of The Adam Carolla Show, Carolla referred to Filipino boxer Manny Pacquiao as a "fucking idiot" and said of the Philippines: "They got this and sex tours, that's all they have over there. Get your shit together, Philippines." A spokesman for President Gloria Macapagal Arroyo called Carolla an "ignorant fool". Carolla subsequently apologized via Twitter.

On May 18, 2011, Carolla noted on Jimmy Kimmel Live! that The Adam Carolla Show had taken the Guinness World Record for the most downloaded podcast ever from previous holder Ricky Gervais by receiving 59,574,843 unique downloads from March 2009 to March 16, 2011.

In 2010, Carolla posed for the NOH8 Campaign. In August 2011, Carolla released a podcast where he mocked a petition to the producers of Sesame Street that demanded Bert and Ernie get married on air. He said on air that gay activists should "[j]ust get married, and please shut up" and that "Y.U.C.K." would be more memorable acronym than LGBT, and referring to transgender people he asked: "When did we start giving a shit about these people?" GLAAD characterized the previous remarks by Carolla as offensive, including an assertion that "all things being equal", heterosexual parents make better parents than homosexual parents. Carolla responded: "I'm sorry my comments were hurtful. I'm a comedian, not a politician."

"Patent Troll" Lawsuit
In 2013, Personal Audio filed a patent infringement lawsuit against Lotzi Digital, Inc., producers of The Adam Carolla Show and several other podcasts on the Carolla Digital Network, in the U.S. District Court for the Eastern District of Texas. The suit alleged that owner Adam Carolla and his network of content infringed on Personal Audio's patent 8,112,504.

Using the crowdfunding site FundAnything.com, listeners contributed more than $475,000 (as of August 2014) to support Carolla throughout the legal proceedings.

Personal Audio dropped the lawsuit July 29, 2014, stating that the defendants were not "making significant money from infringing Personal Audio's patents". However, Carolla countersued, having already spent hundreds of thousands of dollars mounting a defense against claims he deemed unfounded. Among claims sought by the countersuit was a request that the initial patent be invalidated. On August 15, 2014, Carolla and Personal Audio filed a joint motion to dismiss after reaching a settlement, the details of which were not made public but included a six-week "quiet period" during which neither party could speak to the media. Both parties' claims were dropped without prejudice and, as such, could be refiled at a later date.

1996 through 2004
From 1996 to 2000, Carolla and Dr. Drew hosted Loveline on MTV, a television version of the radio show. Carolla began his first original television series with The Man Show, along with partner and friend Jimmy Kimmel, on Comedy Central from 1999 to 2003. He left The Man Show at the same time as Kimmel. Carolla has continued his work with Kimmel as a writer and guest on Jimmy Kimmel Live!. He also appeared on an episode of Space Ghost Coast to Coast around this time.

Carolla and partner Daniel Kellison are the heads of Jackhole Productions. The two created the television show Crank Yankers for Comedy Central, which revived the Mr. Birchum character. The show premiered in 2002 on Comedy Central and returned to MTV2 on February 9, 2007, running again until March 30, 2007. The show screened in Australia on SBS Television and The Comedy Channel between 2003 and 2008. The show was again revived in 2019, returning to Comedy Central.

2005 through 2008
From August 2005 to November 2005, Carolla hosted the talk show Too Late with Adam Carolla on Comedy Central.

Also in 2005, Carolla was featured in a home remodeling program called The Adam Carolla Project wherein he and a crew of old friends renovated his childhood home. The 13 episodes aired on the cable channel TLC (The Learning Channel) from October through December 2005. The house was then sold for 1.2 million dollars.

In 2006, Carolla appeared on the special summer series Gameshow Marathon as a celebrity panelist on the Match Game episode.

On the February 18, 2008, broadcast of his radio show, Carolla announced that he would be one of the contestants on the next season of Dancing with the Stars. Later in the broadcast, it was revealed to Carolla that his partner would be Julianne Hough. He was voted off on the April 8, 2008, episode after his performance of the Paso Doble, after incorporating a demonstration of unicycle riding in his dance routine.

 * Dancing with the Stars performances

On June 16, 2008, Carolla was selected to host a pilot of an American version of the popular BBC show Top Gear for NBC. In December 2008, NBC decided not to pick up the show.

2009 to present
On February 21, 2009, a day after his Los Angeles-based morning radio show was canceled – as part of a format change at KLSX-FM – CBS ordered a comedy pilot, Ace in the Hole, starring Carolla as a husband and father who works as a driving instructor. Carolla created and wrote the pilot with Kevin Hench (Jimmy Kimmel Live!). Carolla stated that Pamela Adlon was to play his wife and Windell Middlebrooks would play his best friend. During his March 30, 2009, podcast, Carolla briefly described the show as being "All in the Family, essentially", with Carolla playing a similar role to that of Archie Bunker. On the July 23, 2009, episode of the Adam Carolla Podcast, Carolla announced that CBS was not picking up the pilot for the 2009 season, "in any way, shape or form".

On October 22, 2009, it was reported in Variety that Carolla had struck a deal with NBC to produce a half-hour pilot for a sitcom. The report was later confirmed on January 4, 2010, and was the first comedy pilot ordered by NBC for the season. The untitled project, written by Carolla and Kevin Hench, was a single-camera sitcom that starred Carolla as a contractor and father who attempts to rebuild his life after his wife leaves him. Carolla was set to executive produce the NBC project along with frequent collaborators Kimmel and Hench, as well as his agent James "Babydoll" Dixon, Jon Pollack, Gail Berman, Daniel Kellison, and Lloyd Braun. Universal Media Studios, BermanBraun, and Carolla and Jimmy Kimmel's own Jackhole Industries.

On the February 13, 2010, episode of Carolla's CarCast podcast, he revealed that The History Channel had picked up Top Gear US, which NBC had decided against in 2008. On the March 26, 2010, episode of CarCast, Carolla said that he would not be co-hosting Top Gear US because of scheduling conflicts with his NBC sitcom project. In June 2010, Carolla said that his NBC pilot had not been picked up and was now "dead".

Premiering on February 19, 2012, Carolla was also one of the contestants in the 12th season of NBC's The Celebrity Apprentice. He was fired in Week 4, because host Donald Trump perceived that Carolla did not utilize teammate Mario Andretti's car background during a Buick presentation.

In 2022, Carolla competed in season eight of The Masked Singer as "Avocado". He was eliminated on "Comedy Roast Night" alongside Chris Jericho as "Bride".

The Car Show
Carolla's The Car Show debuted on Speed TV July 13, 2011. Appearing Wednesdays at 10 pm Eastern, it featured Carolla as the host, along with Dan Neil, John Salley, and Matt Farah. It had a format similar to Top Gear, mixing car reviews, tests and humor. The show was initially met with positive reviews from car enthusiasts and comedy fans. Talk show host and comedian Jay Leno called The Car Show, "a lot of fun". The Car Show was cancelled after one season, after undergoing format changes due to low ratings, as Carolla mentioned on his podcast on January 13, 2012.

Catch a Contractor
Catch a Contractor is a non-scripted, original series on Spike, hosted by Carolla along with "no-nonsense contractor" Skip Bedell and his wife, investigator Alison Bedell. Together they expose unethical contractors and seek retribution for wronged homeowners.

The show premiered on March 9, 2014, to 1.2 million viewers, the largest audience for a series debut on Spike since Coal in March 2011. The show was cancelled in 2015.

Adam Carolla and Friends Build Stuff Live
Premiering on Spike TV on March 14, 2017, Adam Carolla and Friends Build Stuff Live features Carolla building projects live and in studio with some of his Hollywood friends, and tackling viewers' home improvement projects via social media.

Voice acting
Carolla has also done voice acting in animation, including Commander Nebula on the Disney animated series Buzz Lightyear of Star Command, Death on Family Guy (replacing Norm Macdonald) and Spanky Ham on Drawn Together. He was also the voice of the éclair police officer, Wynchell, in the Disney film Wreck-It Ralph. In 2008 and 2009, he was the spokesperson for T.G.I. Friday's.

Film
In 2003, he appeared in Windy City Heat as himself. In 2006, Carolla finished work on The Hammer, a semi-autobiographical independent film he co-wrote and co-produced, in which he stars opposite Heather Juergensen. The film is based loosely on his own life and is filmed at a gym he helped build with his co-star, Ozzie, played by Oswaldo Castillo, his friend in real life whom he met while building the gym when they both worked in construction. The film made its world premiere at the 2007 Tribeca Film Festival in New York City and shortly thereafter received a positive review in Variety. The film was released on March 21, 2008. The film is rated 80% on Rotten Tomatoes.

Carolla made a short appearance in Jeff Balis' Still Waiting... (a sequel to Waiting...) playing a pick-up artist guru.

Carolla helped write an unproduced screenplay for a film entitled Deaf Frat Guy: Showdown at Havasu.

He is the voice of Virgil in the independent short film Save Virgil.

In July 2013, Carolla used crowdfunding for Road Hard; a film he directed and starred in, about the lives of aging road comics. Adam confirmed through a press conference that the film would co-star David Alan Grier, Illeana Douglas, Diane Farr, and Larry Miller. It had limited theatrical release in the United States. Several minutes of the credits are devoted to listing the names of those who helped crowdfund the film.

Carolla also directed the documentary Winning: The Racing Life of Paul Newman on the 35-year car racing career of Paul Newman. The documentary showcases Newman's racing life as both a prolific driver and owner.

In 2017, Carolla and Dennis Prager began filming No Safe Spaces, a documentary about political correctness at universities. No Safe Spaces had a limited opening on October 25, 2019, and did well enough to open nationwide on December 6, 2019.

Books
Carolla and Drew Pinsky co-wrote (with Marshall Fine) the self-help book The Dr. Drew and Adam Book: A Survival Guide to Life and Love, published in 1998. The book is a compilation of some of the advice the pair compiled while producing Loveline.

In November 2010, Carolla's In Fifty Years We'll All Be Chicks... And Other Complaints from an Angry Middle-Aged White Guy was published by Crown Archetype and debuted at number eight on The New York Times Best Seller list for hardcover non-fiction on November 21, 2010. The book was compiled from rants Carolla had delivered on his radio show and podcast along with some new material and was dictated to and ghost-written by Mike Lynch.

Carolla published a short, illustrated e-book entitled Rich Man, Poor Man in January 2012. The book details some similarities in the experiences of the very rich and the very poor which are not shared by the middle class. The book was illustrated by Michael Narren.

Carolla's book Not Taco Bell Material was published by Crown Archetype on June 12, 2012.

In President Me: The America That's in My Head, Carolla presents the comedian's fantasy of the United States with him at the helm. When asked in separate interviews, both before and after the book's release, about whether the "if-I-were-king" critique of America was a serious piece, he said it's both: "Well, there's a lot of jokes in it, but you know, it's like... Well, if you have a fat friend you may make a lot of fat jokes about your fat friend, but he's still fat".

In Daddy, Stop Talking!: And Other Things My Kids Want But Won't Be Getting, Carolla writes about modern parenting. Carolla describes what he believes adults must do if they don't want to have to support their kids forever. Carolla uses his own childhood as a cautionary tale, and decries helicopter parenting.

Carolla's book, I'm Your Emotional Support Animal: Navigating Our All Woke, No Joke Culture, was published by Post Hill Press on June 16, 2020.

Carolla's latest book, Everything Reminds Me of Something, was published by Post Hill Press on July 19, 2022.

Religious
Carolla is an atheist.

Political
Regarding his political views, Carolla has stated, "I guess I would be Republican, in the sense that I want a secure border, I'm not into the welfare state, I'm not into all those freebie lunch programs. It just kind of demeans people." He goes on to state, however, that he is also in favor of typically liberal causes such as the legalization of marijuana (he is a member of the advisory board of the Marijuana Policy Project) and support for some progressive causes such as "[being] against semi-automatic and automatic weapons. I'm not an NRA guy by any stretch of the imagination. I'd like alternative energy to be explored and electric cars to be used, but I want them to be powered by nuclear power plants." Elsewhere, he has stated, "My feeling is this whole country is founded on the principle of 'If you are not hurting anyone, and you're not fucking with someone else's shit, and you are paying your taxes, you should be able to just do what you want to do.' It's the freedom and the independence." In an interview with Reason TV, Carolla described his views as libertarian. Carolla expressed his support for Andrew Yang's 2020 presidential run.

Women and comedy
In June 2012, Carolla gave a printed interview to the New York Post, where among other things he stated that "chicks" are "always the least funny on the writing staff" and that "dudes are funnier than chicks". Carolla's comments were criticized as sexist. Carolla criticized coverage of his comments as over-simplistic and misleading.

Cancel culture
Carolla said, "If you meet anyone over 45, they'll tell you they got paddled, they got swatted, the teacher would smack them with a ruler. … Paddling a kid sounds pretty outrageous in 2020 and nobody would stand for it. ... But the people who engaged in it at the time when it was common practice or had a context, we don't need to build a time machine so we can cancel-culture them". In an interview with Tucker Carlson, Carolla said that cancel culture is "destroying free speech and killing comedy."

Personal life
On September 28, 2002, Carolla married Lynette Paradise. The couple's twins Natalia and Santino "Sonny" Richard Carolla were born June 7, 2006. Carolla announced in May 2021 that he and Lynette were divorcing after 19 years. He currently lives in La Cañada Flintridge, California.

Carolla was a part owner of Amalfi, an Italian restaurant in Los Angeles, saying, "I own about two percent of it, but I've never seen a penny."

Carolla won the 2013 Pro/Celebrity Race as a professional and the 2012 Pro/Celebrity Race at the Toyota Grand Prix of Long Beach as an amateur. The 2012 race was run on April 14, 2012, and was broadcast on Speed TV. Carolla has previously participated in the race in 2010 and 2003. He finished ninth among 19 racers (fifth among the ten celebrities) in 2010 despite being regarded as a pre-race favorite. He is also a serious automobile collector with over 20 cars. His collection includes several Lamborghinis from the 1960s and early 1970s, including two Miuras (of 764 examples ever produced), one of which he has loaned to the Petersen Automotive Museum in Los Angeles, two 400GT 2+2s (of 247 units produced) and a 1965 350GT (one of 135 built). At least one Ferrari, an Aston Martin, and several vintage race cars round out the collection.

Honors
Carolla and Drew Pinsky received a Sexual Health in Entertainment (SHINE) Award from The Media Project in 2000 for "incorporating accurate and honest portrayals of sexuality" in the talk show category for Loveline.

Asteroid (4535) Adamcarolla is named in his honor.

title: Adam Carolla


text:
Autocorrelation

Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable as a function of the time lag between them. The analysis of autocorrelation is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal obscured by noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies. It is often used in signal processing for analyzing functions or series of values, such as time domain signals.

Different fields of study define autocorrelation differently, and not all of these definitions are equivalent. In some fields, the term is used interchangeably with autocovariance.

Unit root processes, trend-stationary processes, autoregressive processes, and moving average processes are specific forms of processes with autocorrelation.

Auto-correlation of stochastic processes
In statistics, the autocorrelation of a real or complex random process is the Pearson correlation between values of the process at different times, as a function of the two times or of the time lag. Let $$\left\{ X_t \right\}$$ be a random process, and $$t$$ be any point in time ($$t$$ may be an integer for a discrete-time process or a real number for a continuous-time process). Then $$X_t$$ is the value (or realization) produced by a given run of the process at time $$t$$. Suppose that the process has mean $$\mu_t$$ and variance $$\sigma_t^2$$ at time $$t$$, for each $$t$$. Then the definition of the auto-correlation function between times $$t_1$$ and $$t_2$$ is

where $$\operatorname{E}$$ is the expected value operator and the bar represents complex conjugation. Note that the expectation may not be well defined.

Subtracting the mean before multiplication yields the auto-covariance function between times $$t_1$$ and $$t_2$$:

Note that this expression is not well defined for all time series or processes, because the mean may not exist, or the variance may be zero (for a constant process) or infinite (for processes with distribution lacking well-behaved moments, such as certain types of power law).

Definition for wide-sense stationary stochastic process
If $$\left\{ X_t \right\}$$ is a wide-sense stationary process then the mean $$\mu$$ and the variance $$\sigma^2$$ are time-independent, and further the autocovariance function depends only on the lag between $$t_1$$ and $$t_2$$: the autocovariance depends only on the time-distance between the pair of values but not on their position in time. This further implies that the autocovariance and auto-correlation can be expressed as a function of the time-lag, and that this would be an even function of the lag $$\tau=t_2-t_1$$. This gives the more familiar forms for the auto-correlation function

and the auto-covariance function:

In particular, note that

$$\operatorname{K}_{XX}(0) = \sigma^2 .$$

Normalization
It is common practice in some disciplines (e.g. statistics and time series analysis) to normalize the autocovariance function to get a time-dependent Pearson correlation coefficient. However, in other disciplines (e.g. engineering) the normalization is usually dropped and the terms "autocorrelation" and "autocovariance" are used interchangeably.

The definition of the auto-correlation coefficient of a stochastic process is

$$\rho_{XX}(t_1,t_2) = \frac{\operatorname{K}_{XX}(t_1,t_2)}{\sigma_{t_1}\sigma_{t_2}} = \frac{\operatorname{E}\left[(X_{t_1} - \mu_{t_1}) \overline{(X_{t_2} - \mu_{t_2})} \right]}{\sigma_{t_1}\sigma_{t_2}} .$$

If the function $$\rho_{XX}$$ is well defined, its value must lie in the range $$[-1,1]$$, with 1 indicating perfect correlation and −1 indicating perfect anti-correlation.

For a wide-sense stationary (WSS) process, the definition is

$$\rho_{XX}(\tau) = \frac{\operatorname{K}_{XX}(\tau)}{\sigma^2} = \frac{\operatorname{E} \left[(X_{t+\tau} - \mu)\overline{(X_{t} - \mu)}\right]}{\sigma^2}$$.

The normalization is important both because the interpretation of the autocorrelation as a correlation provides a scale-free measure of the strength of statistical dependence, and because the normalization has an effect on the statistical properties of the estimated autocorrelations.

Symmetry property
The fact that the auto-correlation function $$\operatorname{R}_{XX}$$ is an even function can be stated as $$\operatorname{R}_{XX}(t_1,t_2) = \overline{\operatorname{R}_{XX}(t_2,t_1)}$$ respectively for a WSS process: $$\operatorname{R}_{XX}(\tau) = \overline{\operatorname{R}_{XX}(-\tau)} .$$

Maximum at zero
For a WSS process: $$\left|\operatorname{R}_{XX}(\tau)\right| \leq \operatorname{R}_{XX}(0)$$ Notice that $$\operatorname{R}_{XX}(0)$$ is always real.

Cauchy–Schwarz inequality
The Cauchy–Schwarz inequality, inequality for stochastic processes: $$\left|\operatorname{R}_{XX}(t_1,t_2)\right|^2 \leq \operatorname{E}\left[ |X_{t_1}|^2\right] \operatorname{E}\left[|X_{t_2}|^2\right]$$

Autocorrelation of white noise
The autocorrelation of a continuous-time white noise signal will have a strong peak (represented by a Dirac delta function) at $$\tau=0$$ and will be exactly $$0$$ for all other $$\tau$$.

Wiener–Khinchin theorem
The Wiener–Khinchin theorem relates the autocorrelation function $$\operatorname{R}_{XX}$$ to the power spectral density $$S_{XX}$$ via the Fourier transform:

$$\operatorname{R}_{XX}(\tau) = \int_{-\infty}^\infty S_{XX}(f) e^{i 2 \pi f \tau} \, {\rm d}f$$

$$S_{XX}(f) = \int_{-\infty}^\infty \operatorname{R}_{XX}(\tau) e^{- i 2 \pi f \tau} \, {\rm d}\tau .$$

For real-valued functions, the symmetric autocorrelation function has a real symmetric transform, so the Wiener–Khinchin theorem can be re-expressed in terms of real cosines only:

$$\operatorname{R}_{XX}(\tau) = \int_{-\infty}^\infty S_{XX}(f) \cos(2 \pi f \tau) \, {\rm d}f$$

$$S_{XX}(f) = \int_{-\infty}^\infty \operatorname{R}_{XX}(\tau) \cos(2 \pi f \tau) \, {\rm d}\tau .$$

Auto-correlation of random vectors
The (potentially time-dependent) auto-correlation matrix (also called second moment) of a (potentially time-dependent) random vector $$\mathbf{X} = (X_1,\ldots,X_n)^{\rm T}$$ is an $$n \times n$$ matrix containing as elements the autocorrelations of all pairs of elements of the random vector $$\mathbf{X}$$. The autocorrelation matrix is used in various digital signal processing algorithms.

For a random vector $$\mathbf{X} = (X_1,\ldots,X_n)^{\rm T}$$ containing random elements whose expected value and variance exist, the auto-correlation matrix is defined by

where $${}^{\rm T}$$ denotes the transposed matrix of dimensions $$n \times n$$.

Written component-wise:

$$\operatorname{R}_{\mathbf{X}\mathbf{X}} = \begin{bmatrix} \operatorname{E}[X_1 X_1] & \operatorname{E}[X_1 X_2] & \cdots & \operatorname{E}[X_1 X_n] \\ \\ \operatorname{E}[X_2 X_1] & \operatorname{E}[X_2 X_2] & \cdots & \operatorname{E}[X_2 X_n] \\ \\ \vdots & \vdots & \ddots & \vdots \\ \\ \operatorname{E}[X_n X_1] & \operatorname{E}[X_n X_2] & \cdots & \operatorname{E}[X_n X_n] \\ \\ \end{bmatrix} $$

If $$\mathbf{Z}$$ is a complex random vector, the autocorrelation matrix is instead defined by

$$\operatorname{R}_{\mathbf{Z}\mathbf{Z}} \triangleq\ \operatorname{E}[\mathbf{Z} \mathbf{Z}^{\rm H}] .$$

Here $${}^{\rm H}$$ denotes Hermitian transpose.

For example, if $$\mathbf{X} = \left( X_1,X_2,X_3 \right)^{\rm T}$$ is a random vector, then $$\operatorname{R}_{\mathbf{X}\mathbf{X}}$$ is a $$3 \times 3$$ matrix whose $$(i,j)$$-th entry is $$\operatorname{E}[X_i X_j]$$.

Properties of the autocorrelation matrix

 * The autocorrelation matrix is a Hermitian matrix for complex random vectors and a symmetric matrix for real random vectors.
 * The autocorrelation matrix is a positive semidefinite matrix, i.e. $$\mathbf{a}^{\mathrm T} \operatorname{R}_{\mathbf{X}\mathbf{X}} \mathbf{a} \ge 0 \quad \text{for all } \mathbf{a} \in \mathbb{R}^n$$ for a real random vector, and respectively $$\mathbf{a}^{\mathrm H} \operatorname{R}_{\mathbf{Z}\mathbf{Z}} \mathbf{a} \ge 0 \quad \text{for all } \mathbf{a} \in \mathbb{C}^n$$ in case of a complex random vector.
 * All eigenvalues of the autocorrelation matrix are real and non-negative.
 * The auto-covariance matrix is related to the autocorrelation matrix as follows:$$\operatorname{K}_{\mathbf{X}\mathbf{X}} = \operatorname{E}[(\mathbf{X} - \operatorname{E}[\mathbf{X}])(\mathbf{X} - \operatorname{E}[\mathbf{X}])^{\rm T}] = \operatorname{R}_{\mathbf{X}\mathbf{X}} - \operatorname{E}[\mathbf{X}] \operatorname{E}[\mathbf{X}]^{\rm T}$$Respectively for complex random vectors:$$\operatorname{K}_{\mathbf{Z}\mathbf{Z}} = \operatorname{E}[(\mathbf{Z} - \operatorname{E}[\mathbf{Z}])(\mathbf{Z} - \operatorname{E}[\mathbf{Z}])^{\rm H}] =  \operatorname{R}_{\mathbf{Z}\mathbf{Z}} - \operatorname{E}[\mathbf{Z}] \operatorname{E}[\mathbf{Z}]^{\rm H}$$

Auto-correlation of deterministic signals
In signal processing, the above definition is often used without the normalization, that is, without subtracting the mean and dividing by the variance. When the autocorrelation function is normalized by mean and variance, it is sometimes referred to as the autocorrelation coefficient or autocovariance function.

Auto-correlation of continuous-time signal
Given a signal $$f(t)$$, the continuous autocorrelation $$R_{ff}(\tau)$$ is most often defined as the continuous cross-correlation integral of $$f(t)$$ with itself, at lag $$\tau$$.

where $$\overline{f(t)}$$ represents the complex conjugate of $$f(t)$$. Note that the parameter $$t$$ in the integral is a dummy variable and is only necessary to calculate the integral. It has no specific meaning.

Auto-correlation of discrete-time signal
The discrete autocorrelation $$R$$ at lag $$\ell$$ for a discrete-time signal $$y(n)$$ is

The above definitions work for signals that are square integrable, or square summable, that is, of finite energy. Signals that "last forever" are treated instead as random processes, in which case different definitions are needed, based on expected values. For wide-sense-stationary random processes, the autocorrelations are defined as

$$\begin{align} R_{ff}(\tau) &= \operatorname{E}\left[f(t)\overline{f(t-\tau)}\right] \\ R_{yy}(\ell) &= \operatorname{E}\left[y(n)\,\overline{y(n-\ell)}\right]. \end{align}$$

For processes that are not stationary, these will also be functions of $$t$$, or $$n$$.

For processes that are also ergodic, the expectation can be replaced by the limit of a time average. The autocorrelation of an ergodic process is sometimes defined as or equated to

$$\begin{align} R_{ff}(\tau) &= \lim_{T \rightarrow \infty} \frac 1 T \int_0^T f(t+\tau)\overline{f(t)}\, {\rm d}t \\ R_{yy}(\ell) &= \lim_{N \rightarrow \infty} \frac 1 N \sum_{n=0}^{N-1} y(n)\,\overline{y(n-\ell)}. \end{align}$$

These definitions have the advantage that they give sensible well-defined single-parameter results for periodic functions, even when those functions are not the output of stationary ergodic processes.

Alternatively, signals that last forever can be treated by a short-time autocorrelation function analysis, using finite time integrals. (See short-time Fourier transform for a related process.)

Definition for periodic signals
If $$f$$ is a continuous periodic function of period $$T$$, the integration from $$-\infty$$ to $$\infty$$ is replaced by integration over any interval $$[t_0,t_0+T]$$ of length $$T$$:

$$R_{ff}(\tau) \triangleq \int_{t_0}^{t_0+T} f(t+\tau) \overline{f(t)} \,dt$$

which is equivalent to

$$R_{ff}(\tau) \triangleq \int_{t_0}^{t_0+T} f(t) \overline{f(t-\tau)} \,dt$$

Properties
In the following, we will describe properties of one-dimensional autocorrelations only, since most properties are easily transferred from the one-dimensional case to the multi-dimensional cases. These properties hold for wide-sense stationary processes.

 * A fundamental property of the autocorrelation is symmetry, $$R_{ff}(\tau) = R_{ff}(-\tau)$$, which is easy to prove from the definition. In the continuous case,
 * the autocorrelation is an even function $$R_{ff}(-\tau) = R_{ff}(\tau)$$ when $$f$$ is a real function, and
 * the autocorrelation is a Hermitian function $$R_{ff}(-\tau) = R_{ff}^*(\tau)$$ when $$f$$ is a complex function.
 * The continuous autocorrelation function reaches its peak at the origin, where it takes a real value, i.e. for any delay $$\tau$$, $$|R_{ff}(\tau)| \leq R_{ff}(0)$$. This is a consequence of the rearrangement inequality. The same result holds in the discrete case.
 * The autocorrelation of a periodic function is, itself, periodic with the same period.
 * The autocorrelation of the sum of two completely uncorrelated functions (the cross-correlation is zero for all $$\tau$$) is the sum of the autocorrelations of each function separately.
 * Since autocorrelation is a specific type of cross-correlation, it maintains all the properties of cross-correlation.
 * By using the symbol $$*$$ to represent convolution and $$g_{-1}$$ is a function which manipulates the function $$f$$ and is defined as $$g_{-1}(f)(t)=f(-t)$$, the definition for $$R_{ff}(\tau)$$ may be written as:$$R_{ff}(\tau) = (f * g_{-1}(\overline{f}))(\tau)$$

Multi-dimensional autocorrelation
Multi-dimensional autocorrelation is defined similarly. For example, in three dimensions the autocorrelation of a square-summable discrete signal would be

$$R(j,k,\ell) = \sum_{n,q,r} x_{n,q,r}\,\overline{x}_{n-j,q-k,r-\ell} .$$

When mean values are subtracted from signals before computing an autocorrelation function, the resulting function is usually called an auto-covariance function.

Efficient computation
For data expressed as a discrete sequence, it is frequently necessary to compute the autocorrelation with high computational efficiency. A brute force method based on the signal processing definition $$R_{xx}(j) = \sum_n x_n\,\overline{x}_{n-j}$$ can be used when the signal size is small. For example, to calculate the autocorrelation of the real signal sequence $$x = (2,3,-1)$$ (i.e. $$x_0=2, x_1=3, x_2=-1$$, and $$x_i = 0$$ for all other values of $f$) by hand, we first recognize that the definition just given is the same as the "usual" multiplication, but with right shifts, where each vertical addition gives the autocorrelation for particular lag values: $$\begin{array}{rrrrrr} & 2 & 3 & -1 \\ \times & 2 & 3 & -1 \\ \hline &-2 &-3 & 1 \\      &   & 6 & 9 & -3 \\     + &   &   & 4 & 6 & -2 \\ \hline & -2 & 3 &14 & 3 & -2 \end{array}$$

Thus the required autocorrelation sequence is $$R_{xx}=(-2,3,14,3,-2)$$, where $$R_{xx}(0)=14,$$ $$R_{xx}(-1)= R_{xx}(1)=3,$$ and $$R_{xx}(-2)= R_{xx}(2) = -2,$$ the autocorrelation for other lag values being zero. In this calculation we do not perform the carry-over operation during addition as is usual in normal multiplication. Note that we can halve the number of operations required by exploiting the inherent symmetry of the autocorrelation. If the signal happens to be periodic, i.e. $$x=(\ldots,2,3,-1,2,3,-1,\ldots),$$ then we get a circular autocorrelation (similar to circular convolution) where the left and right tails of the previous autocorrelation sequence will overlap and give $$R_{xx}=(\ldots,14,1,1,14,1,1,\ldots)$$ which has the same period as the signal sequence $$x.$$ The procedure can be regarded as an application of the convolution property of Z-transform of a discrete signal.

While the brute force algorithm is order $n^{2}$, several efficient algorithms exist which can compute the autocorrelation in order $n log(n)$. For example, the Wiener–Khinchin theorem allows computing the autocorrelation from the raw data $X(t)$ with two fast Fourier transforms (FFT):

$$\begin{align} F_R(f) &= \operatorname{FFT}[X(t)] \\ S(f) &= F_R(f) F^*_R(f) \\ R(\tau) &= \operatorname{IFFT}[S(f)] \end{align}$$

where IFFT denotes the inverse fast Fourier transform. The asterisk denotes complex conjugate.

Alternatively, a multiple $f$ correlation can be performed by using brute force calculation for low $f$ values, and then progressively binning the $X(t)$ data with a logarithmic density to compute higher values, resulting in the same $n log(n)$ efficiency, but with lower memory requirements.

Estimation
For a discrete process with known mean and variance for which we observe $$n$$ observations $$\{X_1,\,X_2,\,\ldots,\,X_n\}$$, an estimate of the autocorrelation coefficient may be obtained as

$$ \hat{R}(k)=\frac{1}{(n-k) \sigma^2} \sum_{t=1}^{n-k} (X_t-\mu)(X_{t+k}-\mu) $$

for any positive integer $$k<n$$. When the true mean $$\mu$$ and variance $$\sigma^2$$ are known, this estimate is unbiased. If the true mean and variance of the process are not known there are several possibilities:
 * If $$\mu$$ and $$\sigma^2$$ are replaced by the standard formulae for sample mean and sample variance, then this is a biased estimate.
 * A periodogram-based estimate replaces $$n-k$$ in the above formula with $$n$$. This estimate is always biased; however, it usually has a smaller mean squared error.
 * Other possibilities derive from treating the two portions of data $$\{X_1,\,X_2,\,\ldots,\,X_{n-k}\}$$ and $$\{X_{k+1},\,X_{k+2},\,\ldots,\,X_n\}$$ separately and calculating separate sample means and/or sample variances for use in defining the estimate.

The advantage of estimates of the last type is that the set of estimated autocorrelations, as a function of $$k$$, then form a function which is a valid autocorrelation in the sense that it is possible to define a theoretical process having exactly that autocorrelation. Other estimates can suffer from the problem that, if they are used to calculate the variance of a linear combination of the $$X$$'s, the variance calculated may turn out to be negative.

Regression analysis
In regression analysis using time series data, autocorrelation in a variable of interest is typically modeled either with an autoregressive model (AR), a moving average model (MA), their combination as an autoregressive-moving-average model (ARMA), or an extension of the latter called an autoregressive integrated moving average model (ARIMA). With multiple interrelated data series, vector autoregression (VAR) or its extensions are used.

In ordinary least squares (OLS), the adequacy of a model specification can be checked in part by establishing whether there is autocorrelation of the regression residuals. Problematic autocorrelation of the errors, which themselves are unobserved, can generally be detected because it produces autocorrelation in the observable residuals. (Errors are also known as "error terms" in econometrics.) Autocorrelation of the errors violates the ordinary least squares assumption that the error terms are uncorrelated, meaning that the Gauss Markov theorem does not apply, and that OLS estimators are no longer the Best Linear Unbiased Estimators (BLUE). While it does not bias the OLS coefficient estimates, the standard errors tend to be underestimated (and the t-scores overestimated) when the autocorrelations of the errors at low lags are positive.

The traditional test for the presence of first-order autocorrelation is the Durbin–Watson statistic or, if the explanatory variables include a lagged dependent variable, Durbin's h statistic. The Durbin-Watson can be linearly mapped however to the Pearson correlation between values and their lags. A more flexible test, covering autocorrelation of higher orders and applicable whether or not the regressors include lags of the dependent variable, is the Breusch–Godfrey test. This involves an auxiliary regression, wherein the residuals obtained from estimating the model of interest are regressed on (a) the original regressors and (b) k lags of the residuals, where 'k' is the order of the test. The simplest version of the test statistic from this auxiliary regression is TR2, where T is the sample size and R2 is the coefficient of determination. Under the null hypothesis of no autocorrelation, this statistic is asymptotically distributed as $\chi^2$ with k degrees of freedom.

Responses to nonzero autocorrelation include generalized least squares and the Newey–West HAC estimator (Heteroskedasticity and Autocorrelation Consistent).

In the estimation of a moving average model (MA), the autocorrelation function is used to determine the appropriate number of lagged error terms to be included. This is based on the fact that for an MA process of order q, we have $$R(\tau) \neq 0$$, for $$ \tau = 0,1, \ldots, q$$, and $$ R(\tau) = 0$$, for $$\tau >q$$.

Applications
Autocorrelation's ability to find repeating patterns in data yields many applications, including:
 * Autocorrelation analysis is used heavily in fluorescence correlation spectroscopy to provide quantitative insight into molecular-level diffusion and chemical reactions.
 * Another application of autocorrelation is the measurement of optical spectra and the measurement of very-short-duration light pulses produced by lasers, both using optical autocorrelators.
 * Autocorrelation is used to analyze dynamic light scattering data, which notably enables determination of the particle size distributions of nanometer-sized particles or micelles suspended in a fluid. A laser shining into the mixture produces a speckle pattern that results from the motion of the particles. Autocorrelation of the signal can be analyzed in terms of the diffusion of the particles. From this, knowing the viscosity of the fluid, the sizes of the particles can be calculated.
 * Utilized in the GPS system to correct for the propagation delay, or time shift, between the point of time at the transmission of the carrier signal at the satellites, and the point of time at the receiver on the ground. This is done by the receiver generating a replica signal of the 1,023-bit C/A (Coarse/Acquisition) code, and generating lines of code chips [-1,1] in packets of ten at a time, or 10,230 chips (1,023 × 10), shifting slightly as it goes along in order to accommodate for the doppler shift in the incoming satellite signal, until the receiver replica signal and the satellite signal codes match up.
 * The small-angle X-ray scattering intensity of a nanostructured system is the Fourier transform of the spatial autocorrelation function of the electron density.
 * In surface science and scanning probe microscopy, autocorrelation is used to establish a link between surface morphology and functional characteristics.
 * In optics, normalized autocorrelations and cross-correlations give the degree of coherence of an electromagnetic field.
 * In astronomy, autocorrelation can determine the frequency of pulsars.
 * In music, autocorrelation (when applied at time scales smaller than a second) is used as a pitch detection algorithm for both instrument tuners and "Auto Tune" (used as a distortion effect or to fix intonation). When applied at time scales larger than a second, autocorrelation can identify the musical beat, for example to determine tempo.
 * Autocorrelation in space rather than time, via the Patterson function, is used by X-ray diffractionists to help recover the "Fourier phase information" on atom positions not available through diffraction alone.
 * In statistics, spatial autocorrelation between sample locations also helps one estimate mean value uncertainties when sampling a heterogeneous population.
 * The SEQUEST algorithm for analyzing mass spectra makes use of autocorrelation in conjunction with cross-correlation to score the similarity of an observed spectrum to an idealized spectrum representing a peptide.
 * In astrophysics, autocorrelation is used to study and characterize the spatial distribution of galaxies in the universe and in multi-wavelength observations of low mass X-ray binaries.
 * In panel data, spatial autocorrelation refers to correlation of a variable with itself through space.
 * In analysis of Markov chain Monte Carlo data, autocorrelation must be taken into account for correct error determination.
 * In geosciences (specifically in geophysics) it can be used to compute an autocorrelation seismic attribute, out of a 3D seismic survey of the underground.
 * In medical ultrasound imaging, autocorrelation is used to visualize blood flow.
 * In intertemporal portfolio choice, the presence or absence of autocorrelation in an asset's rate of return can affect the optimal portion of the portfolio to hold in that asset.
 * In numerical relays, autocorrelation has been used to accurately measure power system frequency.

Serial dependence
Serial dependence is closely linked to the notion of autocorrelation, but represents a distinct concept (see Correlation and dependence). In particular, it is possible to have serial dependence but no (linear) correlation. In some fields however, the two terms are used as synonyms.

A time series of a random variable has serial dependence if the value at some time $$t$$ in the series is statistically dependent on the value at another time $$s$$. A series is serially independent if there is no dependence between any pair.

If a time series $$\left\{ X_t \right\}$$ is stationary, then statistical dependence between the pair $$(X_t,X_s)$$ would imply that there is statistical dependence between all pairs of values at the same lag $$\tau=s-t$$.

title: Autocorrelation