Theu Dinh

Stéphane Goutte

Khuong Nguyen

Thomas Walther
email: t.walther@uu.nl.

Economic drivers of volatility and correlation in precious metal markets

Keywords: Precious metals, long-term volatility, long-term correlation, macroeconomic drivers, financial drivers, economic policy uncertainty, mixed data sampling

We investigate the time-varying dynamics of the precious metal markets. We employ a mixed data sampling technique to identify the impact of macroeconomic and financial drivers from G7 and BRICS countries on the daily volatility and pairwise correlation of Gold, Silver, Platinum, and Palladium. We find that the U.S. and Chinese economies in particular influence the precious metal markets, but in opposite directions. The stock markets and trade balance of both G7 and BRICS countries, as well as the consumer confidence of G7 countries, are the key drivers for the volatility of precious metals. The most influential drivers for correlation are stock markets, money supply, and the inflation rate. Surprisingly, the economic policy uncertainty does not affect the dynamics as much as expected. Lastly, the global financial crisis in 2008 affected the direction of most of the macroeconomic and financial drivers.

Introduction

In the global economy, the trade war between the U.S. and China, the two largest economies in the world, has been becoming more complicated, triggering fears of a global economic slowdown. Many experts have strongly warned that the prolonged U.S.-China trade war could lead to another global financial crisis (GFC). As a consequence of market shocks, investors prefer to keep safe assets and stay away from risky assets, known as the 'flight to quality' phenomenon in financial markets [START_REF] Bernanke | The financial accelerator and the flight to quality[END_REF]. Precious metals, which are considered safe investment assets, outperform traditional assets, such as stocks or bonds, especially in times of high uncertainty [START_REF] Hillier | Do precious metals shine? an investment perspective[END_REF][START_REF] Baur | Is gold a safe haven? international evidence[END_REF][START_REF] Lucey | What precious metals act as safe havens, and when? some us evidence[END_REF]. In addition, precious metals became a key in the trade war between the U.S. and China due to the fact that between 2014 and 2017 around 80% of the precious metals used by the U.S. were imported from China. 1 The resilience of precious metals to financial crises has also been highlighted in recent studies [START_REF] Baur | Is gold a safe haven? international evidence[END_REF][START_REF] Ciner | Hedges and safe havens: An examination of stocks, bonds, gold, oil and exchange rates[END_REF][START_REF] Agyei-Ampomah | Does gold offer a better protection against losses in sovereign debt bonds than other metals[END_REF][START_REF] Lucey | What precious metals act as safe havens, and when? some us evidence[END_REF][START_REF] Batten | Which precious metals spill over on which, when and why? some evidence[END_REF]. As a result, the dynamics of precious metal markets in the current global economic situation and their dynamic trends around times of market turmoil have attracted the special attention of many scholars [START_REF] Figuerola-Ferretti | The shine of precious metals around the global financial crisis[END_REF][START_REF] Klein | Dynamic correlation of precious metals and flight-to-quality in developed markets[END_REF].

Because the precious metal markets are highly volatile and difficult to predict, the proper modelling of the volatility and correlation dynamics is crucial in these markets. Investors and portfolio managers can make better investment decisions if they are provided with a more accurate depiction of the dynamics, including the volatility as well as the correlation, of precious metals markets. Many studies find that the volatility and correlation of commodities markets in general and precious metals markets in particular are not only related to supply and demand dynamics, but are also associated with changes in economic activities [START_REF] Anson | The pricing and economics of commodity futures[END_REF][START_REF] Belousova | On the diversification benefits of commodities from the perspective of euro investors[END_REF]. Macroeconomic and financial variables are well-known as the key potential drivers of dynamic movements in precious metal markets (Tully and Lucey, 2007a;[START_REF] Batten | Which precious metals spill over on which, when and why? some evidence[END_REF][START_REF] Mo | The macroeconomic determinants of commodity futures volatility: Evidence from chinese and indian markets[END_REF]. Another important economic variable linked to high volatility markets, such as precious metal markets, is Economic Policy Uncertainty (EPU), which has also attracted considerable attention [START_REF] Li | Reassessing the role of precious metals as safe havens-what colour is your haven and why[END_REF][START_REF] Huynh | The effect of uncertainty on the precious metals market: New insights from transfer entropy and neural network var[END_REF].

To date, various methods have been applied to measure the impact of economic sources on financial assets' time-varying volatility and correlation, such as modified Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models [START_REF] Hammoudeh | Risk management of precious metals[END_REF][START_REF] Pan | Oil price volatility and macroeconomic fundamentals: A regime switching garch-midas model[END_REF], popular classes of multiple-equation models including Vector Autoregression-(VAR, [START_REF] Andersen | Modeling and forecasting realized volatility[END_REF][START_REF] Apergis | Precious metal markets, stock markets and the macroeconomic environment: a favar model approach[END_REF], Vector Error Correction Model-based approaches [START_REF] Kucher | The long-run relationship between precious metal prices and the business cycle[END_REF], and different Dynamic Conditional Correlation (DCC) models [START_REF] Fernandez-Diaz | Interdependence among agricultural commodity markets, macroeconomic factors, crude oil and commodity index[END_REF], among others. However, these studies predominantly investigate only the separated effect of a single driver or focus solely on a small number of given macro-finance variables. 2 One of the reasons for this may arise from the problem of the low frequency of economic data while the analyses of time-varying movements of precious metals are mainly based on high-frequency data.

In this study, by applying the generalized autoregressive conditional heteroskedasticity mixed data sampling model (GARCH-MIDAS, [START_REF] Engle | Stock market volatility and macroeconomic fundamentals[END_REF] and the dynamic conditional correlation mixed data sampling model (DCC-MIDAS, [START_REF] Colacito | A component model for dynamic correlations[END_REF], we can effectively solve the frequency mismatch problem. The main advantage of GARCH-MIDAS and DCC-MIDAS models is that they disentangle the long-term component from the short-term component of the volatility and correlation, respectively. In particular, advancements in GARCH-and DCC-MIDAS models allow for considering the impact of exogenous variables on the respective long-term component [START_REF] Conrad | On the macroeconomic determinants of long-term volatilities and correlations in us stock and crude oil markets[END_REF][START_REF] Asgharian | Macro-finance determinants of the long-run stock-bond correlation: The dcc-midas specification[END_REF].

Our study's primary objective is to analyze the individual impact of the most important 2 It is worth noting that some authors propose new techniques for measuring the impact of a large number of predictors jointly, e.g., dynamic factor analysis [START_REF] Ludvigson | Macro factors in bond risk premia[END_REF], quantile regression [START_REF] Christiansen | A comprehensive look at financial volatility prediction by economic variables[END_REF], data-rich forecast methodology [START_REF] Aslanidis | Quantiles of the realized stock-bond correlation and links to the macroeconomy[END_REF], Bayesian Model Averaging [START_REF] Díaz | Economic drivers of commodity volatility: The case of copper[END_REF], or component-wise gradient boosting techniques [START_REF] Mittnik | Stock market volatility: Identifying major drivers and the nature of their impact[END_REF].

economic and financial drivers on the time-varying volatility and correlation of precious metals.

Our results indicate the inverse impact of economic drivers from highly developed (Group of Seven, G7) and emerging (Brazil, Russia, India, China, South Africa, BRICS) economies, most notably between the U.S. and China. Among our considered economic and financial factors, stock market returns, interest rates, and consumer confidence are identified as the most helpful predictors for modelling volatility and correlation. In addition, the trade balance growth is the most important variable in driving dynamic volatility whereas money supply and inflation rate are important determinants of long-term correlation between precious metals.

Finally, we find the GFC of 2008 had a significant impact on the influence of economic and financial drivers on the dynamics of the precious metals markets, as many drivers changed the direction of their impact after the crisis.

Our study makes several contributions to the existing literature. Firstly, to the best of our knowledge, our paper is the first work that analyses macroeconomic and financial drivers of the dynamic correlation within the precious metal markets, although many previous studies have investigated the determinants of dynamic correlations between precious metals and other assets, such as stocks [START_REF] Mensi | Correlations and volatility spillovers across commodity and stock markets: Linking energies, food, and gold[END_REF][START_REF] Jain | Dynamic linkages among oil price, gold price, exchange rate, and stock market in india[END_REF][START_REF] Klein | Dynamic correlation of precious metals and equity markets: A mixed data sampling approach[END_REF], oil ( Šimáková, 2011), exchange rates [START_REF] Pal | Multifractal detrended cross-correlation analysis on gold, crude oil and foreign exchange rate time series[END_REF][START_REF] Apergis | Can gold prices forecast the australian dollar movements[END_REF], or cryptocurrencies [START_REF] Klein | Bitcoin is not the new gold-a comparison of volatility, correlation, and portfolio performance[END_REF]. There are a few papers that analyze the time-varying correlation between the precious metals themselves [START_REF] Sensoy | Dynamic relationship between precious metals[END_REF][START_REF] Klein | Dynamic correlation of precious metals and flight-to-quality in developed markets[END_REF], but they do not consider their drivers.

Secondly, in an attempt to answer the question of whether the impact of the economic drivers on the dynamic volatility and correlation of precious metals changes between tranquil and turbulent times, we split the full sample into three sub-periods, namely the pre-crisis period (March 1998-August 2007), the crisis period (September 2007-December 2010) and the postcrisis period (January 2011-August 2018). This helps to provide valuable recommendations to policymakers, investors and portfolio managers for addressing any GFC in the future.

Thirdly, we contribute by investigating the different impact of a set of 19 economic and financial variables from 12 countries (G7 and BRICS) on the volatility and correlation of precious metals. Most of the aforementioned studies only focus on U.S.-based determinants [START_REF] Batten | Which precious metals spill over on which, when and why? some evidence[END_REF].

The rest of the article is organized as follows. Section 2 gives an overview of the existing literature. Section 3 describes the methodology. Our data and the results will be explained in Section 4. Section 5 concludes and discusses the implications of our research.

Literature review

The issue of what determines precious metal prices has been addressed in a range of studies, especially after the GFC of 2008 [START_REF] Radetzki | Precious metals: The fundamental determinants of their price behaviour[END_REF][START_REF] Kucher | The long-run relationship between precious metal prices and the business cycle[END_REF]. However, the factors that determine the volatility of the market for precious metals are less well known.

In addition, a study on the determinants of pair-wise correlation within in precious metal markets is lacking.

Among the existing literature, the first strand focuses on the role of macroeconomic fundamentals in the dynamic movements of the volatility and correlation of precious metal markets. [START_REF] Batten | Which precious metals spill over on which, when and why? some evidence[END_REF] investigate the monthly price volatility of precious metals based on the macroeconomic determinants including the business cycle, monetary environment and financial market sentiment. They conclude that whereas monetary variables can explain the volatility of Gold, they cannot explain the volatility of Silver. Moreover, the same macroeconomic factors do not jointly influence the price series of all four precious metals.

The impact of macroeconomic fundamentals seems much stronger on Palladium than on other precious metals.

In addition, [START_REF] Mo | The macroeconomic determinants of commodity futures volatility: Evidence from chinese and indian markets[END_REF] find that the economic activities and the monetary environment (GDP, Inflation Rate and M2) show a significant and positive relation with precious metals in both China and India. Moreover, the authors show that the volatility of macroeconomic variables causes an increase in the volatility of precious metal futures.

Contrary to the two above-mentioned studies, Fang et al. (2018b) Similarly, [START_REF] Nguyen | Modeling and forecasting commodity market volatility with long-term economic and financial variables[END_REF] also apply the GARCH-MIDAS approach to investigate the time-varying volatility patterns of some major commodities, including Gold, Silver, and Platinum. The authors find that the long-term volatility is significantly affected by the level of Global Real Economic Activity, as well as changes in Consumer Sentiment, Industrial Production, and Economic Policy Uncertainty. Moreover, they find that the Industrial Production has a negative impact on the long-term volatility of Gold and Silver.

The rest of the related studies pay more attention to studying the impact of a specific aspect of macroeconomics on precious metal markets, such as GDP [START_REF] Radetzki | Precious metals: The fundamental determinants of their price behaviour[END_REF], Money Supply [START_REF] Bailey | Money supply announcements and the ex ante volatility of asset prices[END_REF], Business Cycle [START_REF] Kucher | The long-run relationship between precious metal prices and the business cycle[END_REF], Macroeconomic News [START_REF] Smales | Commodity market volatility in the presence of us and chinese macroeconomic news[END_REF], Industrial Production (Tully and Lucey, 2007b), Inflation [START_REF] Gorton | Facts and fantasies about commodity futures[END_REF], Private Inventories [START_REF] Radetzki | Precious metals: The fundamental determinants of their price behaviour[END_REF], Capacity Utilization and Unemployment Rates [START_REF] Apergis | Precious metal markets, stock markets and the macroeconomic environment: a favar model approach[END_REF].

The second strand of literature focuses on the impact of financial variables on the dynamic movements of the volatility and correlation of precious metal markets. Among the financial factors, the short-term interest rate, which is an important tool of monetary policy, affects precious metal returns and volatility through multiple channels [START_REF] Hammoudeh | Metal volatility in presence of oil and interest rate shocks[END_REF]. Therefore, a strong relationship between precious metals and interest rates has been reported in the literature [START_REF] Fortune | The inflation rate of the price of gold, expected prices and interest rates[END_REF][START_REF] Cai | What moves the gold market?[END_REF][START_REF] Hammoudeh | Metal volatility in presence of oil and interest rate shocks[END_REF]. In general, most studies conclude that high interest rates reduce the demand for storing precious metals [START_REF] Hammoudeh | Us monetary policy and sectoral commodity prices[END_REF] and have calming effects on the volatility of precious metals markets [START_REF] Hammoudeh | Metal volatility in presence of oil and interest rate shocks[END_REF][START_REF] Cai | What moves the gold market?[END_REF].

In terms of the relationship between exchange rates and precious metals, [START_REF] Ghosh | Gold as an inflation hedge?[END_REF] and [START_REF] Akram | Commodity prices, interest rates and the dollar[END_REF] show that commodity prices can be attributed to the influence of changes in exchange rates, especially with respect to the U.S. dollar. [START_REF] Sari | Dynamics of oil price, precious metal prices, and exchange rate[END_REF] study the relationship between and information transmission among the spot prices of precious metals and the U.S. dollar/euro exchange rate. The authors find evidence of a weak long-term equilibrium relationship but strong co-movement in the short run.

Another line of research focuses more specifically on the impact of stock markets on the dynamics of precious metals, but the related literature provides inconclusive findings. Tully and Lucey (2007b) and [START_REF] Creti | On the links between stock and commodity markets' volatility[END_REF] find that stock returns negatively affect Gold returns and that this impact becomes slower with a decline in equity prices over time. In contrast, [START_REF] Boako | Analysing dynamic dependence between gold and stock returns: Evidence using stochastic and full-range tail dependence copula models[END_REF] find a positive association between stock prices and Gold.

With the aim of investigating the effects of multiple economic and financial factors on metals price movements, [START_REF] Liberda | Mixed-frequency drivers of precious metal prices[END_REF] Among the financial variables, the equity index has the most significantly negative impact on the metals returns. In addition, the financial variables are better at explaining the movement of the prices of Platinum and Palladium than that of Gold and Silver.

A third strand of literature is concerned with the relationship between the time-varying volatility and correlation of precious metals market with Economic Policy Uncertainty. Due to the fact that precious metals can act as a hedge or safe-haven for stock investment [START_REF] Baur | Is gold a hedge or a safe haven? an analysis of stocks, bonds and gold[END_REF][START_REF] Baur | Is gold a safe haven? international evidence[END_REF], precious metals become a key investment possibility when the degree of policy uncertainty in world financial markets grows [START_REF] Bia Lkowski | The gold price in times of crisis[END_REF][START_REF] Balcilar | Does uncertainty move the gold price? new evidence from a nonparametric causality-in-quantiles test[END_REF]. In particular, Fang et al. (2018a) and [START_REF] Nguyen | Modeling and forecasting commodity market volatility with long-term economic and financial variables[END_REF] find that GEPU positively affects the volatility of precious metals. More specifically, [START_REF] Nguyen | Modeling and forecasting commodity market volatility with long-term economic and financial variables[END_REF] show that the changes in GEPU positively affect the long-term volatility of Gold and Platinum, but not of Silver. Similarly, [START_REF] Prokopczuk | The economic drivers of commodity market volatility[END_REF] find a strong co-movement between commodity market volatility and economic uncertainty, especially during recession periods. [START_REF] Zhou | Is the relationship between gold and the us dollar always negative? the role of macroeconomic uncertainty[END_REF] also use DCC-MIDAS, based on the mixed data sampling technique, combining the threshold VAR model in order to provide international evidence on the impact of macroeconomic policy uncertainty on the correlation between Gold and the U.S. dollar.

The authors conclude that the Gold-dollar relationship has not remained constant over time and greatly depends on unpredictable political or economic uncertainty. Moreover, due to the different sources of economic uncertainty, the impacts are varied. The results also show that both Gold and the dollar, in return, can influence the economic uncertainty of the U.S.

Europe, Russia, and China.

As a very limited literature that provides international evidence on the impact of extreme events such as the 9/11 terrorist attack, the GFC, the European Debt Crisis, and the Brexit vote on the inter-correlation among precious metals, the contributions of [START_REF] Klein | Dynamic correlation of precious metals and flight-to-quality in developed markets[END_REF] and [START_REF] Klein | Dynamic correlation of precious metals and equity markets: A mixed data sampling approach[END_REF] are noteworthy. The authors point out the significant differences in correlation structures between the pair Gold/Silver and the pair Palladium/Platinum in connection to market shocks. This study also concludes that Gold and Silver act as safe-havens.

However, this result does not hold after 2013. Specially, Platinum seems to serve as temporal surrogate safe-haven during periods of market turmoil.

Methodology

In the following, we present our two-step methodology. The first step relates to the heteroskedasticity process of the return series with the GARCH-MIDAS model [START_REF] Engle | Stock market volatility and macroeconomic fundamentals[END_REF] and its extended models for assessing the impact of the economic drivers of the conditional volatility of precious metals. The next section gives an overview of the DCC-MIDAS model [START_REF] Colacito | A component model for dynamic correlations[END_REF] and its modifications for analyzing the effect of economic determinants on the dynamic correlations between precious metals themselves.

GARCH-MIDAS model with economic variables

In order to analyze the volatility drivers, we employ the GARCH-MIDAS model proposed by [START_REF] Engle | Stock market volatility and macroeconomic fundamentals[END_REF], which disentangles the volatility into a short-term (daily) and a long-term (monthly) component.

We consider r i,t as the (logarithmic) return, where i and t denotes short-and long-run indexes, respectively, e.g., i for day and t for month, quarter or half-year. The mean equation of this return is as follows:

r i,t = µ + √ τ t g i,t ε i,t ∀i = 1, . . . , N t (1)
In which N t is the number of trading days in the period t and ε i,

t |Φ i-1,t ∼ N (0, 1) with Φ i-1,t
is the information set up to day (i -1) of period t. The factors τ t and g i,t are the longand short-run variance components, respectively. According to [START_REF] Engle | The spline-garch model for low-frequency volatility and its global macroeconomic causes[END_REF], g i,t

follows a standard GARCH(1,1) model with unit variance:

g i,t = (1 -α -β) + α (r i-1,t -µ) 2 τ t + βg i-1,t (2)
with non-negativity and stationary conditions α, β ≥ 0 and α + β < 1.

Compared to the original GARCH model, which has a constant baseline variance, the GARCH-MIDAS model allows the baseline variance to change slowly over time. We follow [START_REF] Engle | Stock market volatility and macroeconomic fundamentals[END_REF] and model the long-term component τ t as a slowly varying function of an exogenous variable X t :

log(τ t ) = m + θ K k=1 ϕ k (ω 1 , ω 2 )X t-k , (3)
which we denote as GARCH-MIDAS-X . Here, K is the number of lags and m is an intercept of long-term trend. The Beta-weighting scheme ϕ k is determined by a beta lag polynomial [START_REF] Ghysels | Midas regressions: Further results and new directions[END_REF] as follows

ϕ k (ω 1 , ω 2 ) = (k/K) ω 1 -1 (1 -k/K) ω 2 -1 K j=1 (j/K) ω 1 -1 (1 -j/K) ω 2 -1 . (4)
Depending on the parameters ω 1 , ω 2 > 1, the Beta scheme can depict increasing, decreasing, or hump-shaped weights, which sum up to unity.

190

Eventually, we estimate the parameters by Quasi-Maximum-Likelihood-Estimation (QMLE, [START_REF] Engle | Stock market volatility and macroeconomic fundamentals[END_REF].

DCC-MIDAS model with economic variables

The DCC-MIDAS model proposed by Colacito et al. ( 2011) is a natural extension and combination of the DCC model [START_REF] Engle | Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models[END_REF] and the GARCH-MIDAS model that allows us 195 to decompose the short-and long-run correlation components by the mixed data sampling approach.

We assume that the n-dimensional vector of returns r t follows the process

r t i.i.d. ∼ N (µ, C t ), C t = D t Ω t D t , (5)
where µ is the vector of unconditional means, C t is the conditional covariance matrix, D t denotes a diagonal matrix with standard deviations on the diagonal, and Ω t represents the conditional correlation matrix of returns on time (t -1) information:

Ω t = E t-1 [η t η , t ], η t = D -1 t (r t -µ), (6)
where η t is the standardized residuals. Hence,

r t = µ + C 1/2 t η t with η t i.i.d. ∼ N (0, I n ).
It is clear that Equation ( 5) suggests a two-step model specification strategy. It means that we first specify D t by estimating the GARCH-MIDAS model as in Equation ( 2), from which we obtain the standardized residuals η i,t . After that, we estimate the DCC-MIDAS parameters. To be more specific, we initially calculate the conditional statistics, which are denoted as q ij,t (e.g. the short-run correlation between asset i and asset j at time t). The q ij,t are the elements of the (n × n)-dimensional quasi-correlation matrix Q t :

q ij,t = ρ ij,t (1 -a -b) + aη i,t-1 η j,t-1 + bq ij,t-1 , (7)
where ρ ij,t is the slowly moving long-term correlation between asset i and asset j. Here, we follow [START_REF] Conrad | On the macroeconomic determinants of long-term volatilities and correlations in us stock and crude oil markets[END_REF] and model the long-term correlation using a Fisher-z transformation:

ρ ij,t = exp (2z ij,t ) -1 exp (2z ij,t ) + 1 , (8)
where z ij,t is driven by an exogenous variable X t :3

z ij,t = c + γ K k=1 ϕ k (ω 1 , ω 2 )X t-k . (9)
The weighting scheme ϕ k (ω 1 , ω 2 ) is defined as the Equation (4) of Section 3.1. The parameter γ measures the effect of the exogenous variable on the long-run correlations between the 200 precious metals.

Finally, the conditional correlation matrix is given as

Ω t = Diag(Q t ) -1/2 Q t Diag(Q t ) -1/2 . ( 10
)
We also follow [START_REF] Colacito | A component model for dynamic correlations[END_REF] and [START_REF] Conrad | On the macroeconomic determinants of long-term volatilities and correlations in us stock and crude oil markets[END_REF] in terms of estimation and use the QMLE to estimate the coefficients of the dynamic correlation model.

Empirical Application

Data and variables

Precious metals data

Our data consist of daily spot and futures (one month) price series of Gold, Silver, Platinum, and Palladium, which are obtained from Thomson Reuters Datastream.4 Table 1 summarizes the descriptive statistics for the daily spot and futures returns (Panel A and panel B, respectively) divided into a full sample period and the financial crisis-related sub-periods.

The results show that the mean and standard deviation values of the spot returns of each precious metals are similar to those of their futures returns. We can see that the mean is small and positive for most return series in both full sample and sub-samples, with the exception of Platinum and Palladium during the GFC. Interestingly, Gold returns exhibit the highest mean but the lowest volatility during the crisis, reflecting the safe-haven role [START_REF] Baur | Is gold a safe haven? international evidence[END_REF]. Table 1 also reports the results of skewness and kurtosis. The skewness is negative while the kurtosis values are above three for the majority of return series, indicating a non-normally, leptokurtic distribution, which is also confirmed by a Jarque-Bera statistical test.

In addition to the descriptive statistics, the p-values of Ljung-Box (LB) statistics of order 15 for the returns series show the existence of auto-correlation in most of them. For the squared returns series, however, p-values of LB are highly significant, which reveals a long-range serial dependence. This result is confirmed by the results of the ARCH test, hence motivating our decision to use the GARCH-model to filter the daily returns.

Exogenous variables

Following our literature review in Section 2, we select a set of exogenous variables with respect to data availability. We divide the exogenous variables into three categories:

Macroeconomic variables, Financial variables, and Economics Policy Uncertainty (see Table 7 in the Appendix).5

The monthly data for the macroeconomic and financial variables are retrieved for 12 countries (G7 and BRICS) from March 1998 to August 2018 from Thomson Reuters Datastream, the FRED database at the Federal Reserve Bank of St. Louis, OECD database, and World Bank database. Additionally, monthly data for EPU indices is collected from https://www.policyuncertainty.com. In order to ensure consistency between countries and to remove the potential adverse impact of different currencies, the macroeconomic variables used in the study are index variables calculated according to the same formula, or transformed in terms of growth variables.

Results and discussions

We begin our analysis by testing the impact of various macroeconomic and financial drivers on the conditional volatility of each precious metal and six pairs of correlations of four major precious metals6 in our sample by employing the GARCH-MIDAS-X model and DCC-MIDAS-X.

In the first step, we estimate standard and asymmetric GARCH and GARCH-MIDAS variants in order to check whether a decomposition in short-and long-term volatility components is actually useful. For all metals, we find that the GARCH-MIDAS model using monthly realized volatility as a driver of the long-term volatility outperforms the other variants in terms of the Bayesian Information Criterion (BIC). For Platinum only, the GJR-MIDAS-RV has a slightly better BIC. We report the results in Table 6 in the Appendix. Additionally, we determine that K = 36, i.e. three years of monthly observations, is the optimal lag-length for the MIDAS component with regards to the BIC.

In the following sub-sections, we analyze the impact of the various macroeconomic and financial variables on the volatility and correlation of precious metals. To this end, we focus on the statistical significance of coefficients θ in Equation ( 3) and γ in Equation ( 9) which determine the size and direction of the impact of an exogenous variable on the long-term volatility and inter-correlation of precious metals, respectively. Following this, the signs of θ and γ reveal whether an upside or downside trend in the long-term volatility and correlation can be caused by an increase in the respective economic variables.7

4.2.1. Macro-finance drivers of precious metals volatility and correlation -opposite evidence between the U.S. and China

Due to the escalating tension between the U.S. and China after 2018 and its subsequent persistent headwind for all financial markets, we start our analysis with a focus on these two countries.

In general, the results in Tables 2 and3 show that Chinese economic drivers have less impact on volatility and correlation among precious metals pairs than their U.S. counterparts.

In addition, the long-term volatility of Gold and long-term correlations of the Gold-Silver and Platinum-Palladium pairs appear to be the most affected by economic variables. This is consistent with the findings of [START_REF] Klein | Dynamic correlation of precious metals and flight-to-quality in developed markets[END_REF], who concludes that there are significant differences in correlation structures for two groups of precious metals: (1) Gold and Silver as investment assets and (2) Palladium and Platinum as mainly industrial metals.

Interestingly, the results reveal a totally contrary scenario between the U.S. and China in terms of the impact of almost all macro and financial drivers on the precious metals return volatility and their pairwise correlations. A few exceptions have a similar directional impact for volatility: EPU growth (positive impact), Exchange rate (negative impact), and Gold & Foreign Reserves growth (positive impact); and on correlation: import growth.

In particular, the effect of Consumer Confidence on both volatility and correlation can be observed more clearly. This U.S. indicator has a negative impact on long-term volatility while a positive effect can be seen on the inter-correlation of most precious metals. Meanwhile, the figure for China shows no effect on any precious metals volatility or correlation. In contrast, China's Composite Leading Indicator (CLI) seems to have been an important determinant of precious metals volatility except for Gold, but the U.S. CLI does not indicate any statistically significant effect. Additionally, the long-run volatility of precious metals ia significantly affected by the foreign trade of both countries. However, Chinese export growth has more influence on volatility than that of the U.S., whereas the import growth of China has less impact on volatility than that of the U.S. This result can be explained by China's dominance in exporting rare metals. This country produced around 90% of the world's rare earth metals in 2019.8 Meanwhile, the U.S. remains one of the world's top importers of precious metals, although the U.S. has recently made it a priority to diversify their sources of rare metals in order to reduce its dependence on China.9

Notably, all four precious metals (spot and futures) react significantly and negatively to the U.S. stock market returns, while only the long-term volatility of spot precious metal returns has a significantly positive response to the stock returns in China. This result indicates that, in the long-term, an upward trend of stock returns in the U.S. would help to stabilize precious metal markets. However, this is not true for the Chinese stock market because almost all θ coefficients of the Chinese stock returns are insignificant. With respect to correlation, Table 3 reveals that the U.S. stock market returns are positively associated with almost all correlation pairs between precious metals spot returns. Meanwhile, their Chinese counterparts do not appear to affect any conditional correlation. These findings are similar to the conclusion of [START_REF] Uddin | Characteristics of spillovers between the us stock market and precious metals and oil[END_REF] in regard to the key role of the largest stock market (i.e., the U.S. market, which has over 5 000 listed firms) in driving the precious metals markets. In contrast, the Chinese stock market shows a poor long-run performance and it has not played a role as prominent as the banking sector in providing financing for firms and promoting economic growth in China and globally. In addition, many companies, including mining companies, are publicly listed, but none of them are listed in the domestic market. Finally, several other factors also show an opposite impact between the U.S. and China on the dynamic correlation levels among precious metal returns (e.g., M1, M2, and inflation).

The global financial crisis of 2008 and macro-finance drivers of precious metals volatility and correlation

The safe-haven ability of precious metals against market shocks such as the GFC of 2008, is proven in many prior works [START_REF] Baur | Is gold a hedge or a safe haven? an analysis of stocks, bonds and gold[END_REF][START_REF] Batten | Which precious metals spill over on which, when and why? some evidence[END_REF]. In addition, Generally, the period after the 2008 GFC has witnessed a greater number of economic determinants in China affecting the long-term volatility of all four precious metals as well as their correlation compared to other periods (e.g., there are more significant coefficients Note: The table reports estimated results for parameters θ of macroeconomic and financial variables of the U.S. and China over three sub-periods of GFC from GARCH(1,1)-MIDAS-X model. Three periods include Pre-crisis (Mar, 1998to Aug, 2007); Crisis (Sep, 2007to Dec, 2010), and Post-crisis (Jan, 2011to Aug, 2018). The asterisks * * * , * * , and * denote significance at 1%, 5%, and 10%, respectively. Otherwise the field is left blank. Note: The table reports estimated results for parameters γ of macroeconomic and financial variables of the U.S. and China over three sub-periods of GFC from DCC-MIDAS-X model. Three periods include Pre-crisis (Mar, 1998to Aug, 2007); Crisis (Sep, 2007to Dec, 2010), and Post-crisis (Jan, 2011to Aug, 2018). The value is given if the parameter γ is statistically significant, i.e. the critical values at significance level is 10%. Otherwise the field is left blank.

of θ and γ). In addition, the opposite trend can be seen between the signs of significant coefficients θ and γ of several drivers in China during the crisis and after the crisis. More specifically, some economic drivers of China make pair-correlations turn from positive to negative (e.g., M1 on the GoldF-PlatinumF and GoldF-PalladiumF) or the reverse (e.g., M2

on PlatinumF-PalladiumF). These findings align with the conclusion of Agyei-Ampomah et al.

(2014), who find that the superior role of precious metals is to protect investors' wealth against shocks in the U.S. financial market. One possible explanation is that the precious metals demand increases in emerging countries like China, which have not been strongly affected by the financial crisis or before. Additionally, this evidence denotes the growing influence of

Extensive Estimation Results for other G7 and BRICS countries

In this section, we extend our analysis to other G710 and BRICS11 countries, which are top-ranked in precious metals exchanges. Tables 8 to 12 in the Appendix present the estimates of statistically significant θ and γ signs for each of the macroeconomic and financial variables of the 10 countries in the full sample from 1998 to 2018.

We first focus on the macroeconomic factors in other G7 and BRICS countries. Tables 8 and9 indicate that neither the export nor the import growth of G7 and BRICS countries affect the correlations between metals to a large extent, despite acting as important drivers of the volatility of precious metals. Here, we find that the influence of the export growth of almost all G7 and BRICS nations on long-term volatility is negative or positive, respectively.

More precious metals are affected by the export of BRICS than that of G7 countries. The export growth of Russia, is considered the strongest determinant of the long-term volatility of all precious metals in both spot and future returns, followed by the export growth of South Africa, the United Kingdom, and France. With respect to the impact of import growth on precious metals volatility, we find the strongest positive effect from India and South Africa.

For G7 countries, we observe a varying impact of countries' import growth on volatility with mostly negative effects.

The Gold & Foreign Reserves Growth of G7 and BRICS appear to be important drivers for long-term volatility, but not applicable for long-term correlations. In particular, Table 8 illustrate that the Gold & Foreign Reserves Growth of BRICS have considerably more impact on the volatility of precious metal markets than G7's Gold & Foreign Reserves Growth. This finding is in accordance with the fact that approximately two-thirds of global Gold and foreign currency reserves are held by emerging and developing economies. 12 Additionally, the positive figures for most of the statistically significant coefficients of this variable reveal that the rise in Gold and foreign currency reserves of countries, especially BRICS, may contribute to the increase in the volatility of the global precious metals market.

Tables 8 and9 also show that the impacts of the Composite Leading Indicator (CLI),

Consumer Confidence (CC), and Industrial Production (IP) of both G7 and BRICS on volatility are negative, but CLI and CC increase correlation between precious metals. CLI represents the future expectation of the business cycle, therefore, the results mean that an increase in the future expectations of real economic activity leads to a decrease in volatility and an increase in correlation. Moreover, the CLI of the United Kingdom and India appears to be more important than the CLI of other countries. The results also suggest that the impacts of CC and the IP of G7 countries on both volatility and correlation are much stronger than that in BRICS countries. Apart from the positive impact of Russia and Brazil's CC on the long-term volatility of Gold, the negative signs of all θ and γ coefficients of CC can be observed. This implies that the increase in consumer confidence along with the decrease in the volatility and correlation between precious metals returns may raise diversification benefits among them.

Regarding the variables of the monetary environment (i.e. M1, M2, INF), the results of Table 10 reveal that these variables have a stronger influence on the long-term correlation between precious metals than on their volatility. In addition, the empirical results illustrate that the impact of the monetary supply growth is much more influential on Gold volatility than on any other precious metals, which is reasonable since Gold is still regarded as surrogate money. Moreover, according to the money supply, the positive sign of θ of M2 and the negative one of its γ in almost all cases indicate that precious metal prices are more volatile and more closely linked during the recession period (i.e., because an increase in M2 reflects the recession of the economy). Although Gold and Silver are known as a hedge for inflation [START_REF] Ghosh | Gold as an inflation hedge?[END_REF], our results show that higher inflation rates in both G7 and BRICS countries explain the rise in the volatility of all four precious metals (except for Japan). Meanwhile, we find that G7 (BRICS) inflation rates have a negative (positive) association with correlation.

In terms of financial variables, the results from Table 11 show the influence of equity market returns on both precious metals volatility and correlation is larger than any other financial variables. Notably, the volatility of all the precious metals are negatively linked to the stock market returns of both G7 and BRICS countries, while the correlations among these metals respond positively to equity market returns. 13 In addition, a mainly positive impact from the government bond returns of the G7 and BRICS countries on volatility as well as on correlation among precious metal markets can be found. With respect to interest rates, we can see clearly that while there are varying effects across countries on volatility, the impact on long-term correlations is consistently negative. This could be an illustration of the decline in correlations between precious metals during periods of high interest rates. In regard to the impact of the exchange rate, our major finding is a significant but negative effect of the exchange rate of each country on precious metals volatility, while there is a minor impact on correlation.

Finally, Table 12 shows the influence of the EPU growth of each country in our sample on the long-term volatility and correlation of precious metals markets. Our analysis reveals that the EPU growth of G7 and BRICS cannot explain the dynamic correlations. In contrast, EPU growth is associated with the volatility of precious metals. Except for the negative impact of the EPU growth of Japan on the volatility of Gold, the EPUs of all other countries increase the volatility of precious metals. This result is in line with the findings of Fang et al.

(2018b) and [START_REF] Nguyen | Modeling and forecasting commodity market volatility with long-term economic and financial variables[END_REF] who point out that EPU has a positive effect on the long-run volatility of precious metals. Notably, the EPU growth of G7 countries seem to have a stronger effect on volatility than the EPU growth of BRICS. This finding strongly confirms the leading role of the G7 group in shaping the stability of the global financial market in general and the precious metals market in particular.

In regard to the long-term correlations' reaction to the EPUs of two groups, we can observe that while the positive response of Gold-Platinum, Gold-Palladium, and Silver-Palladium to the change of the EPU of Russia can be seen, other pairs are all negatively related to EPUs with significant coefficients. This means an increase in EPU growth would lead to a decrease in the long-run correlations between precious metals markets. Hence, we find a decoupling of precious metal markets in times of higher economic uncertainty.

Conclusion

Our study contributes to the current literature by investigating the impact of macroeconomic and financial drivers on the long-term volatility and correlation of precious metals markets over the last 20 years. Using GARCH-MIDAS-X and DCC-MIDAS-X, we find that the stock market returns of G7 and BRICS countries play the most important role in determining both the long-term volatility and correlations among precious metals. In particular, stock market returns leave a negative impact on the long-term volatility of four precious metals while having a positive effect on the long-run correlation of these metals. Besides stock market returns, other variables including M1, M2, inflation rate, and the short-term interest rate of considered countries are also helpful predictors of both volatility and correlations, albeit with mixed effects.

Additionally, economic drivers cause a stronger effect on the volatility than on the correlation. To be more specific, the EPU growth of G7 countries has a significantly positive influence on the volatility of precious metals; however, no effect caused by this driver can be seen on the long-term correlations between precious metals to a similar extent. Therefore, in periods of policy instability, it is recommended that investors invest into these metals to reduce risks. Similarly, the volatility of precious metals is closely linked to the growth of import, export, Gold & foreign reserves, and exchange rates, but there is no such association in the case of correlations between precious metals.

We find considerable differences in the impact of drivers between G7 and BRICS, especially in terms of consumer confidence. In detail, consumer confidence in G7 countries makes the volatility of precious metals follow a negative direction, but drives the pairwise correlation in a positive way. On the contrary, consumer confidence in BRICS countries has almost no effect on either volatility or correlation. As a result, the more consumer confidence is improved in G7 countries, the better the portfolio hedging benefits that precious metals would offer.

Similarly, this trend can be investigated in the influence of industrial production on both volatility and correlation, bond return on volatility, or short-term interest rate on correlation.

Notably, our study also shows that the 2008 GFC plays a key role in the change of the impact of determinants on precious metals markets as the signs of many determinants are reversed over the course of this crisis. Palladium is the most strongly influenced by the GFC while Silver is the least responsive to this crisis.

Finally, we find that the return volatility of Gold markets and the correlation between Gold and Silver have the closest relationship to the changes in the economic drivers of both the G7 and BRICS countries.

With the above analysis, our findings may help both investors and portfolio managers to make optimal and timely choices based on forecasting the changes in financial markets as well as macroeconomic activity. In addition, predicting the future development of low-frequency real economic variables also helps policymakers to formulate appropriate and early policy responses to prevent possible recessions. Note: Estimation results θ and γ of Stock Market Returns, Bond Market Returns, Interest Rate and Exchange Rate of G7 and BRICS nations from GARCH-MIDAS-X and DCC-MIDAS-X, respectively. The asterisks * * * , * * , and * denote significance at 1%, 5%, and 10%, respectively. Otherwise, the field is left blank. The results of the U.S. and China in gray format are for reference.

  solely pay attention to identifying the economic drivers of the long-term volatility of the Gold futures market in the U.S. by employing the GARCH-MIDAS method. The results show that the macroeconomic variables have a significant impact on Gold volatility during and after the GFC of 2008. More specifically, Economic Policy Uncertainty, Employment Rate and Inflation Rate have a positive effect on the long-run volatility of Gold futures while the effects of Capacity Utilization, Diffusion Index, New Consumer Goods and Materials Orders, and Consumer Confidence are negative and significant.

  [START_REF] Morales | Comparative analysis on the effects of the asian and global financial crises on precious metal markets[END_REF] suggest that the precious metal markets are less influenced by times of market stress than other financial markets. Therefore, we use a sub-period analysis, still focusing on the U.S. and China, to investigate any change in the role of economic drivers of precious metals across the various phases of the GFC 2008. Tables4 and 5report the estimation results of the potential drivers of volatility and correlation in precious metal futures over three periods of the 2008 crisis. This selection arises as the futures contracts on precious metals have become the most-widely used instruments for risk management in more volatile periods, and the U.S. and China have played an important role in global derivatives trading for metals[START_REF] Klein | Night trading with futures in china: The case of aluminum and copper[END_REF].

  China on the global financial market in general and the precious metals market in particular after the financial crisis of 2008.With respect to the case of the U.S., the signs of the coefficients θ and γ of the macrofinance factors of this country show the most significant change between the pre-crisis and crisis periods compared to other periods. In detail, several drivers of the U.S. turn from negative to positive (i.e., signs of θ of the Export, Gold & Foreign Reserves growth or Stock on the long-term volatility of GoldF and PalladiumF and signs of γ of M1 on GoldF-SilverF, Exchange Rates on GoldF-PlatinumF and GoldF-PalladiumF, T-Bill 3M on GoldF-PlatinumF, Interest rate on PalladiumF-PlatinumF). This confirms the significant impact on the U.S. economy during the GFC of 2008. Finally, the long-term volatility of Silver futures and long-term correlations of Silver and other metals are the least responsive to any changes of economic variables during the crisis period (i.e., only the Capacity Utilization and Exchange rate of the U.S. and Gold & Foreign Reserves growth of China influence the volatility of Silver futures 1 month and only M1 growth of the U.S. impact on the correlation of the Silver-Palladium futures pair) in comparison with non-crisis periods. Meanwhile, the volatility of Palladium futures is the most strongly influenced by the GFC. A similar tendency can be found in Platinum volatility under the impact of the economics drivers of China (in the case of M2, Inflation, Stock and Interest rate), apart from Gold and Silver futures volatility.

Table 2 :

 2 Coefficients θ of economics variables of the U.S. and China The table reports estimated results for parameters θ of macroeconomic and financial variables of the U.S. and China from GARCH(1,1)-MIDAS-X model. The symbols * * * , * * , and * denote statistical significance at the levels of 1%, 5% and 10%, respectively. Otherwise the field is left blank.

	Assets	Gold	GoldF	Silver	SilverF	Platinum	PlatinumF Palladium PalladiumF
	Panel A: United States
	Macroeconomic variables
	M1 Growth		-0.1345	-0.9366	-0.8870		0.1692
	M2 Growth	0.4923	0.6750	0.2682	0.3155			0.2331
	Inflation Rate	0.4079	0.2641				0.0989		0.1749
	Unemployment Rate	0.0974	0.0858			0.0663		-0.1251	-0.1251
	Saving Ratio	-0.1909			-0.2569	-0.0796	0.0658
	Capacity Utilisation	-0.0512						-0.0881	-0.0881
	Industrial Production	-0.0494	-0.0411		-0.1195	-0.1718		-0.0710	-0.0645
	Consumer Confidence	-0.2731		-0.2762	-0.3054	-0.1691	-0.1754	-0.2116
	Composite Leading Indicator							-0.1630
	Export Growth	0.4668	-0.0548			-0.1999	-0.0762	-0.1011
	Import Growth	0.4283		0.7013	0.8101	-0.2011		0.1029
	Gold&Foreign Reserves	0.1813	0.1813	0.4138	0.5142		0.0749	0.2495	0.2495
	Financial variables
	Stock market	-0.0775	-0.0652		-0.0569	-0.3542	-0.2593	-0.0395	-0.5079
	Bond market							0.0802	0.2028
	Interest Rates		0.1978
	Interbank 3M Rates	0.1677			-0.3911			0.1647	0.1475
	T-bill 3M Rates					0.0923		0.1685
	Exchange Rates	-0.0313	-0.0304	-0.0492	-0.0527			0.0158
	EPU					0.2242
	Panel B: China
	Macroeconomic variables
	M1 Growth		0.3164		-0.0730		0.3275		0.1788
	M2 Growth	0.6364						3.7941
	Inflation Rate	0.1505		0.2840	0.1989
	Unemployment Rate	1.2893	1.6245	2.1366	2.1216			2.5641	2.2086
	Saving Ratio
	Capacity Utilisation
	Industrial Production
	Consumer Confidence
	Composite Leading Indicator			-0.1976	-0.2054	-0.1848	-0.1635	-0.2376	-0.1906
	Export Growth	0.2379	0.2070	0.4766	0.5682	0.0495			0.0199
	Import Growth			0.6376	0.6859
	Gold&Foreign Reserves	0.1892	0.0638		0.0897	0.9346		-0.0714
	Financial variables
	Stock market	-0.0230		0.2049		0.1382	0.1567	-0.0953
	Bond market
	Interest Rates	0.5162			-4.0609		0.2120
	Interbank 3M Rates
	T-bill 3M Rates
	Exchange Rates	-0.0252	-0.0219	-0.0201
	EPU					0.0489
	Note:

Table 3 :

 3 Coefficients γ of economics variables of the U.S. and China Note: The table shows estimation results γ of macro-finance drivers of the U.S. and China from DCC-MIDAS-X model. The asterisks * * * , * * , and * denote significance at 1%, 5%, and 10%, respectively. Otherwise the field is left blank.

	Pairs of Assets	Gold-Silver	Gold-Platinum	Gold-Palladium	Silver-Platinum	Silver-Palladium	Platinum-Palladium
	Countries	US	China	US	China	US	China	US	China	US	China	US	China
	Macroeconomic variables
	M1 Growth	0.3568		0.6277 -1.0963			0.5191				0.4717
	M2 Growth	0.9507 -1.1396		-1.1596 -1.1347			-0.1537			-0.6549
	Inflation Rate	-0.1382	0.8183 -1,2895				-0.2543	0.1238		0.1377
	Unemployment Rate								0.8990	0.9423
	Saving Ratio
	Capacity Utilisation	0.1139		0.3390								0.3466
	Industrial Production			0.3386
	Consumer Confidence	1.5113		1.9844		1.7165		1.4700		1.7635		2.7214 -2.7959
	Composite Leading Indicator			1.5281	1.7337								1.2851
	Export Growth	-0.1739				0.1772			-0.1161	0.1812
	Import Growth	-0.1969 -1.0317
	Gold&Foreign Reserves		-0.1214		-0.2788							0.1599	0.5301
	Financial variables
	Stock market	0.1486		0.1774		0.0996				0.0854		0.1019	1.1359
	Bond market			0.9956
	Interest Rates	-0.0745		-0.1362		-0.1007		-0.1059		-0.5612		-0.2331
	Interbank 3M Rates	-0.0700						-0.1102
	T-bill 3M Rates
	Exchange Rates												0.4757
	EPU	-0.0138

Table 4 :

 4 Coefficients θ of economics variables of the U.S. and China over three sub-periods of global financial crisis 2008

	Assets		GoldF			SilverF			PlatinumF			PalladiumF
	Periods	Pre.	Crisis	Post.	Pre.	Crisis	Post.	Pre.	Crisis	Post.	Pre.	Crisis	Post.
	Panel A: United States
	Macroeconomic variables
	M1 Growth	0.6574	0.5116				-0.5661		-0.9755		2.000	-0.0971 -4.3327
	M2 Growth		0.5156				-2.1543	1.5155			2.5460	5.9999	0.5708
	Inflation Rate						-0.2459		-0.2992		-5.000
	Unemployment Rate			0.2545	0.6734				-0.1142		0.7296 -1.0059
	Saving Ratio		-0.0956	1.4900	0.5112			0.3332	0.0845		0.4423 -1.0127 -0.5491
	Capacity Utilisation		-0.1305			-0.1175		-0.4908 -0.1304		-0.1813 -0.1011
	Industrial Production		-0.1006 -0.0872					-0.1005	0.3610			0.2344
	Consumer Confidence	-0.7209 -0.1070 -0.3744				-0.6422 -0.1069		-0.9405
	Composite Leading Indicator		-0.1047				0.5631 -0.2758 -0.1042			-0.1000
	Export Growth	-0.1360 -0.9966 -0.6751	1.5884		-0.2692	0.1923	0.5179	1.1469	0.2323	0.4974 -0.2170
	Import Growth	-0.0783	0.9827				0.1724		-1.0089	0.4602			0.1016
	Gold&Foreign Reserves	0.0966					0.2893 -0.1509 -0.5357 -0.2692	0.7883 -5.0050	0.2390
	Financial variables
	Stock market			-0.4932				-0.3412 -0.4945 -0.3036		0.5001 -0.5848
	Bond market						-0.8942	0.4082			1.0565
	Interest Rates		1.0021 -0.6683 -0.2628						-0.2174
	Interbank 3M Rates		-0.9674 -0.8399 -0.2483				0.9754		-0.2075		0.9339
	T-bill 3M Rates		1.0026		-0.2670					7.0128
	Exchange Rates		-0.1365 -0.0531		-0.1235			-0.1364			-0.1297
	EPU		-0.1069		-0.0382			0.0095 -0.0969		0.0116 -0.1009
	Panel B: China
	Macroeconomic variables
	M1 Growth		-0.9797 -0.7815					5.0030 -0.6633	2.8881	0.4993	0.0482
	M2 Growth		-1.0026						5.0078	4.4239
	Inflation Rate	0.2282		0.3384 -0.3139		-0.2140		-0.1072	0.3529
	Unemployment Rate		0.1085	0.5031	1.1528				0.1099		-0.7097
	Saving Ratio
	Capacity Utilisation
	Industrial Production
	Consumer Confidence			-0.3606					-0.1051			-0.1001
	Composite Leading Indicator -0.1041		-0.3842			-0.5557 -0.2022	-0.9907		-0.1001 -1.4815
	Export Growth		0.5091	0.5005	0.5141		0.0990					-0.0674
	Import Growth			-0.4602				-0.1579 -0.1079		0.6196	0.5030
	Gold&Foreign Reserves	0.1145	5.0001	0.1370	0.2192	1.0295	0.5627	0.1955	0.4796	0.4398		1.0010	0.9180
	Financial variables
	Stock market returns		0.0955	0.1510			0.3050		-1.0 -245	0.3307	-0.3608	-0.0518
	Bond market returns			-0.6495			-1.0820		0.1132			-0.7091
	Interest Rates			0.5539					0.0884 -0.4786	1.4465	0.1397 -1.0604
	Interbank 3M Rates
	T-bill 3M Rates
	Exchange Rates		-0.1039 -0.0368 -0.1413							-0.1001
	EPU	-0.0070 -0.0979 -0.0015				0.0106 -0.0979	' -0.0050 -0.0113

Table 5 :

 5 Coefficients γ of economics variables of the U.S. and China over three sub-periods of global financial crisis of 2008

	Pairs of Assets	GoldF-SilverF	GoldF-PalladiumF	GoldF-PlatinumF	SilverF-PalladiumF	SilverF-PlatinumF	PalladiumF-PlatinumF
	Periods	Pre.	Crisis	Post.	Pre.	Crisis Post.	Pre.	Crisis Post.	Pre.	Crisis Post.	Pre.	Crisis Post.	Pre.	Crisis	Post.
	Panel A: U.S.
	Macroeconomic variables
	M1 Growth	-0.5358 0.7505			1.7138	1.6702 1.1398		1.0211	1.1721 1.1312			1.2181
	M2 Growth		-2.7528 -0.3771 -1.7955		-0.0953 1.1712			-0.8140	0.5250 -0.5866		0.8350
	Inflation Rate					0.9332	-1.0377 -0.1336					0.2356		0.4387
	Unemployment Rate
	Saving Ratio								0.9640
	Capacity Utilisation		1.7927		1.5556 1.3446 -0.1372 1.4774 -0.0963	0.7210		0.3148	-0.2685 0.9914		0.0193
	Industrial Production		0.4717		1.8865 1.4699	0.3422		0.8095		0.1577		0.6883		1.6340
	Consumer Confidence			-0.5650		1.3006	1.9444	0.3107 1.7336					1.0868
	Composite Leading Indicator		48.4845 1.4141 0.5378 0.9870	1.9899 0.4509	0.7966	-0.7738 0.3750		0.0386
	Export Growth			0.1252 0.3972 1.1659	0.4960 1.3114	0.4645		0.4336			3.2115 0.7872
	Import Growth	0.2478 5.6445 0.2018 0.7123 1.3338	0.6336 1.5653			0.6044		0.4464 1.5078
	Gold&Foreign Reserves			0.2192 1.0438			0.6474 -0.0931			1.3503		-0.2093
	Financial variables
	Stock market
	Bond market
	Interest Rates		-12.446			1.0907 0.7091 -27.307		1.9066		3.5705		-0.1527 0.1988 -0.1480
	Interbank 3M Rates		0.4258			1.8672	-0.2132 0.0470	-0.3100		-0.1865		-2.8012		-0.1279
	T-bill 3M Rates	7.9615 1.6404			-9.2773 0.8577 -23.022 1.3426	-0.3578		-0.2084 0.3164	0.0860 1.2322
	Exchange Rates			-0.2061 -1.1922 0.5773	-0.9044 1.9272		-0.0640			-0.7224
	EPU	-0.6191		0.0912 -0.2343					0.6190 -0.0055		-0.0063 -0.1557 -0.9037 -0.1054
	Panel B: China
	Macroeconomic variables
	M1 Growth					0.6738 -0.0987		0.7189 -0.0860						1.2647 -0.1537
	M2 Growth	-2.6774		-1.2394		1.4732			0.2851		0.3078			-0.3109 0.2315
	Inflation Rate				0.2654		0.2592				0.2215		0.1844
	Unemployment Rate				0.7609		0.6690
	Saving Ratio
	Capacity Utilisation
	Industrial Production
	Consumer Confidence			0.6557 -1.4576		-1.5888			-0.4440 -0.1048 -0.2537
	Composite Leading Indicator 0.9995 1.1891		1.0021		1.9121	1.0008 0.6243	-0.0879 0.6952			0.6286
	Export Growth									1.0538	0.4659		0.3466		0.3883
	Import Growth			0.1003 -0.1685 0.8596	-0.1730					-0.1466 -2.7245
	Gold&Foreign Reserves		1.7590 -0.3707		0.6474	1.5735 0.7948				1.6200
	Financial variables									-0.0258
	Stock market		1.2630				-0.5088 0.8928 0.0376					0.0329 1.0091 -0.1691
	Bond market								0.9922
	Interest Rates					0.3312	0.9830						-1.1517		0.9544
	Interbank 3M Rates
	T-bill 3M Rates
	Exchange Rates			-0.2724 -0.3934 1.4551	-0.0223		-0.2085		-1.5215
	EPU	-0.0642 -0.8463					-0.0358			-0.1518 -0.1042		-1.8683 -0.0614

Table 6 :

 6 Parameter estimation results of GARCH, GJR, GARCH-MIDAS-RV and GJR-MIDAS-RV respectively for both spot returns and future 1 month returns of four precious metals. The full sample covers the period from 1998 to 2018. The symbols * * * , * * , and * denote statistical significance at the levels of 1%, 5% and 10%, respectively. LL is the Log-Likelihood and BIC is the Bayesian Information Criterion. Numbers in italic and bold show the model with the best goodness-of-fit (i.e. lowest BIC) and best statistical fit (i.e. highest LL), respectively.

	Asset	Model	µ	α	β	m	LL	BIC
		GARCH	0.0158	0.0508 * * * 0.9366 * * *	0.1970	-6624.20	13282.13
	Gold	GJR GARCH-MIDAS-RV 0.0201 0.0249 *	0.0678 * * * 0.9392 * * * 0.0288 * * * 0.9664 * * *	0.2277 0.1212	-6612.13 -5576.00	13266.40 11209.67
		GJR-MIDAS-RV	0.0280 *	0.0405 * *	0.9604 * * *	0.0376	-5909.39	11263.80
		GARCH	0.0034	0.0408 * * * 0.9531 * * *	1.1818 * * * -8973.04	17979.80
	Silver	GJR GARCH-MIDAS-RV 0.3387 * * * 0.0899 * * * 0.9101 * * * -0.0440 * * * -8565.24 0.0130 0.0552 * * * 0.9510 * * * 1.2803 * * * -8966.31	17974.76 17188.16
		GJR-MIDAS-RV	0.0322	0.0864 * * * 0.8613 * * *	0.6445 * * * -8669.08	17208.46
		GARCH	0.0153	0.0718 * * * 0.9101 * * *	0.7567 * * * -7811.90	15657.51
	Platinum	GJR GARCH-MIDAS-RV 0.0143 0.0221	0.0843 * * * 0.9092 * * * 0.0946 * * * 0.8457 * * *	0.7828 * * * -7809.45 0.1896 * -6315.86	15661.06 12689.40
		GJR-MIDAS-RV	0.0158	0.0982 * * * 0.8500 * * *	0.1981 *	-6315.69	12697.29
		GARCH	0.0764 * * * 0.0778 * * * 0.9100 * * *	1.6448 * * * -9565.36	19164.44
	Palladium	GJR GARCH-MIDAS-RV 0.0601 * * * 0.0279 * * * 0.9155 * * * 0.0740 * * * 0.0757 * * * 0.9095 * * *	1.6384 * * * -9565.23 1.2577 * * * -8084.97	19172.62 16227.63
		GJR-MIDAS-RV	0.0465 *	0.0703 * * * 0.9183 * * *	1.2206 *	-8384.70	16822.96
		GARCH	0.0199	0.0456 * * * 0.9407 * * *	0.2060	-6720.80	13475.34
	GoldF	GJR GARCH-MIDAS-RV 0.0260 * 0.0258 *	0.0571 * * * 0.9410 * * * 0.0406 * * * 0.9459 * * *	0.2307 0.3078 *	-6716.34 -5664.93	13474.83 11387.54
		GJR-MIDAS-RV	0.0278 *	0.0392 * * * 0.9605 * * *	0.3870 *	6011.17	12072.15
		GARCH	0.0114	0.0385 * * * 0.9540 * * *	1.2137 * * * -9149.26	18332.24
	SilverF	GJR GARCH-MIDAS-RV 0.0387 * 0.0198	0.0506 * * * 0.9529 * * * 0.0727 * * * 0.8404 * * *	1.2944 * * * -9143.54 0.7658 * * * -7782.28	18329.23 15622.23
		GJR-MIDAS-RV	0.0375 *	0.0802 * * * 0.8713 * * *	0.7274 * * * -8207.01	16487.18
		GARCH	0.0183	0.0589 * * * 0.9262 * * *	0.7318 * * * -7887.02	15807.76
	PlatinumF	GJR GARCH-MIDAS-RV 0.0151 0.0225	0.0660 * * * 0.9254 * * * 0.0569 * * * 0.9237 * * *	0.7519 * * * -7883.11 0.4255 * * * -6447.86	15804.38 12953.41
		GJR-MIDAS-RV	0.0159	0.0585 * * * 0.9237 * * *	0.4310 * *	-6447.82	12961.56
		GARCH	0.0759 * * * 0.0778 * * * 0.9060 * * *	1.6166 * * * -9634.40	19302.53
	PalladiumF	GJR GARCH-MIDAS-RV 0.0692 * * 0.0774 * * * 0.0791 * * * 0.9061 * * * 0.0759 * * * 0.8892 * * *	1.6193 * * * -9634.36 0.9678 * * * -7816.59	19310.87 15690.86
		GJR-MIDAS-RV	0.0788 * *	0.0798 * * * 0.9070 * * *	0.1064 *	-8464.81	16918.54
	Note: This table presents the estimates of GARCH(1,1), GJR(1,1,1), GARCH(1,1)-MIDAS-RV and GJR(1,1,1)-MIDAS-RV
	general coefficients,

Table 8 :

 8 Impact of macroeconomic variables of G7 and BRICS countries on the long-term volatility of precious metals Note: Estimation results θ of Trade Balance Growth, Gold and Foreign Reserves Rate, Consumer Confidence, Composite Leading Indicator and Industrial Production of other G7 and BRICS nations from GARCH(1,1)-MIDAS-X. The asterisks * * * , * * , and * denote significance at 1%, 5%, and 10%, respectively. Otherwise, the field is left blank. The results of the U.S. and China in gray format are for reference.

		US	UK	Canada	Japan	Germany	France	Italy	Brazil	Russia	India	China	South Africa
	Export Growth
	Gold	0.4668		-0.0238			-0.1464			0.0988	0.2046	0.2379	0.1153
	GoldF	-0.0548					-0.1686		-0.0619	0.0967	0.2211	0.2070	0.0088
	Silver		0.2218		0.6540		-0.1875	0.7427	0.4429	0.4318		0.4766
	SilverF		0.7227		0.6710		-0.1915		0.4986	0.3138	0.2350	0.5682 -0.4694
	Platinum		0.0512	0.1530 -0.2883 -0.0148		0.1569		-0.1215	0.0503	0.0495	0.1942
	PlatinumF	-0.0855		0.1375				0.1181		-0.4809	0.0394		0.1394
	Palladium	-0.1011	0.2425 -0.0267 -0.0249		-0.0353 -0.0951		0.0966
	PalladiumF		0.1723									0.0199
	Import Growth
	Gold	0.4283			-0.0451		0.2374	0.1628	0.2263		0.2487		0.2317
	GoldF			-0.0155 -0.1244						0.2509		0.2108
	Silver	0.7013	0.3077 -0.0885 -0.1210					0.2860		0.6376
	SilverF	0.8101								0.4051	0.2858	0.6859	0.1119
	Platinum	-0.2011		0.1440 -0.2539 -0.0129 -0.3025	0.0057	0.0746
	PlatinumF			0.1246			0.1181		-0.0738		0.0969		0.1848
	Palladium		0.2907 -0.0280 -0.2991		-0.0951
	PalladiumF		-0.0290					-0.0266 -0.0385	0.0207	0.2154		-0.1538
	Gold&Foreign Reserves
	Gold	0.1813 -0.0386	0.5165		-0.0597		-0.0474	0.0517	0.3566	0.0650	0.1892	0.2964
	GoldF	0.1813		0.5073		-0.0517	0.0459 -0.0432	0.2797		0.0616	0.0638	0.1077
	Silver	0.4138		-0.1015					0.3342		0.1094		0.0583
	SilverF	0.5142					0.2188 -0.0490	0.2017		0.0897	0.0897	0.1913
	Platinum			0.3667	0.0884	0.1279		0.2039	0.2061		0.0345	0.9346	0.0870
	PlatinumF				-0.1378	0.1051		0.1912		0.0358			-0.2977
	Palladium	0.3077			0.1588	0.3145		0.3316	0.1375		-0.0714 -0.0714	0.0471
	PalladiumF	0.2495						0.3517	0.1873
	Consumer Confidence
	Gold	-0.2731 -0.2215 -0.0484 -0.2031 -0.1289		-0.2100	0.2109	0.1350 -0.1373
	GoldF		-0.2358 -0.0391 -0.1949		-0.3923		0.2128	0.1256 -0.1310
	Silver	-0.2762 -0.2919 -0.0949		-0.3519
	SilverF	-0.3054		-0.0774 -0.2493 -0.4052		-0.3284			-0.2869
	Platinum	-0.1691 -0.1905 -0.0578 -0.2653					-0.0820 -0.2292
	PlatinumF	-0.1754 -0.1819		-0.1911
	Palladium		-0.1856 -0.0574 -0.4122 -0.2452 -0.2733		-0.1007
	PalladiumF	-0.2157 -0.1736 -0.0481		-0.2209
	Composite Leading Indicator
	Gold		-0.1425						0.2373				-0.1848
	GoldF		-0.1974										-0.2100
	Silver		-0.1376		-0.3088					-0.1095 -0.3397 -0.1976
	SilverF		-0.1466 -0.2366 -0.3250 -0.2202			-0.0348		-0.3629 -0.2054
	Platinum		-0.2342		-0.2762		0.2393					-0.1848
	PlatinumF		-0.2243								-0.2004 -0.1635
	Palladium	-0.1611 -0.2623 -0.2776							0.2145 -0.2376 -0.2464
	PalladiumF		-0.2431 -0.2474		-0.1448					0.2485 -0.1906
	Industrial Production
	Gold	-0.0494		-0.0595		-0.0326		0.0187					-0.0336
	GoldF	-0.0411		-0.0607		0.0262							-0.0277
	Silver		-0.1975 -0.0918 -0.0579			-0.0969 -0.0635
	SilverF	-0.1195 -0.2074 -0.1004 -0.0652			-0.1011 -0.0709
	Platinum
	PlatinumF				0.0626
	Palladium	-0.0728		-0.0478		-0.0352		0.0184
	PalladiumF	-0.0645		-0.0365

Table 10 :

 10 Impact of macroeconomic variables of G7 and BRICS countries on the long-term volatility and correlations of precious metals

		US	UK	Canada	Japan	Germany	France	Italy	Brazil	Russia	India	China	South Africa
	Panel A: Long-term volatility
	M1 Growth
	Gold				-0.1222		-0.5119	-0.6396	-0.0350	0.1423	0.6701		0.8812
	GoldF	-0.1345		-0.4013	-0.1188	0.0886	-0.4449	-0.7019				0.3164
	Silver	-0.9366			-1.2088	-0.4155	-0.2401			-0.0938	1.1034		0.3100
	SilverF	-0.8870									0.8483	-0.0730	0.4788
	Platinum		-0.5808	0.7389	0.2325				0.2790				0.4741
	PlatinumF	0.1692	0.1934	0.2451	-0.2535				0.2606			0.3275	0.3843
	Palladium		0.1849	-0.1676	-0.0616			0.1092		0.0842	0.3241		0.2911
	PalladiumF										0.3883	0.1788	0.3065
	M2 Growth
	Gold	0.4923	1.4255		-1.4092		-1.3128	0.4357	0.2004				0.7124
	GoldF	0.6750	1.1178	1.0012	-3.7169	0.6718	-1.1919		0.2066			0.6364	0.5385
	Silver	0.2682		0.7192		1.7430	-1.1935	-0.1394	0.8198		1.0820
	SilverF	0.3155		0.4262	0.2505		-1.1816		0.3845		0.7887
	Platinum	1.2215		1.1187	1.5943	1.5663	1.5550	-0.4514
	PlatinumF					1.5598	1.5424		0.5624
	Palladium	0.2331	-0.5053	0.9162			-0.1733		0.5905	-0.0490	0.3156	3.7941	0.0554
	PalladiumF		0.9777	1.0379					0.6782		0.3685		-0.3157
	Unemployment Rate
	Gold	0.0974	0.1633		0.2210	0.1659	-0.2351	-0.1442		0.1460		1.2893
	GoldF	0.0858	0.1811	-0.1309		0.1482	-0.2085	-0.1356		0.1288		1.6245	-0.1830
	Silver				-1.2091	-0.6962	-0.8011	-0.4145	-0.3236	-0.6840	-2.1264	2.1366
	SilverF				-1.2157	-0.6186		-0.5021	-0.3374			2.1216	-0.2324
	Platinum						0.2941				-0.5543		-0.1378
	PlatinumF						-0.2940			0.1145	-1.0268		-0.1085
	Palladium	0.1374			0.3907				0.0794	0.1238		2.5641	0.1327
	PalladiumF	-0.1251			0.2704		-0.3595			0.2653		2.2086
	Inflation Rate
	Gold	0.4079	0.2742	0.1817	-0.1739		0.2342	0.2128	0.0629	0.0518	0.0744	0.1505
	GoldF	0.2641	0.2641						0.0581	0.0465	0.0813		-0.0870
	Silver		0.1861			0.4219			-0.1352	-0.0366		0.2840	-0.0975
	SilverF									-0.1172	0.1378	0.1989
	Platinum			0.3644			-0.2551			-0.0716			0.1122
	PlatinumF	0.0989								-0.0341
	Palladium			0.5363	-0.1426		0.2626	0.2062	0.1277	0.0709			0.0727
	PalladiumF	0.1749		0.5444			0.2600			0.0669

Table 11 :

 11 Impact of financial variables of G7 and BRICS countries on long-term volatility and correlations of precious metals

		US	UK	Canada	Japan	Germany	France	Italy	Brazil	Russia	India	China	South Africa
	Panel A: Long-term volatility
	Stock Market Returns
	Gold	-0.0775	0.0438	-0.1332		-0.0713		-0.1213	-0.0473	-0.0691	-0.0590	-0.0230	0.3294
	GoldF	-0.0652	-0.1026	-0.1294		-0.0594					0.0903		0.2845
	Silver		-0.1070	0.0979		-0.0533		-0.1016	-0.0562	-0.0347	-0.0360	0.2049
	SilverF	-0.0569	-0.1014	-0.0945		-0.0479			-0.0569	-0.0308
	Platinum	-0.3542	-0.0886	-0.3749	-0.2118	-0.2170	-0.2785	-0.2678		0.0260		0.1382	0.1283
	PlatinumF	-0.2593		-0.3002		-0.3504						0.1567	-0.2657
	Palladium	-0.6221	-0.6200		-0.2973	-0.0333	-0.4602	-0.4310	0.0322	0.0286	-0.0289	-0.0953	-0.1793
	PalladiumF	-0.5079						-0.1129			0.0923
	Bond Markets Returns
	Gold		0.3220	0.1562	0.7560	0.1720	0.1914	0.2654
	GoldF		0.1593			0.1375	0.1456	0.1517			0.2479		-0.2818
	Silver		0.2791		0.5234								-0.5378
	SilverF		-0.1737	-0.5924									-0.7090
	Platinum				0.4937						0.1692
	PlatinumF										0.1469
	Palladium		0.2585			0.1531					-0.3194		0.3017
	PalladiumF	0.2028		0.1747		0.1591	-0.4547				-0.2726
	Interest Rate
	Gold		0.0864	0.1996		0.2351	0.1244	0.2351			0.1837	0.5162
	GoldF	0.1978	0.0940	0.1703			0.1849	0.1849			0.1971
	Silver				-2.5648			-0.6129	1.3216	1.1509		-4.0609	-0.3187
	SilverF		-0.5317		1.3974						-0.1983		-0.2284
	Platinum				1.9709							0.2120	0.0952
	PlatinumF												0.0955
	Palladium	0.1691		0.4122	-1.6181	0.2074	0.2074	0.2074	0.7550		-0.1630		0.0850
	PalladiumF		0.0963	0.3380		0.1823	0.1823	0.1823
	Exchange Rate
	Gold	-0.0313	-0.0908	0.0355	0.0150			0.0357				-0.0252	0.0332
	GoldF	-0.0304	-0.0963	0.0353			0.0454				-0.0462	-0.0219	0.0285
	Silver	-0.0492	-0.1074	-0.0291	-0.0811		-0.0536	-0.0534				-0.0201	-0.0332
	SilverF	-0.0527		-0.0383	-0.0784	-0.0696	-0.0685	-0.0685		-0.0310			0.0342
	Platinum							-0.0048	-0.0322
	PlatinumF				-0.0148
	Palladium					0.0265							-0.0197
	PalladiumF					0.0407		0.0407		-0.0256			0.0302

https://www.reuters.com/article/us-usa-trade-china-rareearth-explainer-idUSKCN1TS3AQ

We do not present the formula from the realized correlation framework of[START_REF] Colacito | A component model for dynamic correlations[END_REF] here, as we focus on the effects of macroeconomic and financial drivers on the dynamic correlation only.

We use both, spot and futures prices to account for their different dynamics[START_REF] Pindyck | The dynamics of commodity spot and futures markets: a primer[END_REF].

We note that the distinction between economic and financial variables is not mutually exclusive as some of the financial variables can also be regarded as economic variables and vice versa (e.g. the EPU or the exchange rates).

Gold-Silver (G-S), Gold-Platinum (G-Pl), Gold-Palladium (G-Pa), Silver-Platinum (S-Pl), Silver-Palladium (S-Pa) and Platinum-Palladium (Pl-Pa).

An alternative approach is presented by[START_REF] Walther | Exogenous drivers of bitcoin and cryptocurrency volatility-a mixed data sampling approach to forecasting[END_REF] for the case of cryptocurrencies. Instead of statistical inference, the authors focus solely on the predictive accuracy of volatility drivers.

https://www.investopedia.com/insight/chinese-mining-companies/

https://www.visualcapitalist.com/chinas-dominance-in-rare-earth-metals/

United Kingdom, Canada, Japan, Germany, France and Italy

Brazil, Russia, India and South Africa

https://www.ecb.europa.eu/pub/economic-bulletin/articles/2019/html/ecb.ebart201907_ 01 ~c2ae75e217.en.html

This finding is in line with[START_REF] Arouri | World gold prices and stock returns in china: Insights for hedging and diversification strategies[END_REF] and[START_REF] Mishra | Gold price volatility and stock market returns in india[END_REF].

https://corporatefinanceinstitute.com/resources/knowledge/finance/ what-is-corporation-overview/

Acknowledgement

The first author acknowledges the financial support from the National Economics University, Hanoi, Vietnam.

Note: Estimation results θ and γ of EPUs of G7 and BRICS nations from GARCH-MIDAS-X and DCC-MIDAS-X, respectively. The asterisks * * * , * * , and * denote significance at 1%, 5%, and 10%, respectively. Otherwise the field is left blank. The results of the U.S. and China in gray format are for reference.