Steve Cook

Mike Clements

Grayham Mizon

forecasting performance of the Treasury Model: Forecasting the growth in UK consumers' expenditure

Keywords: Forecasting, Forecast evaluation Macroeconomic forecasting, Consumers' expenditure, Forecast evaluation, Forecast bias, Forecast encompassing

 tests provides evidence of the longest horizon forecasts failing to capture the full movement of changes in consumption growth. Using simple regression and a selection of forecast encompassing tests, shorter horizon forecasts are found to dominate longer horizon forecasts, a feature which might be expected logically, but need not occur in practice. Finally, forecast performance is related to changes in model specification and modelling methodology.

Given its obvious importance for economic policy, the forecasting performance of the Treasury Model (TM) has been the focus of attention of perhaps a relatively limited number of research articles. 1While [START_REF] Burns | The interpretation and use of economic predictions[END_REF] and [START_REF] Mills | Assessing the forecasters: An analysis of the forecasting records of the Treasury, the London Business School and the National Institute[END_REF] have considered the accuracy of the TM in terms of forecasting the growth in GDP and inflation in the UK, [START_REF] Church | Econometric evaluation of consumers' expenditure equations[END_REF] examined the ability of the TM to forecast consumers' expenditure via an analysis of the properties of one-step ahead forecasts of non-durable consumption over the period from 1989 to 1992. 2 The present paper aims to complement this latter work of [START_REF] Church | Econometric evaluation of consumers' expenditure equations[END_REF] by providing a more detailed analysis of the forecasting of consumers' expenditure by the TM. Drawing upon Treasury Official Economic Forecasts Vols. I & II, a series of one-, two-and three-step ahead TM forecasts of the percentage growth in real total consumers' expenditure have been derived for the period 1967 to 1989. Construction of this data set therefore provides the opportunity to examine forecasts of differing horizons over an interesting sample period capturing changes in Government and economic policy, booms, slumps and major economic shocks, thereby allowing a detailed analysis of the forecasting of consumption by the TM.

To achieve its aims, this paper will proceed as follows. In Section [START_REF] Chong | Econometric evaluation of macro-economic models[END_REF] the nature of the data to be examined are discussed. Section [START_REF] Church | Econometric evaluation of consumers' expenditure equations[END_REF] provides an initial examination of the properties of the alternative forecasts via the calculation of a battery of forecast evaluation statistics. The issue of forecast bias is examined in section [START_REF] Clements | Evaluating Econometric Forecasts of Economic and Financial Variables[END_REF]. Initially this is analysed using [START_REF] Holden | On testing for unbiasedness and efficiency of forecasts[END_REF] tests of unbiasedness before presenting a split sample analysis of forecast evaluation statistics for the differing horizon forecasts. This section also contains tests of partial rationality and 'modified' Holden-Peel tests to further examine the properties of the forecasts. In section [START_REF] Clements | Forecast combination and encompassing[END_REF] the relative properties of differing horizon forecasts are examined directly via the application of alternative tests of forecast encompassing. Although shorter horizon forecasts might logically be expected to encompass longer horizon forecasts, the recent research of [START_REF] Clements | Evaluating Econometric Forecasts of Economic and Financial Variables[END_REF]Hendry (2003, 2008) recognises this might not occur in practice where the idealised conditions of the textbook can be violated by, inter alia, data revision and mismeasurement, location shifts, unknown model misspecification and intercept F o r P e e r R e v i e w correction. Section [START_REF] Clements | Towards a theory of economic forecasting[END_REF] provides some concluding remarks.

Data

The data considered in this study are actual values (a t ) and forecasts (f t ) of the growth in the real value of total consumers' expenditure over the period 1967 to 1989. More precisely, the figures are annual growth rates which consider both growth from the first half of one year to the first half of the following year (e.g. 1968.1 to 1969.1) and the second half of one year to the second half of the following year (e.g. 1967.2 to 1968.2). Given the timing of the preparation of the forecasts, this results in one-and three-step ahead forecasts (denoted as f t-1,t and f t-3,t respectively) being made for annual growth between the first halves of adjacent years, and two-step ahead forecasts (denoted as f t-2,t ) for growth between the second halves of adjacent years. Consequently, while direct comparison can be made between f t-1,t and f t-3,t as they provide forecasts for the same period, any comparison with f t-2,t has to acknowledge that this series is producing forecasts for different periods.

Before analysing the forecasting ability of the TM in detail, the behaviour of consumption growth over the period in question can be examined. Looking at the full set of growth rates from 1967.2-1968.2 to 1988.2-1989.2 provided in Figure One below, it can be seen that there are three main peaks in the growth of consumption (1971.2-1972.2, 1978.1-1979.1 and 1987.1-1988.1) each of which is followed almost immediately by a sharp fall. Relatedly, three noteworthy episodes are (i) the slump of the mid to late seventies, (ii) the slump of the early eighties and (iii) the boom of the mid to late eighties. This can all be highlighted with reference to the average growth rate throughout the period of 2.6%, as from 1974.1 to 1977.2 the growth rate averaged -0.4%, from 1980.1 to 1982.1 it averaged 0.3% and from 1986.1 to 1989.1 it averaged 5.4%. However, while volatility may prove problematic when forecasting, there is a distinction between volatility and predictability. In particular, when considering the current sample, the boom of the late 1980s provided a period which saw the growth in consumption outstripping that of income, a marked increase in consumer debt relative to income and an asset-price boom in the stock and housing markets [START_REF] Muellbauer | The assessment: Consumer expenditure[END_REF]. These three factors represented wholly new phenomena which provided difficulties for existing model specifications as the possibility of their occurrence had not been entertained by modellers.

Plots of {f t-1,t , f t-3,t } and {f t-2,t } against their corresponding actual values of consumption growth (a t ) are provided in Figures Two and Three respectively. In a similar fashion, the one-, two- and three-step forecast errors (e t-i,t = y tf t-i,t for i = 1, 2, 3) can be plotted to gauge the extent of errors made when forecasting the growth in consumption. Considering the behaviour of {e t-1,t , e t-3,t } depicted in Figure Four, it appears that a tendency exists in both series towards overprediction in the period to 1977 and underprediction thereafter. Figure Four also suggests that in addition to one-step ahead predictions faring better than the three-step ahead predictions, both sets of forecasts manage to miss the major changes in consumption growth. For the three-step forecasts the worst individual errors occur for 1973. 1-1974.1, 1977.1-1978.1, 1982.1-1983.1 and 1987.1-1988.1. The worst series of errors for the three-step forecasts occurs in trying to predict consumption growth from 1973. 1-1974.1 to 1978. 1-1979.1, where an average absolute error of 2.9% is made. This compares to an average absolute actual value of 2.8% for consumption growth over the same period. For the one-step ahead predictions the worst error is -2.3% (-1.1%-3.4%) for 1974. 1-1975.1. Figure Five provides a similar depiction for the errors associated with the two-step forecasts suggesting a similar movement from overprediction to underprediction around 1977. It can be noted that these findings concerning overand underprediction for consumption are line with those presented by [START_REF] Burns | The interpretation and use of economic predictions[END_REF] for GDP. Figure

Five also shows that the main forecasting errors occur in 1967. 2-1968.2, 1974.2-1975.2, 1983.2-1984.2, 1986.2-1987.2 and 1987.2-1988.2.

Figures One to Five about here

While the above figures provide a snapshot of the alternative sets of forecasts and their closeness, or otherwise, to the actual consumption data, a more detailed analysis can be obtained via consideration of various forecast evaluation statistics. This is provided in the following section.

Forecast evaluation statistics

To examine the basic properties of the alternative for differing horizons,

U = n t=1 [(a t -f t-i,t )] 2 n t=1 f 2 t-i,t + n t=1 a 2 t (1)
Considering the results presented in Table One, an immediately striking feature is the consistency between the differing horizon forecasts, with a general worsening of forecasting performance apparent as the forecast horizon is increased. It is also clear that the apparent small values obtained for the unscaled evaluation statistics (e.g. ME, MAE, MSE) need to be interpreted with care as the series being forecast is a percentage growth rate which takes small values. To reinforce this issue, some summary statistics for a t are provided in the lower portion of Table One. In light of this, the scaled evaluation statistics are of greater interest, and these provide a less pleasing view of the forecasting performance of the TM. For example, the mean absolute percentage errors for {f t-1,t , f t-2,t , f t-3,t } take values of 41.36%, 79.88% and 96.01%. A similar pattern is present in the calculated values for U which increase with the forecast horizon. The previous graphical analysis suggested possible forecasting bias. To examine this more formally, the tests of unbiasedness of Holden and Peel (1990) can be employed. To illustrate these tests, consider the following testing equation:

a t = α + βf t-i,t + ε t (2)
A familiar test for unbiasedness is given by the joint hypothesis, H 0 : α = 0, β = 1. However, [START_REF] Holden | On testing for unbiasedness and efficiency of forecasts[END_REF] show that this is a sufficient but not necessary condition for f t-i,t to be an unbiased forecast of a t , as the forecast could still be unbiased when

β = 1 if α = (1 -β)E[f t-i,t ].

Holden and

Peel propose the necessary and sufficient condition, H 0 : δ = 0, in: presented show that while the GLS Dickey-Fuller rejects the unit root null for all series, the null of stationarity is not rejected by the KPSS test at conventionally considered levels of significance. It is therefore concluded that all series can be treated as stationary processes. In Table Three results are presented from application of the Holden-Peel tests to the alternative forecast series. In addition to applying the tests to the full samples available for each set of forecasts, the tests are also applied to sub-samples up to and beyond 1977. This split-sample analysis is motivated by the previously noted possibility of a change in forecasting bias around this period. In all cases the Newey-West (1994) variance-covariance matrix estimator is employed when estimating the Holden-Peel regressions of (4) to overcome potential serial correlation (see Clements 1995). 4 The results obtained from the Holden-Peel tests are presented in Table Three. Considering these results, it is clear that over the whole sample there is no evidence of significant bias. However, turning to the split-sample results, the previously noted movement from overprediction to underprediction is supported to some extent with the one-step forecasts exhibiting marginally significant overprediction in the earlier sample and the two-and three-step forecasts displaying significant underprediction in the later sample period.

a t -f t-i,t = δ + ν t (3)
Interestingly, movement from two-to three-step forecasts results in increased and more significant evidence of underprediction being detected in the later sample via the estimated value of δ in [START_REF] Clements | Evaluating Econometric Forecasts of Economic and Financial Variables[END_REF] and its standard error. This reversal of bias reflects the findings of [START_REF] Burns | The interpretation and use of economic predictions[END_REF] for the growth in GDP, but contrasts with his findings for inflation where a movement in the opposite direction from underprediction to overprediction was detected.

Tables Two and Three about here

To supplement the above discussion concerning the potential differing properties of forecasts either side of 1977, the forecast evaluation statistics of

Partial rationality

The above analysis has considered the possibility of bias in the alternative forecasts. However, the presence of unbiasedness is only a necessary condition for partial rationality. To test this latter issue, the work of Pain and Britton (1992) can be drawn upon using the following testing equation:

a t = α + β f t-i,t + γa t-i + ε t (4)
The significance (or otherwise) of β can be used to compare the forecasts of the TM with forecasts from a simple time-series model based upon the latest value actual value at the time of forecasting.

The significance of β would indicate that the forecast f t-i,t adds information, with β = 1 being the important hypothesis for unbiasedness. Consideration of the significance of γ allows testing for omitted factors in the forecast. The results obtained from estimation of (5) for the alternative forecast series are presented in Table Five. From inspection of the results obtained, it can be seen that β is significantly different from zero for all of the forecast series, while α and γ are insignificant. Testing the hypothesis H 0 : β = 1 for the differing forecast series via a Wald test leads to p-values of 0.324, 0.494 and 0.371 for the one-, two-and three-step forecasts thus indicating non-rejection of the null in all instances, thereby providing no evidence against partial rationality.

'Modified' Holden-Peel tests

The standard Holden-Peel forecasting bias tests above consider the sign and significance of the forecast error. When considering this over the whole sample period, it was found that significant bias was not detected for any of the different horizon forecasts. However, these tests can be modified or extended

+ ν t (5)
where the p-value for the significance of the estimated constant term is provided in square brackets.

The difference between the absolute errors is therefore highly significant and also large relative to 5 For an overview of the nature of data revision in economics and its effects see, inter alia, Mankiw et al.

a t = µ + λ 1 f t-1,t + λ 2 f t-3,t + ζ t (6)
The simplest of the tests to consider is that of [START_REF] Fair | The informational content of ex ante forecasts[END_REF] where the forecast encompassing of f t-3,t by f t-1,t (denoted as f t-1,t FE f t-3,t ) is examined via the null hypothesis H 0 : λ 2 = 0 in [START_REF] Clements | Intercept corrections and structural change[END_REF].

In a similar fashion, f t-3,t FE f t-1,t is examined via the null hypothesis H 0 : λ 1 = 0. To derive the [START_REF] Granger | Some comments on the evaluation of economic forecasts[END_REF] forecasting encompassing test, the restrictions µ = 0 and λ 1 + λ 2 = 1 are imposed in [START_REF] Clements | Intercept corrections and structural change[END_REF] to give:

e t-1,t = γ (e t-1,t -e t-3,t ) + ω t (7)
with f t-1,t FE f t-3,t examined via the null hypothesis H 0 : γ = 0. An analogous test of

f t-3,t FE f t-1,t
is provided by swapping the positions of e t-1,t and e t-3,t in [START_REF] Clements | Intercept corrections and structural change[END_REF]. The final encompassing test of [START_REF] Chong | Econometric evaluation of macro-economic models[END_REF] imposes the restrictions µ = 0 and λ 1 = 0 in ( 6) to arrive at the following equation in which f t-1,t FE f t-3,t is examined via δ = 0:

e t-1,t = δ f t-3,t + t (8)
Again encompassing in the opposite direction can be examined with e t-3,t replacing e t-1,t and f t-1,t replacing f t-3,t .

Table Seven presents the results obtained from estimation of the relevant forecast encompassing testing equations above using the Newey-West covariance matrix estimator. From inspection of Table Seven it is apparent that very decisive results are obtained. In particular, while it is possible for rejection or non-rejection to occur in both directions thereby leading to inconclusive results, in all instances considered herein, encompassing is unidirectional, with f t-1,t forecast encompassing f t-3,t but the reverse not holding. It can be noted that while the superior informational qualities of shorter horizon forecasts detected here reflects the findings of [START_REF] Burns | The interpretation and use of economic predictions[END_REF] for TM forecasts of inflation, it contrasts with findings presented by [START_REF] Burns | The interpretation and use of economic predictions[END_REF]

Concluding remarks

In this paper the Treasury Model's ability to forecast the growth in consumers' expenditure over the period from the second half of 1967 to the second half of 1989 has been examined. The sample examined proved to be an interesting period, capturing several booms and slumps, including the largely unexplained boom of the late 1980s, as well as factors such as the OPEC oil price shocks and the arrival of the Thatcher Government. The work complements existing studies such as those of [START_REF] Burns | The interpretation and use of economic predictions[END_REF] and [START_REF] Mills | Assessing the forecasters: An analysis of the forecasting records of the Treasury, the London Business School and the National Institute[END_REF] by restricting attention to a single variable, thereby permitting a detailed analysis to be conducted. This analysis included examination of forecasts of different horizons and the consideration of issues such as unbiasedness, rationality and forecast encompassing. The calculation of a battery of forecast evaluation statistics and the application of a variety of tests uncovered a number of interesting results. While inferences of unbiasedness and partial rationality were drawn over the whole sample period, split sample analysis provided evidence of a switch from overprediction to underprediction around 1977. This was detected from both application of Holden-Peel (1990) tests of unbiasedness and forecast evaluation statistics. While further analysis of the properties of the forecasts provided no evidence against rationality, application of 'modified' Holden-Peel tests using the percentage error as a dependent variable uncovered a significant test result for the longest horizon forecast considered. Given the nature of the test employed, this provided evidence of a tendency for underprediction when the actual growth in consumption is positive, and overpredict when it is negative.

In short, this indicates a failure to capture the full movement of the actual series when forecasting. 6 To complete the analysis, the one-step and three-step forecasts for the same data points were compared using a simple regression of absolute forecast errors and a selection of forecast encompassing tests.

The results obtained show that while recent research has indicated that longer horizon forecasts need not necessarily encompass shorter horizon forecasts, it was the case for the TM forecasts with the one-step forecasts encompassing the three-step forecasts under all of the tests considered.

  percentage error as a dependent variable. Application of this test leads to the results presented in TableSix. Inspection of these results shows that in contrast to the insignificance of the Holden-Peel tests over the whole sample period, a significant result is obtained for the three-step forecasts. However, given the transformation made to the dependent variable relative to the standard Holden-Peel test, the results derived need to be interpreted carefully. The positive coefficient obtained for the three-step forecast series indicates a tendency for errors and actual values to have the same sign. This then indicates underprediction for positive actual values and overprediction for negative actual values, or alternatively expressed, that the forecasts fail to move fully with movements in the actual series. Interestingly, as noted, this is found only for the longest horizon forecast considered.

  (1984),[START_REF] Croushore | A real-time data set for macroeconomists: Does the data vintage matter?[END_REF],[START_REF] Garratt | UK real-time macro data characteristics[END_REF] and[START_REF] Cook | Cross-data-vintage encompassing[END_REF].

  of 2.6 for the actual series. To further investigate the relative properties of the series, the forecast encompassing tests of[START_REF] Fair | The informational content of ex ante forecasts[END_REF],[START_REF] Granger | Some comments on the evaluation of economic forecasts[END_REF] and[START_REF] Chong | Econometric evaluation of macro-economic models[END_REF] are performed. Each of the above tests is based upon the informational redundancy, or otherwise, of one set of forecasts given the presence of another. As noted by[START_REF] Clements | Forecast combination and encompassing[END_REF], the above forecast encompassing tests can be derived via consideration of the following equation:

A

  final point which can be noted concerns the changes in model specification and modelling methodology which occurred during the period considered. It is obviously difficult to directly relate any change in forecasting performance to changes in model specification with confidence for a variety of reasons.In particular, it is uncertain to what extent subjective adjustments, or intercept corrections, are applied to model based forecasts. Similarly, the different model specifications are employed over different sample periods and hence the impact of model specification cannot be assessed even in the absence of intercept correction. However, it can be noted that the TM model of consumers' expenditure was heavily influenced by the works of[START_REF] Davidson | Econometric modelling of the aggregate time series relationship between consumers' expenditure and income in the United Kingdom[END_REF] and Hendry and von Ungern-Sternberg (1980), with the approaches of these papers swiftly adopted. It can be noted also that this period coincides with the increased forecasting accuracy noted in the latter split-sample considered herein. It is therefore tempting to conclude that improved model specification resulted in increased forecasting accuracy.

Figure One: Annual percentage growth in consumers' expenditure 22 PageFigure 23 PageFigure

 2223 Figure One: Annual percentage growth in consumers' expenditure

Table One

 One

	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	presents the
	calculated values of a range of forecast evaluation statistics. The initial rows in Table One present
	familiar, straightforward evaluation statistics based upon the forecast errors. These statistics are the
	maximum error (Max E), minimum error (Min E), mean error (ME), mean absolute error (MAE),
	mean square error (MSE), mean percentage error (MPE) and mean absolute percentage error (MAPE).
	The following row contains calculated values Theil's Inequality Statistic, U , which is given as: 3

  Before applying this test to the alternative forecasts series, the orders of integration of a t and f t-i,t are examined to ensure they are stationary and hence avoid problems of spurious regression. The results obtained from application of the[START_REF] Elliott | Efficient tests for an autoregressive unit root[END_REF] GLS-based Dickey-Fuller unit root test and the Kwiatkowski et al. (KPSS) (1992) stationarity test are presented in Table Two. The results

	F o r
	P
	e
	e r
	R
	e
	v i e
	w

  Table One are presented for the pre-and post-1977 split-samples in TableFour. To summarise the information provided by the range of statistics consid-mean error statistics for all of the differing horizon forecasts. The results presented also indicate that forecasting performance is worse in the earlier sample with, inter alia, higher values of U reported for the earlier sample for all of the sets of forecasts. As noted above, it may have been expected that the latter part of the sample would prove more problematic for forecasting as a result of a number of new and perhaps unexpected phenomena. That the TM should witness an increase in forecasting performance over this period, suggests a marked improvement in underlying forecasting ability.

	Table Four about here
	F o r
	P
	e
	e r
	R
	e
	v i e
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ered, the movement from overprediction to underprediction around 1977 is present in the calculated

  for the growth in GDP where it is suggested that longer horizon forecasts may outperform those over a shorter horizon. However, it should be noted that[START_REF] Burns | The interpretation and use of economic predictions[END_REF] does not examine this formally using encompassing tests.

	Table Seven about here
	F o r
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	e r
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	e
	v i e
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	9

Table One :

 One Forecast evaluation statistics The upper portion of the above table contains calculated values of the forecast evaluation statistics of Section[START_REF] Church | Econometric evaluation of consumers' expenditure equations[END_REF] for the forecast errors relating to the alternative (differing horizon) forecasts f t-i,t . For comparative purposes, the lower portion of the table contains some summary statistics for the actual values (a t ) (annual percentage consumption growth) being forecast. The above table contains calculated test statistics for the[START_REF] Elliott | Efficient tests for an autoregressive unit root[END_REF] τ GLS Fuller test and the KPSS η µ test. Significance at the 5% and 1% levels of significance are denoted by * and * * respectively. The relevant 10%, 5% and 1% critical values for the η µ test are 0.347, 0.463 and 0.739 respectively.

	f t-1,t 1.50 -2.30 -0.09 0.80 0.98 -7.65 41.36 0.14 7.10 -1.70 2.62 2.75 R Standard Deviation (a t ) Max E Min E ME MAE MSE MPE MAPE U Max (a t ) Min (a t ) Mean (a t ) e r e e f t-2,t 3.10 -2.60 0.46 1.26 2.41 26.08 79.88 0.24 6.70 -2.30 2.57 2.29 i v Notes: F o r P e Table Two: Unit root tests 1968.1-1969.1 to 1988.1-1989.1 1967.2-1968.2 to 1988.2-1989.2 f t-3,t 4.40 -5.60 0.45 1.78 5.16 76.95 96.01 0.34 7.10 -1.70 2.62 2.75 a t f t-1,t f t-3,t a t f t-2,t τ GLS µ -3.100 * * -3.483 * * -2.458 * -3.435 * * -2.222 * η µ 0.287 0.192 0.104 0.222 0.096 Notes: µ based Dickey-Page GLS-
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Table Three :

 Three Holden-Peel tests Notes: The above table contains estimated regressions for the forecast bias test of Holden and Peel (1990). Figures in square brackets represent p-values for the test of coefficient insignificance. For f t-1,t and f t-3,t , Sample I contains actual and forecasted consumption growth for 1968.1-1969.1 to 1976.1-1977.1, while Sample II contains data for 1977.1-1978.1 to 1988.1-1989.1. Samples I and II for f t-2,t cover 1967.2-1968.2 to 1976.2-1977.2 and 1977.2-1978.2 to 1988.2-1989.2. Notes: The above table contains estimated regressions for the partial rationality tests of Pain and Britton (1992). Figures in square brackets represent p-values for the test of coefficient insignificance. Notes: The above table contains estimated regressions for 'modified' Holden-Peel tests using percentage forecast errors, rather than forecast errors, as a dependent variable. Figures in square brackets represent p-values for the test of coefficient insignificance.

		Submitted Manuscript
		Table Four: Forecast evaluation statistics Table Five: Partial rationality tests Table Six: 'Modified' Holden-Peel tests
		f t-1,t		f t-2,t		f t-3,t
	Full sample Sample I Sample II a t = -0.667 [0.105] + 1.097 [0.000] f t-1,t + 0.114 Sample I Sample I Sample II [0.161] a t-1 + u t One-step forecasts: e t-1,t a t = -7.648 [0.603] + η t	Sample II Sample I Sample II
	Max E	0.30		1.50	3.10	3.00	1.70	4.40
	One-step forecasts: Min E ME Two-step forecasts: e t-1,t = -0.086 [0.730] -2.30 -1.20 + u t -0.67 0.35 a t = 0.237 [0.681] + 0.915 [0.000] f t-2,t + 0.114 e t-1,t = -0.667 [0.060] -2.60 -2.10 + u t -0.06 0.89 [0.444] a t-2 + v t e t-2,t a t = 26.079 [0.321] + t	e t-1,t = 0.350 [0.138] -5.60 -1.10 + u t -0.78 1.38
	Two-step forecasts: Three-step forecasts: F o e t-2,t = 0.459 [0.234] e t-3,t = 0.452 [0.350] r MAE 0.84 MSE 1.26 MPE -18.42 MAPE 67.29 F o r a t = 1.152 [0.264] + 0.810 + v t + w t 0.77 0.78 0.97 20.62 [0.001] f t-3,t -0.156 e t-2,t = 0.060 [0.912] e t-3,t = -0.778 [0.232] 1.20 1.31 + v t + w t 2.31 2.49 17.58 33.16 80.60 79.29 [0.499] a t-3 + w t r o F Three-step forecasts: e t-3,t a t = 76.952 [0.033] + ξ t	e t-2,t = 0.892 [0.049] e t-3,t = 1.375 [0.020] 1.89 1.69 + v t + w t 5.71 4.75 106.63 53.21 138.99 61.63
	U	P 0.17 P P	0.11	0.25	0.24	0.38	0.32
	Max (a t )	e 6.10 e e	7.10	6.70	6.00	6.10	7.10
	Min (a t ) Mean (a t )	-1.70 1.50	e r 0.00 3.46 e r e r	-2.30 2.01	-0.40 2.96	-1.70 1.50	0.00 3.46
	Standard Deviation (a t )	2.89		R 2.43 R R	2.40	2.22	2.89	2.43
				e e e
	v i e Notes: For f t-1,t and f t-3,t , Sample I contains actual and forecasted consumption growth for 1968.1-1969.1 to 1976.1-1977.1, while Sample II contains data for 1977.1-1978.1 to 1988.1-1989.1. Samples I and II for f t-2,t cover 1967.2-1968.2 to 1976.2-1977.2 and 1977.2-1978.2 to 1988.2-1989.2. v i e v i e
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Table Seven :

 Seven Forecast encompassing testsNotes:The above table contains estimated regressions for the forecast encompassing tests of Fair and Shiller (1989),[START_REF] Granger | Some comments on the evaluation of economic forecasts[END_REF] and[START_REF] Chong | Econometric evaluation of macro-economic models[END_REF]. Figures in square brackets represent p-values for the test of coefficient insignificance.

		Fair-Shiller (1989)
	a t = -0.406 [0.288]	+ 1.077 [0.000]	f t-1,t + 0.052 [0.746]	f t-3,t + u t
	Granger-Newbold (1973)
	e t-1,t = 0.020 [0.868]
	e t-1,t = 0.026 [0.715]	f t-3,t + η t
	e t-3,t = 0.341 [0.005]	f t-1,t + t

(e t-1,te t-3,t ) + v t e t-3,t = 1.020 [0.000] (e t-3,te t-1,t ) + w t

[START_REF] Chong | Econometric evaluation of macro-economic models[END_REF]

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		6
	Annual growth (%)	-2 0 2 4		r o F
		-4			P
		1968	1970	1972	1974 e 1976 r 1978 e Year	1980	1982	1984	1986	1988
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This relative lack of attention is perhaps unsurprising given the asymmetry in information available to those inside and outside of the Treasury. As an illustration of this, Burns (1986, p.105) notes that his research uses "mainly unpublished, internal, forecasts, although some use is made of forecasts published at budget time".

The TM was one of a number of macroeconometric models considered by[START_REF] Church | Econometric evaluation of consumers' expenditure equations[END_REF] in their examination of the forecasting of UK consumers' expenditure.

The U statistic is bounded between 0 and 1, and has a straightforward interpretation with 0 denoting perfect forecasting and 1 denoting the worst possible forecasting performance.

It should be noted that the testing equations for the Holden-Peel tests and all subsequent equations are estimated using the Newey-West covariance matrix estimator.

Page 6 of 26 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

This finding could be related to the results ofGranger and Newbold (1986, p.131), where it is shown that the variance of a process exceeds the variance of an optimal forecast of it.


Hyeyoen Kim

Large Data Sets, Nonlinearity and the Speed of Adjustment to Real Exchange Rate Shocks

Keywords: diffusion indices, nonlinearity, real exchange rate diffusion indices, nonlinearity, real exchange rates

A well known puzzle in international finance concerns the observed very slow speeds of adjustment of real exchange rates in response to shocks. In this paper, we explore whether allowing for a wide range of influences on the real exchange rate in a nonlinear framework can help resolve this puzzle. Using recently proposed econometric methods for summarising very large macroeconomic data sets into a small number of observable factors, we find that there is a long-run relationship between these factors and real exchange rates. When put into a nonlinear framework, we find that allowing for the effects of macroeconomic factors dramatically increases the measured speed of adjustment of the real exchange rate.

I. Introduction

The empirical research effort on real exchange rates over the past two decades or so has tended to concentrate on necessary conditions for long-run purchasing power parity (PPP) to hold, in particular whether the real exchange rate reverts towards some constant equilibrium level over time. The upshot of this research programme is that, insofar as PPP does hold, it holds only in a very long run sense since shocks to the real exchange rate-which may be construed as deviations from PPP-tend to persist for long periods of time. In a survey of this literature, Rogoff (1996) describes the average measured speed of adjustment of real exchange rates as 'glacial', with a half-life of some three to five years. Given that the observed high volatility of real exchange rates under floating regimes suggestes that they must be driven largely by nominal shocks, and since it is hard to credit a half-life of adjustment of three to five years to nominal macroeconomic shocks, Rogoff terms this stylised of 'glacial' real exchange rate adjustment 'the PPP puzzle'.

There have been a number of attempts to resolve or at least explain Rogoff's PPP puzzle. One possibility is that adjustments of the real exchange rate towards PPP are nonlinear, since larger deviations may adjust back towards equilibrium faster than smaller deviations. This nonlinear adjustment may arise either because of transactions costs in international goods arbitrage (Balke and Fomby, 1997; Taylor et al, 2001; Imbs et al, 2003, 2005 1 ) or because of the presence of heterogeneous foreign exchange market agents that have competing views of the equilibrium rate (Kilian and Taylor, 2003), or because the authorities are more likely to intervene in the foreign exchange market when there are large deviations from exchange rate equilibrium [START_REF] Taylor | Is official exchange rate intervention effective?[END_REF][START_REF] Reitz | The coordination channel of foreign exchange intervention: a nonlinear microstructural analysis[END_REF]. By modelling the adjustment process towards equilibrium as a nonlinear process, researchers have indeed found that the speed of adjustment of the real exchange rate is significantly raised [START_REF] Taylor | Nonlinear mean-reversion in real exchange rates: toward a solution to the purchasing power parity puzzles[END_REF]Kilian and Taylor, 2003), thus making some progress towards resolving the PPP puzzle.

In more recent work, however, researchers have also analysed whether time variation in the equilibrium real exchange rate may be modelled within a nonlinear framework, largely through an examination of whether the real exchange rate is impacted by international differences in aggregate factor productivity [START_REF] Paya | A new analysis of the determinants of the real dollarsterling rate: 1871-1994[END_REF][START_REF] Lothian | Real Exchange Rates Over the Past Two Centuries : How Important is the Harrod-Balassa-Samuelson Effect? forthcoming[END_REF]. By allowing for time variation in the equilibrium real 1 The essence of the [START_REF] Imbs | PPP Strikes Back: Aggregation and the Real Exchange Rate[END_REF] study is that transactions costs generate differing speeds of adjustment at a disaggregated goods level that translate into an econometric bias in aggregate studies that employ linear econometric techniques. exchange rate, this work therefore moves away from examining necessary conditions for long-run PPP (mean-reversion of the real exchange rate towards a constant equilibrium) towards examining the speed of adjustment of the real exchange rate towards an equilibrium that may in fact vary over time. While productivity differentials are obvious candidates to examine for their effect on the equilibrium real exchange rate, a less restrictive analysis would allow for the real exchange rate to be impacted by a wide range of macroeconomic variables. Indeed, the failure properly to control for these variables in econometric studies may in part be responsible for the observed slow speed of real exchange rate adjustment. The purpose of this paper, therefore, is to investigate this possibility. In particular, we combine the diffusion index or factor method of Stock and Watson (2002a,b), which allows large amounts of data to be summarised parsimoniously, with linear and nonlinear models of real exchange rate adjustment. 2 The remainder of the paper is organised as follows. The next section briefly describes the estimation of nonstationary macroeconomic factors and the nonlinear econometric techniques that we employ. In Section III we describe the data and some preliminary econometric results. Section IV presents our fitted nonlinear models and measures the effect on the measured speed of real exchange rate adjustment of introducing diffusion indices into the analysis. A final section concludes.

II. Model Specification

II.1 Summarising large data sets

The main advantage of factor models is to summarise the information in large data sets in a parsimonious fashion. Suppose that X t denotes an n-dimensional vector of I(1) time series variables at time t, where n may be very large. If X t is described by a factor model, it can be written as the sum of two orthogonal components:

t t t t F X ξ + Λ = (1)
where X t =(x 1t … x nt )' and ξ t is the (n×1) idiosyncratic disturbance, which may be serially correlated. F t is the (r×1) vector of integrated process latent common factors such that

t t t u F F + = -1
(2)

2 Our investigation is at least partly inspired by the recent study of [START_REF] Bernanke | Measuring the effects of monetary policy: a factor-augmented vector autoregressive (FAVAR) approach[END_REF], who find that by using the diffusion index methods due to Stock and Watson (2002a,b) they are able to solve the 'price puzzle' of monetary economics-namely that vector autoregressive simulations of small macro systems typically generate an initial price rise following a monetary tightening. where u t is a vector zero-mean I(0) process. F t is, however, unobservable. There are several indirect ways to estimate unobservable factors. In this study, we use a two-step principal components method, following Stock and Watson (2002a) and Bai (2004). 3 Since the principal components are by construction orthogonal to one another, there is no redundant information in individual factors. The estimated common factors are I(1) processes since the I(1) process X t is represented in levels.

In practice, n, the number of time series making up X t , may be very large -of the order of fifty or a hundred. If most of the variation in X t is contained in the first r common factors, however, then the dimensionality of the data problem may be reduced from n to r, and r will typically be a small number. Insofar as the resulting factors or diffusion indices can be used to augment an econometric model, the applied modeller may then be able to reflect the complexities of the economy in a parsimonious fashion with a workable number of degrees of freedom.

II.2 Nonlinear real exchange rate adjustment

Smooth transition autoregressive (STAR) models are introduced in econometrics literature by [START_REF] Granger | Modelling Nonlinear Economic Relationships[END_REF]. In STAR model, the speed of adjustment towards equilibrium takes place in every period but the speed varies smoothly with the extent of the deviation from equilibrium. The STAR model is adequate to explain the nonlinear feature of real exchange rates, being employed by a number of researchers as discussed in Section 2. Among smooth transition functions, we focus on the exponential smooth transition autoregressive or ESTAR specification, which implies symmetric adjustment above and below equilibrium and which has been found to be particularly applicable to real exchange rates. The general ESTAR specification for a time series process q t may be written:

t d t j t p j j j t p j j t e q q q q + - Φ - + = - - - ∑ ∑ ] ; [ ] [ µ γ µ β α (3) where 1 = ∑ p j j α and 1 ] [ < - ∑ j p j j β α
. In the present application, q t is the real 3 This involves solving the eigenvalue problem for the sample covariance matrix:

r r r D Y Y = Ξ 0
where Ξ 0 , estimated as XX'/(T 2 N) is the covariance matrix of the standarised data matrix for a sample size T¸ X=[X 1 X 2 … X T ]' and Y r =[y 1 …y r ] is the (n×r) matrix whose columns are the r eigenvectors that corresponds with the first r largest eigenvalues of covariance matrix, Ξ 0 , which we defined here as first r principal components.

F

) ( exp[ 1 ] ; [ 2 µ γ µ γ - - - = - Φ - - d t d t q q
(5)

The exponential transition function determines the degree of mean reversion and is itself governed by the nonlinear adjustment parameter, γ, which effectively determines the speed of mean reversion and the parameter µ which is the equilibrium level of real exchange rates. Φ[γ; q t-d -µ] is bounded by zero to unity with symmetrically inverse bell-shaped around zero. The transition parameter γ>0, determines the speed of transition between the two extreme regimes of random walk and different AR(p) specification, with lower absolute values of γ implying slower transition.

When the real exchange rate is close to the equilibrium level µ, for instance, the nonlinear part of equation ( 3) disappears as Φ(0)=0, and the real exchange rate is close to AR(p) model:

t j t p j j t e q q + = - ∑ α (6)
As departures from the equilibrium increase, however, the argument of the transition function gets larger and larger and, in the limit, the transition function approaches unity:

lim |x|→∞ Φ[γ; q t-d -µ]=1.
In the limit, therefore, (3) becomes a difference AR (p) model:

t p j j j t p j j j t e q q ∑ ∑ + + + = - µ β β α ] [ (7)
with a correspondingly difference speed of mean reversion so long as α j ≠0 in (3) for at least one value of j.

q q + - Φ - + = - - - - - ∑ ∑ ] ; [ ] [ γ β α (8)
where F t is the vector of factors characterising the common stochastic components of the macroeconomy data.

By the specification of ( 8), the key innovation of this paper is the incorporation of diffusion indices into the determinants of the long-run equilibrium real exchange rate.

It is already known that allowing for nonlinearities in real exchange rate adjustment mitigates the PPP puzzle [START_REF] Taylor | Nonlinear mean-reversion in real exchange rates: toward a solution to the purchasing power parity puzzles[END_REF]. Moreover, previous attempts to allow for time-variation of the equlibrium real exchange rate in a nonlinear framework have typically focused on a very small number of variables such as relative productivity [START_REF] Paya | A new analysis of the determinants of the real dollarsterling rate: 1871-1994[END_REF][START_REF] Lothian | Real Exchange Rates Over the Past Two Centuries : How Important is the Harrod-Balassa-Samuelson Effect? forthcoming[END_REF]. By allowing for the effect a large number of macroeconomic factors on the real exchange rate in the context of nonlinear adjustment, we wish to investigate whether a faster speed of real exchange rate adjustment can be ascertained.

III. Data and Preliminary Analysis

Our data base is composed of two parts, each covering a sample period from January 1973 through to June 2006. The first part consists of the monthly US dollar spot exchange rate for UK sterling, Japanese yen, and Australian dollar together with monthly observations on consumer price indices for the UK, Japan, Australia, and the US. The real exchange rate is constructed in logarithmic form as in Equation ( 6), with s t the US dollar price of foreign currency, p t the logarithm of the US consumer price index (CPI), and p* t as the logarithm of the CPI of the corresponding country.

The second part of our data base consists of large data sets of macroeconomic time series for the UK, Japan, Australia, and the US. The composition of the monthly data sets was determined by data availability which represents the real variables (real production, employment, orders, retail sales, etc.), nominal macroeconomic variables (e.g. monetary aggregates), asset prices (stock prices, interest rates, etc.), and international trade variables (import, exports, etc.). 4 The each time series of data sets are transformed to be seasonally adjusted and logarithms are taken for for nonnegative 4 Details of data sets are available from the authors on request. If the series are characterized by a few strong comovements, a small number of factors should account for a sizeable percentage of the overall variance while the remaining principal components have small marginal contribution. We found in each case that two factors appeared adequate and explained more than 30 percent of total variability.

As a preliminary exercise to investigate the long run relationship between real exchange rates and the common stochastic movements, we obtained a simple estimate of the long-run or fundamental equilibrium level of the real exchange rate by rotating two factors each from the home and foreign countries toward q t by running the following regression.

error F F a q t t t + + + = ∧ ∧ , 2 ' 2 , 1 ' 1 λ λ (9) where ) ( * , , , ∧ ∧ ∧ = t i t i t i f f F
for i=1,2 with f i,t and f* i,t indicating the i-th home and foreign factors, respectively. When we plot the actual logarithmic real exchange rate and our simple estimates of the factor-based fundamental levels for the whole sample period, there is clear evidence suggesting that the real exchange rate is explained by the stochastic trends summarized by factors. As illustrated in Figure 1, the movement of the real exchange rates seems to track the fundamental level and turning points look correct in general.

The fact that factors fail to explain the high US dollar during the mid 1980s accords with the received wisdom that this was a period of large scale dollar overvaluation.

This exercise, however, is clearly very primitive and incomplete, given that the on either side of (9) are I(1) variables. In order to detect the common movement among these stochastic series in the long run, Johansen's cointegration analysis was therefore conducted. 6 The results are reported in Table 1, and indicate that we can reject at standard significance levels the the null hypothesis of no cointegration between the real exchange rate and the factor indices. Given this evidence of a long-run relationship between q t and F t , we are motivated to construct the nonlinear real exchange rate 5 For the Australian data, many series are on a quarterly basis and only available for a recent twenty-year period. Hence the volume of data which covers the last thirty-four years is smaller for Australia than for the other countries. 6 As noted by [START_REF] Balke | Threshold cointegration[END_REF], linear cointegration analysis is still applicable in cases where adjustment towards that equilibrium is nonlinear.

IV. Empirical Results

IV.1 Nonlinear estimation results

When a long-run relationship exists between real exchange rates and factors, such a relationship should say something about the speed of adjustment of real exchange rates.

For this purpose, we specify a model which combines the long-run relationship between factors and real exchange rates into a nonlinear system and investigate the persistence of shocks to the real exchange rate.

Following the procedure suggested by [START_REF] Teräsvirta | Specification, estimation and evaluation of smooth transition autoregressive models[END_REF] for the specification and estimation of STAR models, we found that a first delay parameter is adequate, based on a set of nested likelihood ration tesets. Further, we tested the restrictions on the autoregressive parameters α=1, β=-1 and in no case could we reject at the five percent significance level. These restrictions imply an equilibrium of the real exchange rate, in the neighborhood of which q t is close to a random walk, becoming increasingly mean reverting with the absolute size of the deviation from equilibrium.

The fitted ESTAR models are reported in Table 2. The simple ESTAR model of real exchange rates was then modified as a factor-augmented ESTAR or FESTAR model by adding factors into the transition function. Initially, we included four factors in the FESTAR specification (two home factors and two foreign factors) such that:

t t t t t t t t t t t t t e c f f f f q c f f f f q q q + - - - - - - - × - - - - - - = - - - - - - - - - - - } ] ( exp[ 1 { ) ( 2 * 1 , 2 4 * 1 , 1 3 1 , 2 2 1 , 1 1 1 * 1 , 2 4 * 1 , 1 3 1 , 2 2 1 , 1 1 1 1 β β β β γ β β β β (10)
Following a general-to-specific specification search, we then arrived at our parsimonious FESTAR specifications which are presented in Table 3. All of these estimations were conducted using nonlinear least squares.

A notable feature of the results reported in Table 3 is that the estimated transition parameter, γ, is larger absolute value than in the FESTAR specifications than in the simpler ESTAR specifications. In both nonlinear models, 't-statistics' of the estimated value of γ suggest that it is significantly different from zero. However, standard t-values are not valid in this specification since the presence of a unit root under the null hypothesis complicates the testing procedure. 7 We therefore calculated the empirical significance levels using Monte-Carlo simulation under the null hypothesis assumption of a unit root AR(1) process, i.e. γ=08 , and the resulting empirical marginal significance levels show strong support in favour of nonlinearity in q t in both the ESTAR and FESTAR formulations.

IV.2 Estimated half-lives of adjustment

Based on the estimated models reported in Tables 2 and3, we calculated the half-lives of a range of shocks to the real exchange rates. In contrast to the linear case, estimating half-lives is complicated in nonlinear models since the ultimate effect of a shock can vary depending on the state of the system at the time of the impact of the shock as well as on the sign and magnitude of the shock. In the present analysis we follow the approach of [START_REF] Koop | Impulse response analysis in nonlinear multivariate models[END_REF] and [START_REF] Gallant | Nonlinear dynamic structure[END_REF] to estimate the generalised impulse response functions by Monte Carlo integration.

In particular, the impulse response function (IRF) is defined as the evolution of the effects of shocks on variables at N horizons expressed as {IRF[1,s(t),h(t)], IRF[2,s(t),h(t)],…, IRF[N,s(t),h(t)]}. s(t) is an arbitrary shock occurring at time t and h(t) indicates the history set of q t . The IRF is defined as the distance between the path of q which is expected to prevail at time t through t+N following an additive shock of size s(t) at time t, and a baseline path assuming that a shock does not take place at time t. Formally, this can be expressed as:

IRF[N, s(t), h(t)]=E[q(t+n)/s(t), h(t)]-E[q(t+n)/h(t)], n=1,2,…N. (11)
In a nonlinear model, estimation of ( 11) is not simple due to the difficulties in generating n-period ahead expectations directly from available information at time t. In particular, the effects of future innovations cannot be simply set to an expected value of zero since the expected value of a nonlinear function of innovations will typically be non-zero.

As an alternative solution, Monte Carlo integration can be exploited. In the present analysis, 5,000 replications of the sample paths (N=100), based on the nonlinear specification in Table 2 and3, with and without a shock of size s at time t are simulated by randomly drawn residuals as noise for future horizons. The realizations of the differences between the two paths with and without a shock are calculated and saved.

We then move up one data point and conduct this procedure again. Once the difference of the simulated paths are stored for every data point from January 1973 through June 2006, the impulse response function is estimated as an average over all the simulated sequences of differences in the paths of the deviations from fundamental equilibrium with and without the shock. Therefore, the IRFs are conditional on the average history of the given q t series.

Since the size of shock matters in a nonlinear system, five different sizes of shock were considered. With s taken from the set {1,5,10,20,30}. 9 This allows us to compare how large and small shocks affect real exchange rates over time in our two different nonlinear frameworks, ESTAR and FESTAR. In addition, for purposes of comparison, we also estimated simple AR(1) models and used them to estimate halflives of adjustment under the assumption of linearity.

Figures 2 andTable 4 summarise the estimated impulse response functions. As clearly illustrated, all of the impulse response functions show a nonlinear pattern with steeper degrees of mean reversion as the size of the shock increases. When the half-lives of shocks are compared between FESTAR and ESTAR, a faster speed of adjustment is found in the FESTAR case for all sizes of shocks considered and for all currencies. In the FESTAR model, for instance, the half-lives range from 3 to 30 months depending on the exchange rate, while the corresponding range is 5 to 70 months in ESTAR formulation.

Focusing on the FESTAR results, the fastest speed of adjustment is observed in dollar-sterling for a 30 percent shock, which has a half-life of only 3 months. For 1 percent shocks, the real exchange rate exhibits slow mean reversion consistent with a half-life as long as 30 months, as seen in dollar-Australian dollar, but this nevertheless still faster than implied by the univariate ESTAR model. Similarly, for Japan, the halflife of a 1 percent shock is much shortened with the inclusion of macro factors, reducing from 70 months in the estimated ESTAR formulation to just 24 months in the estimated FESTAR specification.

Compared to the half-lives estimated using a liner specification, our findings are consistent with the existing literature which shows that measured half-lives of adjustment of real exchange rate shocks are shorter when measured in an explicitly nonlinear framework. The innovation in the present study, however, is the finding that the measured half-life shrinks even further when diffusion indices or macro factors are added into the nonlinear system.

V. Conclusion

In this paper, we have shown that the information in large macroeconomic data sets is relevant for resolving a well known puzzle in international finance concerning the slow speed of adjustment of real exchange rates in response to shocks. In particular, using measures of macroeconomic factors that summarise large amounts of macroeconomic data, our estimated factor-augmented ESTAR, or FESTAR models are designed to incorporate the long-run relationship between real exchange rates and economic fundamentals into the nonlinear property of real exchange rates. Similar to the nonlinear ESTAR formulation employed in a number of previous studies of the real exchange rate, the FESTAR specification allows the real exchange rate to behave as a random walk near the equilibrium and as mean-reverting far away from the equilibrium in a nonlinear fashion, consistent with a number of theoretical analyses of the real exchange rate. In addition, however, the FESTAR specification allows the influence of a complex set of macroeconomic variables on the real exchange rate in a parsimonious fashion.

The FESTAR specification was applied to three major real exchange rates against the US dollar: dollar-sterling, dollar-yen, and US dollar-Australian dollar. When we estimate the half-life of real exchange rate adjustment using these estimation results, the FESTAR specification exhibits a much faster speed of mean reversion than univariate linear and nonlinear models. These results therefore suggest that the finding of slow mean reversion in the real exchange rate may result from a failure properly to allow for the wide range of macroeconomic influences on the equilibrium real exchange rate. US Dollar-Japanese Yen [-3.3824(q t-1 -3.7826f US Dollar-Japanese Yen t q ∧ = q t-1 -(q t-1 +6.2467f 1,t-1 -2.7431f 2,t-1 -7.902f* US Dollar-Australian dollar t q ∧ = q t-1 -(q t-1 -0.2058f* 1,,t-1 -0.034){1-exp[-3.7672(q t-1 -0.2058f* 1,,t-1 -0.034) 2 ]}

F

t t t t t e c q c q q q + - - - - - = - - - ]} ) ( exp[ 1 ){ ( 2 1 1 1 γ US Dollar-UK sterling t q ∧ = q t-1 -(q t-1 -0.0616){1-exp[-2.5517(q t-1 -0.0616) 2 } (4.
t q ∧ = q t-1 -(q t-1 -0.2258){1-exp[-0.8717(q t-1 -0.
F q q q + - - - - - - - = - - - - - } ] ( exp[ 1 ){ ( 2 1 1 1 1 1 β γ β US Dollar-UK sterling t q ∧ = q t-1 -(q t-1 -3.7826f 1,t-1 +3.8448f* 1,t-1 -0.0593){1-exp

  not represented in percentage unit. The total number of time series collected was 75, 81, 49, and 85 for the UK, Japan, Australia, and US, respectively. 5

  factors as determinants of long-run equilibrium.

  , z1=[0.000], z2=[0.711], z3=[0.197] Notes: Figures in parenthesis are estimated 't-ratios'; s is the standard error of the regression. z1 is the Jarque-Bera test statistic for normality of the residuals; z2 is the Eitrheim-Teräsvirta test statistic for serial correlation up to order three; z3 is White's test statistic for heteroscedasticity. Figures in square brackets are marginal significance levels. The marginal significance levels for the estimated transition parameter 't-ratios' were calculated by Monte-Carlo simulation under the null hypothesis that the transition parameter was zero.

Figure 2 .

 2 Figure 2. Impulse Response Functions

  For intermediate deviations of the real exchange rate from equilibrium, the process will display a finite speed of adjustment.relationship between factors and the real exchange rate into the transition function if such a relationship exists. When the factors are included, equation (3) may be modified

	as
	t	p j	j	t	j	p j	j	q	t	j	t bF	j	q	t	d	t bF	d	e	t
	F o r
			P
				e
					e r
							R
										e
											v i e
													w
	By combining the factors in a nonlinear function, the equilibrium real exchange rate
	becomes time varying and dependent on macroeconomic fundamentals estimated by the
	common factors or diffusion indices. We term ESTAR models of this kind, in which
	macroeconomic fundamentals have been added into the specification by mean of factors,
	'factor-augmented ESTAR' or FESTAR models.

Equation (3) implicitly assumes that the real exchange rate has a constant equilibrium, µ, but we can relax this assumption by incorporating the long-run

Table 1 . Johansen cointegration tests

 1

	o r
	P
	e
	e r
	R
	e
	v i e
	w

Table 2 . ESTAR estimated by country (Jan. 1973 -Jun. 2006)

 2

	ESTAR model:

  is the standard error of the regression. z1 is the Jarque-Bera test statistic for normality of the residuals; z2 is the Eitrheim-Teräsvirta test statistic for serial correlation up to order three; z3 is White's test statistic for heteroscedasticity. Figures in square brackets are marginal significance levels. The marginal significance levels for the estimated transition parameter 't-ratios' were calculated by Monte-Carlo simulation under the null hypothesis that the transition parameter was zero.

		F o r
			P
			e
	(10.709)	(2.510) [0.088]	2258) 2 } s=0.0125, z1=[0.000], z2=[0.708], z3=[0.611] (10.709) e r
	US Dollar-Australian dollar t q ∧ = q t-1 -(q t-1 -0.0395){1-exp[-3.6232(q t-1 -0.0395) 2 } R (-3.081) (2.711) (2.911) e
		[0.033]	s=0.0128, z1=[0.000], z2=[0.686], z3=[0.115] v i e
			w

Notes: Figures in parenthesis are estimated 't-ratios'; s

Table 3 : FESTAR estimates by country (Jan. 1973 -Jun. 2006)

 3

	FESTAR model:

  1,t-1 +3.8448f* 1,t-1 -0.0593) 2 ]}

	(3.395) (-3.207)	(4.832)	(3.351)	(3.395) (-3.207)	(4.832)
		[0.0336]
				s=0.0129, z1=[0.000], z2=[0.686], z3=[0.000]

  1,t-1 -0.2676)×

	(-4.631) (3.636)	(-5.355) (11.315)
		{1-exp[-1.6941(q t-1 +6.2467f 1,t-1 -2.7431f 2,t-1 -7.902f* 1,t-1 -0.2676) 2 ]}
		(1.765) (-4.631) (3.636) (5.355) (11.315)
	[0.3150]
		s=0.0122, z1=[0.000], z2=[0.695], z3=[0.119]

Table 4 . Estimated Half-lives Conditioning on Average Initial History

 4 Notes: The half-lives for the estimated nonlinear ESTAR and FESTAR models were calculated by Monte Carlo integration.

			Submitted Manuscript
	Shock (%)	1	5	10	20	30
	UK	Linear AR	26	26	26	26	26
		ESTAR	50	26	15	8	5
		FESTAR	24	14	9	5	3
	JAPAN	Linear AR	43	43	43	43	43
		ESTAR	70	43	27	15	10
		FESTAR	24	18	14	7	5
	AUSTRALIA	Linear AR	28	28	28	28	28
		ESTAR	40	20	12	6	4
		FESTAR	30	17	10	5	4

Page 17 of 19 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK 1 Figure 1.

Real exchange rate and stochastic macroeconomic trends.

	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	2

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Analogous to the way in which the distribution of the Dickey-Fuller statistic cannot be assumed to be Student's t

The method of estimation of the empirical significance levels follows the procedure described in[START_REF] Taylor | Nonlinear mean-reversion in real exchange rates: toward a solution to the purchasing power parity puzzles[END_REF].

A shock of s percent to the level of the real exchange rate is equivalent to adding log(1+s/100) to q t ; the half-life is the time taken for the impulse response function to fall below 0.5log(1+s/100).


Table of Contents

Developing the Web

 Site: www.choreos.eu ................................................................. 2.2. Social Networks: Twitter and SlideShare .....................................................................
CHOReOS

HAL:

Introduction

As outlined in the project's DOW, the following dissemination activities are targeted toward raising awareness and further fostering the taking up of project results, as part of the dedicated task of WP9:

1. Publishing and maintaining CHOReOS web site and a social network (i.e., dedicated sub-groups Obviously, concrete dissemination results are expected to become increasingly effective over the years, according to the project's RTD progress. Hence, in the first year, project dissemination has been mainly focused on the first activity listed above, i.e., publishing and maintaining CHOReOS web site and social network platforms, as already reported in Deliverable D9.1.

Still, the consortium has been very active regarding presentations and publications about CHOReOS, although the project is in the first year and hence has been concentrating on the design of the CHOReOS IDRE and associated elements, while publications require concrete artefacts for the sake of assessment and validation.

As for the other dissemination activities, they will be implemented in the next years, according to the project's plan.

Last but not least, dissemination about CHOReOS is actually supported by all the tasks of WP9 on "Technology transfer, Dissemination and Collaboration", beyond the task that is specifically devoted to dissemination and whose results are reported in this deliverable. Further information about the achievements of these related tasks may be found in the various Deliverables D9.xs According to the above, the report is structured as follows:  Chapter 2 outlines achievements regarding dissemination using the Web and social networks.  Chapter 3 concentrates on publication-related activities, further summarizing publications of the 1 st year as well as participation of the CHOReOS consortium in conference committees, which help promoting awareness about the CHOReOS fields of study.  Chapter 4 concludes with the CHOReOS dissemination plan for the next periods, which will in particular build on targeted implementation results.

CHOReOS 2 FP7-257178

CHOReOS Web Site and Social Networks

The first year of the project was dedicated to setting up the dissemination resources and starting to experience them. The development of these efforts was constrained by the limited availability of CHOReOS deliverables due to the early stage of the project. The second year will build upon this experience and leverage the growing availability of CHOReOS deliverables.

Developing the Web Site: www.choreos.eu

The CHOReOS public web site has been reported upon in Deliverable D9.1. The Web site has been designed so as to ease access to core information and further attract the interest of the user, by limiting verbose presentation and promoting timely release of information. The figure below illustrates the look & feel of the CHOReOS public Web site:

As stressed in Deliverable D9.1, unlike a printed brochure, a web site is a flexible artefact: it can be modified and updated at will. The web site evolves in its technical structure and in its content.

The structure of the site described in the « D9.1 Public CHOReOS website report » has evolved with the addition, for instance, of new sections such as "Project Deliverables" where we publish all public reports, and "Useful Resources" that provide external resources relevant for the CHOReOS project, coming from other projects or from the community at large. The evolution of the web site content is driven by the publication of: reports on CHOReOS events (including internal meetings, industry and academic/scientific events), the interviews of consortium members providing their perspectives and updates on the project, and the project deliverables (public reports, software, marketing collateral), as they become available. The Web site also features a Web page dedicated to "Related projects" so as to foster dissemination and possible collaboration across projects (see http://www.choreos.eu/bin/About/Related_Projects).

CHOReOS 3 FP7-257178

To conclude, the Web site registers increasing visits over months although it is expected that the number of visits will drastically increase as concrete results get released and made known to the relevant communities, in particular through the support of social networks.

Social Networks: Twitter and SlideShare

CHOReOS uses Twitter and LinkedIn as its preferred social networks. On the other hand, the project team has decided that Facebook is not a priority communication channel for CHOReOS.

Twitter, LinkedIn and SlideShare icons are visible from all the CHOReOS web site pages, inviting visitors to follow the project activities or browse the past project public presentations. The use of social networks is gradually ramping up. However, progress is slow as the project has not yet delivered software.

We use SlideShare to disseminate the CHOReOS presentations. Like a social network, SlideShare is an on-line service allowing storage and comfortable viewing of slide-based presentations. The SlideShare viewer is embedded in the CHOReOS web site, the advantage is that presentations can be viewed with the comfort of SlideShare without leaving the CHOReOS web site. All consortium partners have been invited to use the SlideShare CHOReOS account for posting their CHOReOS presentations and linking them with other social networks, and in particular with Twitter.

As an illustration, the picture below gives an excerpt of CHOReOS twitts: CHOReOS 4 FP7-257178

CHOReOS Presentations and Publications

CHOReOS targets dissemination in both leading academic venues and strong industriallyoriented events, so as to foster take up of CHOReOS results in the various communities of relevance.

Regarding leading academic venues that are targeted by the consortium, these have already been listed in the DOW, and cover the various areas studied by the project, i.e.:

 Software, services and systems engineering: As for industry-focused exhibits, the following major industrial conferences and exhibitions were identified: ICT Event, CeBIT, OOP, JavaOne, JAX World, Software Engineering Today, Software Architect, …


Still, as we are in the first year of the project, results are mainly oriented toward state of the art analysis and IDRE components design. On the other hand, major publications are expected based on concrete, assessed results, which is to become available in the second year. Hence, presentation and publications in the first year have also targeted workshops, which are the venue of choice to exchange about vision and initial design.

Next to presentations and publications, another important dissemination-oriented activity lies in participating to conference organization committees and especially programme committees so as to raise awareness in the research fields of interest in the community.

Main achievements regarding presentations and publications are quantitatively summarized in the table below.

Dissemination path Achievements

Industry-oriented presentations FP7-257178

The following sections then detail achievements of the CHOReOS consortium in the first year regarding Presentations at industry-oriented (Section 3.2) and academic events (Section 3.3), Publications (Section 3.4), and Programme committee membership (Section 3.5), where the provided lists are ordered according to the alphabetical order of contributing members.

Further, as discussed in Section 3.1, CHOReOS uses HAL for greater dissemination of the project's presentations and publications.

HAL: Multi-disciplinary Open Access Archive

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research papers, whether they are published or not, and for PhD dissertation. The documents may come from teaching and research institutions in France or abroad, or from public or private research centres.

As such, HAL allows for broad dissemination of scientific research papers (including research presentations).

CHOReOS publications may then be accessed through the CHOReOS web site (http://www.choreos.eu/bin/Download/Publications) but also directly at:

http://hal.inria.fr/choreos (see screen shot below).

Presentations and participation at industry-oriented events

CHOReOS partners gave presentation at industry-oriented events, which were so far centred on open source initiatives.

Presentations include one about CHOReOS and related OW2

Presentations at academic events

Besides the presentations associated with journal and workshop publications given in the next section, the following CHOReOS presentations were given in the first year:  Andrea Polini. The CHOReOS Project. Presentation at MeTTeG 2011 http://conferences.cs.unicam.it/metteg11/  Andrea Polini. Choreographies and Testing for Quality Assurance -The CHOReOS way for the Future Internet. Presentation at QASBA 2011. http://www.inf.usi.ch/phd/bianculli/qasba2011/  Darius Silingas. Model-Driven Service Choreographies in the Future Internet.

The 11th IFIP Conference one-Business, e-Service, e-Society (I3E 2011) October 12th -14th1 , Kaunas, Lithuania. http://isd.ktu.lt/i3e2011/#key_notes

Publications

The following sections list the publications of the project in the first year by major categories of venue.

Journals and

Conclusion

While the CHOReOS project has achieved good results in terms of dissemination despite being in its first year, dissemination achievements are expected to significantly grow in the 2 nd and even more 3 rd year, in particular due to available software prototypes.

Concretely, dissemination activities will be along the line of the objectives recalled in the introduction:

1. CHOReOS web site and social networks: these are expected to become increasingly lively, benefiting from RTD achievements and especially release of software prototypes, as well as other dissemination results that will be pro-actively advertised on the CHOReOS web and social networks.

2. Publications: CHOReOS publications will increasingly target leading venues, such as the ones listed in the introduction.

3. Presentations at leading industrial conferences and expositions. Such presentations will be planned during the 2 nd year, in close connection with CHOReOS activities in the area of open source software community building.

Organization of 2 open international CHOReOS workshops:

The CHOReOS workshops are planned to be held in the project's 3 rd year. However, organization will start during the 2 nd year, in particular selecting the events with which the workshops should be co-located for greater impact, as well as preparing the calls for contributions for early publicity.

5. Final dissemination reports: This activity will be undertaken during the 3 rd year, building upon the various CHOReOS results and supporting material.

1.

  Introduction ................................................................................................................... 2. CHOReOS Web Site and Social Networks...................................................................

  Presentations and Publications ................................................................

  .

4 .

 4 Conclusion .....................................................................................................................

systems, middleware, services, Internet, grids, clouds, mobile ad hoc and sensor networks

	Journals & magazines: IEEE TSE, ACM TOSEM, SoSyM (Springer), JSS
	(Elsevier);
	 Conferences: ICSE, ACM SIGSOFT FSE, Joint ESEC/ACM FSE, IEEE ASE,
	FASE, IEEE ICST, IEEE/IFIP WICSA, ICSOC, IEEE ICWS, IEEE SCC, IEEE
	CAiSE, ACM SAC, ACM/IEEE MODELS, ServiceWave, …
	 Distributed

:  Journals & magazines: IEEE TPDS, ACM TOCS, JPDC (Elsevier), CACM, IEEE Computer, IEEE TMC, PMC (Elsevier), IEEE Pervasive Computing, IEEE TSC, IEEE Internet Computing, Journal of Internet Services and Applications (Springer)…;  Conferences: ACM/IFIP/USENIX Middleware, IEEE ICDCS, IFIP DAIS, IEEE/IFIP DSN, ACM/USENIX Mobisys, IEEE PerCom, IEEE Pervasive, International Conference on Ubiquitous Computing, Internet of Things Conference, IEEE CCGrid, ACM Conference SenSys, IEEE DCOSS

  France. The slides and video of the presentation are available at: http://www.ow2.org/view/Events2010AnnualConference/Program CHOReOS partners further participated to the following events:  Felipe Besson, Pedro Leal, Fabio Kon, Alfredo Goldman, Dejan Milojicic. Towards Automated Testing of Web Service Choreographies. Poster in FISL 12 -International Free Software Forum 2011, Porto Alegre, Brazil.  Felipe Besson, Guilherme Nogueira, Leonardo Ferreira Leite. Opensource framework for web service testing with dynamic clients creation. Talk in FISL 12 -International Free Software Forum 2011, Porto Alegre, Brazil.  Emilio Francesquini, Felipe Besson, Leonardo Ferreira Leite. Web Service Orchestrations. Talk in FISL 12 -International Free Software Forum 2011, Porto Alegre, Brazil.  USP Choreos Group. A Service-Oriented Middleware for the Ultra Large Scale Future Internet. Poster in FISL 12 -International Free Software Forum 2011, Porto Alegre, Brazil.

initiative, at the OW2 Annual Conference:

 Pierre Chatel. "The CHOReOS FP7 project and the Future Internet OW2 initiative". OW2 Annual Conference 2010 "Open Source for Open Clouds", November 24 th 2010, FP7-257178

Paris,

3.4.3. Workshops and posters 

  Antonia Bertolino, Guglielmo De Angelis, Andrea Polini, Antonino Sabetta, Valeria Cardellini, Emiliano Casalicchio, Kalinka Regina, J.L. Castelo Branco, Julio Cezar Estrella, Francisco Jose Monaco. Trends and research issues in SOA validation. Performance and Dependability in Service Computing: Concepts, Techniques and Research Directions, 2011.  Valérie Issarny, Nikolaos Georgantas, Sara Hachem, Apostolos Zarras, Panos Vassiliadis, Marco Autili, Marco Aurélio Gerosa, Amira Ben Hamida. Service-Oriented Middleware for the Future Internet: State of the Art and Research Directions. Journal FP7-257178 of Internet Services and Applications (JISA) -2011. ISSN: 1867-4828 (print version). ISSN: 1869-0238 (electronic version). Online First: June 2011.  Sherif Sakr, Anna Liu, Daniel Batista, Mohammad Alomari. A Survey of Large Scale Data Management Approaches in Cloud Environments. IEEE Communications Surveys & Tutorials, IEEE, 2011, 13 (3), pp. 311-336. Marco Autili, Davide Di Ruscio, Paola Inverardi, James Lockerbie, Massimo Tivoli. A Development Process for Requirements Based Service Choreography. Service-Oriented Computing: Consequences for Engineering Requirements Workshop colocated with the 19th IEEE International Requirements Engineering Conference, Aug 2011, Trento, Italy.  Zan Barkane, Egils Ginters. Introduction to Technologies Acceptance and Sustainability. Annual Proceedings ICTE in Regional Development 2009/2010, Socio-technical Systems Engineering Institute, ISBN 978-9984-633-20-6, 2011, pp. 61-89.  Felipe Besson, Pedro Leal, Fabio Kon, Alfredo Goldman, Dejan Milojicic. Towards Automated Testing of Web Service Choreographies. Poster in AST '11 -6th international workshop on Automation of software test. Waikiki, Honolulu, HI, USA, 2011. ACM. Fabio Kon: ACM/IFIP/USENIX International Middleware Conference'2011 (PC co-Chair), Brazilian Symposium on Computer Networks and Distributed Systems'2011, ACM Symposium on Applied Computing -Cloud Computing track'2011.  Andrea Polini: Quality Assurance for Service-based Applications (QASBA 2011) International Workshop at ECOWS 2011 (PC co-chair).  Darius Silingas: 17th International Conference on Information and Software Technologies, 1st International Workshop on Alignment of Business Process and Security Modelling.  Massimo Tivoli: CBSE 2011: 4th International ACM SIGSOFT Symposium on Component Based Software Engineering, CAMPUS 2011: 4th DisCoTec Workshop on Context-aware Adaptation Mechanisms for Pervasive and Ubiquitous Services, EternalS'11: 1st International Workshop on Eternal Systems, WAS4FI'11: 1 st International Workshop on Adaptive Services for the Future Internet.  Apostolos Zarras: ICSE 2011: ACM/IEEE 33rd International Conference on Software Engineering.

	3.4.2. Conferences
	 Dionysis Athanasopoulos, Apostolos Zarras, Panos Vassiliadis, Valérie Issarny.
	Mining Service Abstractions (NIER Track). 33rd International Conference on Software
	Engineering (ICSE), May 2011, Hawaii, United States.
	 Dionysis Athanasopoulos, Apostolos Zarras. Fine-grained Metrics of Cohesion Lack
	for Service Interfaces. 9th IEEE International Conference on Web Services (ICWS),
	Jul 2011, Washington, United States.
	 Antonia Bertolino, Guglielmo De Angelis, Andrea Polini. (role) CAST: A Framework for
	On-line Service Testing. Proc. of the 7th International Conference on Web Information
	Systems and Technologies (WEBIST 2011), May 2011, Noordwijkerhout,
	Netherlands.
	 Egils Ginters, Zane Barkane, Hugues Vincent. Systems Dynamics Use for
	Technologies Assessment. The 22th European Modeling & Simulation Symposium
	(EMSS 2010), Oct 2010, Fes,Morocco. DIPTEM University of Genoa, ISBN2-952474-
	78-8, pp. 357-363.
	 Marcelo Medeiros Eler, Antonia Bertolino, Paulo Cesar Masiero. More Testable
	Service Compositions by Test Metadata. International Symposium on Service-
	Oriented System Engineering, Dec 2011, Irvine, United States.
	 Pengcheng Zhang, Henry Muccini, Andrea Polini, Li Xuandong. Run-time Systems
	Failure Prediction via Proactive Monitoring. Automated Software Engineering (ASE
	2011), Nov 2011, Lawrence, Kansas, United States.
	 Thiago Teixeira, Sara Hachem, Valérie Issarny. Service Oriented Middleware for the
	Internet of Things: A Perspective (Invited). Service Wave 2011.

Book chapters  Antonia Bertolino, Guglielmo De Angelis, Sampo Kellomäki, Andrea Polini. Enhancing Trustworthiness within Service Federations by Continuous On-line Testing. IEEE COMPUTER. 2011.   Felipe Besson, Pedro Leal, Fabio Kon, Alfredo Goldman, Dejan Milojicic. Supporting Test-Driven Development of Web Service Choreographies. Poster in Open Cirrus Summit, Moscow, Russian, 2011. IEEE. FP7-257178 

Journal papers & Book chapters 4Conference papers 7Workshop, posters & tutorials

This presentation formally falls under Year

but it is listed here as the presentation was prepared in the 1st year.