Amélie Charles

Olivier Darn É

Lemna

Jae H Kim

Charles Amélie

Darné Olivier

Kim Jae

Etienne Redor

Charlot Philippe

Marimoutou Vêlayoudom

Will Precious Metals Shine? A Market Efficiency Perspective

Keywords: Adaptive markets hypothesis, martingale difference hypothesis, Market Efficiency, Trading Strategy. JEL Classification: G14, G15

Precious metals (gold, silver, and platinum) have become an important part of investment portfolios for individuals as well as for institutions. A key question is whether investors should actively trade these metals to time the market or whether they should take a buy-and-hold strategy. This paper examines the weak-form efficiency of precious metals markets with this question in mind, using the automatic portmanteau and variance ratio tests. It is found that return predictability of these markets has been changing over time, depending on prevailing economic and political conditions. The return predictability of gold and silver markets have been showing a downward trend, implying that the degree of the weak-form efficiency of these markets have been gradually improving. In particular, the gold market has been highly efficient recently, showing the highest degree of market efficiency among the three precious metals markets. The overall evidence suggest an buyand-hold strategy, but profit opportunities may arise from time to time depending on prevailing economic or political conditions.

Introduction

Precious metals (gold, silver, and platinum) play an important role in portfolio selection and management, and their properties have attracted much attention recently (see, for example, Conover et al. 2009;[START_REF] Jaffe | Gold and gold stocks as investments for institutional portfolios[END_REF]Emmrich and McGroarty;[START_REF] Reboredo | Is gold a safe haven or a hedge for the US dollar? Implications for risk management[END_REF]. [START_REF] Hillier | Do precious metals shine? An investment perspective[END_REF] list a range of key research questions in relation to these precious metals markets, such as their roles in diversification, hedging, and risk management (see also [START_REF] Marshall | Can commodity futures be profitably traded with quantitative market timing strategies[END_REF][START_REF] Belousova | On the diversification benefits of commodities from the perspective of euro investors[END_REF]. Among these research questions, the properties of the return distributions are an issue of fundamental importance to market participants. In particular, the market efficiency (or return predictability) has strong implications to the speed of information transmission and existence of profit opportunities in these markets. Gold and silver are traditionally regarded as an "investment of last resort", while platinum is primarily used for industrial purposes as a commodity (see [START_REF] Hillier | Do precious metals shine? An investment perspective[END_REF].

They are becoming more and more important as an investible assets in recent years, as the degree of uncertainty of world financial markets grows. In addition, the attractiveness of gold as an investment is growing fast, with the emergence of gold exchange traded products (see [START_REF] Shafiee | An overview of global gold market and gold price forecasting[END_REF]. [START_REF] Hillier | Do precious metals shine? An investment perspective[END_REF] and [START_REF] Daskalaki | Should investors include commodities in their portfolios after all? New evidence[END_REF] find that all three metal returns have low correlations with stock returns, indicative of their capability as a diversification and hedging tools. They also find that the precious metals have ability to improve portfolio efficiency, in terms of higher reward-to-risk ratio. Bauer and Lucey (2010) and [START_REF] Bauer | Is gold a safe haven? International evidence[END_REF] find strong evidence for gold as a hedge or safe haven for stock investment. Agyei-Ampomah et al. (2014) test whether the three precious metals offer similar or better investment opportunities in the periods of market turmoil and find that silver and platinum offer investors greater compensation for their bond market losses than gold. Furthermore, Morales and Andreosso-O'Callaghan (2011) find that the precious metals markets were less affected by the Global Financial Crisis than other major financial markets around the world. [START_REF] Erb | The strategic and tactical value of commodity futures[END_REF] and Roache and Rossi (2010) also find that gold and silver prices are counter-cyclical, implying that precious metals other than gold may also protect investors' wealth in the events of negative stock market conditions.

In this study, we examine the weak-from efficiency (or return predictability) of the precious metal markets. Despite being a fundamental issue, the efficiency of these markets has not examined extensively in the recent literature. Under the weak-form efficiency, all past price and return information is fully and instantly reflected in the current price. As a result, the returns are purely unpredictable, and no investors are able to make abnormal profits consistently over time by exploiting the past price information [START_REF] Fama | Efficient capital markets: A review of theory and empirical work[END_REF]. This property has strong implications to market participants who consider the precious metals as investible assets for the purpose of diversification, hedging, and risk management. A key question is whether investors should actively trade these precious metals to time the market or whether they should take a buy-and-hold strategy. Past empirical studies on the weak-form efficiency of precious metals markets include [START_REF] Tschoegl | Efficiency in the gold market[END_REF], [START_REF] Solt | On the efficiency of the markets for gold and silver[END_REF], [START_REF] Ho | Test of the incrementally efficient market hypothesis for the London gold market[END_REF], [START_REF] Aggarwal | The nature and efficiency of the gold market[END_REF], and [START_REF] Smith | Tests of the random walk hypothesis for London gold prices[END_REF].

However, their results are now outdated, and are obtained using the statistical tests that are well-known to have undesirable small sample properties.

In order to evaluate the degree of return predictability and test for weak-from efficiency in this study, we employ the automatic variance ratio test of [START_REF] Kim | Automatic variance ratio test under conditional heteroskedasticty[END_REF] and the automatic portmanteau test of [START_REF] Escanciano | An automatic portmanteau test for serial correlation[END_REF]. These tests perform highly desirably in small samples as a means of testing for the martingale difference property (no return predictability) of asset returns (see [START_REF] Charles | Small sample properties of alternative tests for martingale difference hypothesis[END_REF]. In particular, these tests are robust to non-normality and (conditional) heteroscedasticity that are stylized features of precious metals returns (see, e.g., Hammoudeh et al., 2011;[START_REF] Cochran | Volatility persistence in metal returns: A FIGARCH approach[END_REF]. Using a moving sub-sample window approach, we examine how the degree of return predictability has evolved over time, depending on economic, political, and financial events. This time-varying return predictability is consistent with the implications of the adaptive markets hypothesis (AMH) of [START_REF] Lo | The adaptive markets hypothesis: Market efficiency from an evolutionary perspective[END_REF], which is a modified version of the efficient market hypothesis of [START_REF] Fama | Efficient capital markets: A review of theory and empirical work[END_REF]. An important implication of the AMH is that return predictability may arise time to time, due to changing market conditions (cycles, bubbles, crashes, crises, . . . ) and institutional factors. To the best of our knowledge, this study is the first that evaluates the return predictability using time-varying measures in precious metals markets, in close association with the AMH.

The main finding of the paper is that all three precious metals markets show return predictability changing over time, depending on the prevailing economic and political conditions, which is consistent with the predictions of the AMH. The gold and silver markets show a strong tendency towards the market efficiency over time.

In particular, the gold market has been the most efficient, which may be the reflections of the increasingly important roles that it plays in world financial markets.

The overall evidence suggest that investors take a buy-and-hold strategy for the precious metals, but profit opportunities may arise from time to time depending on prevailing economic and political conditions. In the next section, we provide a background of precious metals markets in relation to the AMH. Section 3 presents a review of the test for return predictability used in this paper. Section 4 presents the empirical results and Section 5 concludes the paper.

Precious Metal Markets and Adaptive Markets Hypothesis

During the periods of uncertainty caused by the financial crises, certain precious metals may have desirable characteristics, such as being considered as an intrinsic store of wealth. In particular, Gold, through the centuries, has possessed unique characteristics that are comparable to a monetary unit in that it acts as a store of wealth, medium of exchange, and a unit of value (see, e.g., [START_REF] Goodman | The price of gold and international liquidity[END_REF][START_REF] Solt | On the efficiency of the markets for gold and silver[END_REF]. In addition, gold plays a significant role as a "flight to quality" asset during the periods of political crises, economic crises, and equity market crashes and; thus, it enjoys significant portfolio diversification properties (see, e.g., [START_REF] Ciner | On the long-run relationship between gold and silver: A note[END_REF]. Gold has been a traditional investment vehicle since it serves as a hedge against inflation and a safe haven in the periods of market crises (see Cai et Silver is also widely used, both as a valuable industrial commodity and as an important financial instrument for inclusion in investment portfolios. It is an amazingly versatile metal that has the highly desirable qualities for various industrial uses. Technological innovations are making silver an increasingly important component of the goods such as batteries, electronics, solar energy and medicine. As the global economy expands in size and as more ways to buy silver become available, silver will continue to play a major role in the global markets [START_REF] Cochran | Volatility persistence in metal returns: A FIGARCH approach[END_REF].

Platinum is the rarest of the precious metals and is also one of the strongest and most enduring metals. World production of platinum peaked at 514 tons in 2006. Subsequently, production declined, with (approximately) less than five hundred tons of the metal being produced per year. Because of its internationally standardized form and purity, platinum, like gold and silver, is acceptable as a means of exchange. The unique physical properties of platinum make it a very desirable industrial metal, especially for jewelery and automotive industries. Platinum is also integral to the production of about 20% of all consumer goods. 1Given these unique and diverse characteristics of the precious metals markets, it is quite likely that their properties are heavily affected by the prevailing economic and political conditions. In this respect, the AMH provides a suitable paradigm for evaluating efficiency or return predictability of these markets. A test for efficient market hypothesis often leads to a dichotomous decision, where the market is judged to be either perfectly efficient or inefficient, which is highly unrealistic. Under the AMH, however, the market may show a departure from the state of perfect efficiency, depending on market conditions. The AMH is developed by coupling the evolutionary principle with the notion of bounded rationality (Simon, 1955).

A bounded rational investor is said to exhibit satisfying rather than optimal behavior. Optimization can be costly and market participants with limited access to information or abilities to process information are merely engaged in attaining a satisfactory outcome. [START_REF] Lo | The adaptive markets hypothesis: Market efficiency from an evolutionary perspective[END_REF] argues that a satisfactory outcome is attained not analytically, but through an evolutionary process involving trial error and natural selection. The process of natural selection ensures the survival of the fittest and determines the number and composition of market participants. Market participants adapt to constantly changing environment and rely on heuristics to make investment choices. Based on the evolutionary perspective, profit opportunities do exist from time to time. Though they disappear after being exploited by investors, new opportunities are continually being created as groups of market participants, institutions and business conditions change.

For the precious metal markets, a number of studies have found that changing market conditions, caused by the events such as the changes in international institutional and macroeconomic factors (fluctuations of exchange rates, business cycle, monetary environment and financial market sentiment) as well as the episodes of world geopolitical tensions (e.g.,the Gulf wars, the Asian crisis, worries over Iranian nuclear plans), can affect market efficiency and other market features: see, for example, [START_REF] Kaufmann | The price of gold: A simple model[END_REF], [START_REF] Rockerbie | Gold prices and gold production: Evidence for South Africa[END_REF]

Tests for Martingale Difference Hypothesis

As mentioned earlier, we employ the automatic portmanteau test of [START_REF] Escanciano | An automatic portmanteau test for serial correlation[END_REF] and automatic variance ratio test of [START_REF] Kim | Automatic variance ratio test under conditional heteroskedasticty[END_REF], to test for market efficiency or return predictability in this study. The portmanteau test [START_REF] Ljung | On a measure of lack of fit in time series models[END_REF] and variance ratio test [START_REF] Lo | Stock market prices do not follow random walk: Evidence from a simple specification test[END_REF]) have been widely used in empirical finance as a means of evaluating asset return predictability. However, they are well-known to suffer from deficient properties in small samples, especially under conditional heteroskedasticity widely observed in financial data.

In addition, they require ad hoc choices of the lag length or holding periods, further undermining their small sample properties. There have been a number of recent contributions to these tests, which attempt to improve their small sample properties under conditional heteroskedasticity: see, for example, [START_REF] Lobato | Testing for autocorrelation using a modified Box-Pierce Q test[END_REF] for the modified portmanteau test and [START_REF] Kim | Wild bootstrapping variance ratio tests[END_REF] for the wild bootstrap variance ratio tests.

To overcome the problem of choosing the lag length or holding period in an ad hoc way, [START_REF] Escanciano | An automatic portmanteau test for serial correlation[END_REF] propose an automatic portmanteau (AQ) test where selection of lag length is made fully automatic based on fully datadependent procedure; and [START_REF] Kim | Automatic variance ratio test under conditional heteroskedasticty[END_REF] proposes the use of an automatic variance ratio (AVR) test where the optimal holding period is automatically chosen. In their Monte Carlo study, [START_REF] Charles | Small sample properties of alternative tests for martingale difference hypothesis[END_REF] report that the AVR and AQ tests show highly desirable small sample (size and power) properties, under a wide range of conditionally heteroskedastic asset returns. This section presents brief details of the these automatic tests.

Automatic Portmanteau Test

Q p = T p i=1 ρ 2 (i), (1)
where ρ(i) is the sample autocorrelation of Y t of order i. When Y t shows conditional heteroscedasticity, [START_REF] Lobato | Testing for autocorrelation using a modified Box-Pierce Q test[END_REF] propose the use of a robustified test statistic of the form

Q * p = T p i=1 ρ 2 (i), (2)
where ρ(i) = γ 2 (i)/ τ (j), γ(i) is the sample autocovariance of Y t of order i, and τ (i)

is the sample autocovariance of Y 2 t of order i . The choice of p should be made to implement the test. In order to avoid an ad hoc selection, [START_REF] Escanciano | An automatic portmanteau test for serial correlation[END_REF] propose an automatic test where the optimal value of p is determined by a fully data-dependent procedure. The test statistic, which asymptotically follows the χ 2 1 distribution under the null hypothesis, is written as

AQ = Q * p (3) where p = min{p : 1 ≤ p ≤ d; L p ≥ L h , h = 1, 2, ..., d} and d is a fixed upper bound, while L p = Q * p -π(p, T )
, where the penalty term π(p, T, q) = p log(T ) if

max 1≤i≤d √ T | ρ(i)| ≤ 2.
4 log(T ) and π(p, T, q) = 2p if otherwise. Note that the penalty term is a balance between AIC and BIC. The null hypothesis of no return predictability is rejected at α level of significance, if the AQ statistics is greater than its asymptomatic critical value χ 2 1,α , which is the 100(1-α)th percentile of the χ 2 1 distribution.

Automatic Variance Ratio Test

The variance ratio test is based on the statistic of the form

V R(k) = 1 + 2 k-1 i=1 (1 - i k ) ρ(i), (4)
where k denotes the holding period. Under the null hypothesis of no return predictability, a standardized version of (4) asymptotically follows the standard normal distribution [START_REF] Lo | Stock market prices do not follow random walk: Evidence from a simple specification test[END_REF]. However, the test often requires an ad hoc choice of the value of k. [START_REF] Choi | Testing the random walk hypothesis for real exchange rates[END_REF] proposes an automatic variance ratio (AVR) test where k is chosen optimally using a fully data-dependent method of Andrews (1991). [START_REF] Kim | Automatic variance ratio test under conditional heteroskedasticty[END_REF] finds that small sample properties of Choi's (1999) test can be substantially improved under conditional heteroskedasticity, by employing the wild bootstrap of [START_REF] Mammen | Bootstrap and wild bootstrap for high dimensional linear models[END_REF].

Let the AVR test statistic with the optimal choice of k be denoted as AV R(k * ).

Kim's (2009) wild bootstrap AVR test is conducted in three stages as follows:

1. Form a bootstrap sample of size T as Y * t = η t Y t (t = 1, ..., T ), where η t is random variable with zero mean and unit variance; 2. Calculate AV R * (k * ), the AV R(k * ) statistic calculated from {Y * t } T t=1 ;

3. Repeat 1 and 2 B times, to produce the bootstrap distribution of the AVR

statistic {AV R * (k * ; j)} B j=1 .
It can be shown that the bootstrap sample {Y * t } T t=1 is serially uncorrelated, while effectively replicating the heteroscedastic structure of the asset return Y t . As a result, the bootstrap distribution {AV R * (k * ; j)} B j=1 provides a small-sample approximation to the sampling distribution of AV R(k * ) statistic, under the null hypothesis.

The test for the null hypothesis of no return predictability can be conducted using the confidence interval for the population value of V R under the null hypothesis. That is, let AV R * τ be the τ th percentile of {AV R * (k * ; j)} B j=1 . Then, 100(1-α) percent confidence interval for the population variance ratio under H 0 is constructed as [AV R * 0.5α , AV R * 1-0.5α ]. If the AV R(k * ) statistic lies outside the 100(1-α) percent confidence interval, the null hypothesis of no return predictability is rejected at α percent level of significance. For η t , we use the two point distribution proposed by [START_REF] Mammen | Bootstrap and wild bootstrap for high dimensional linear models[END_REF]. The number of bootstrap replications B is set at 500 in this study, which is well-known to be sufficient for the construction of bootstrap confidence interval.

Measuring the Degree of Return Predictability

The AQ and AV R(k * ) tests described above are used to evaluate statistical significance of return predictability. However, evaluation of effect size is also important, which in this case represents the magnitude of the degree of return predictability.

Note that the AQ and AV R(k * ) statistics can be used as natural measures of return predictability3 . Since the AQ statistic is the sum of squared sample autocorrelations of Y t to the optimal order (scaled by the sample size), a higher value of AQ statistic indicates a higher degree of return predictability. Similarly, the AV R(k * ) statistic is one plus a weighted sum of the autocorrelations to the optimal order, with positive and declining weights. The main difference between the AQ and AV R(k * ) statistics is that the former treats all sample autocorrelations to the optimal order with equal weights, while the latter provides higher weights to lower order sample autocorrelations. An attractive feature of the AV R(k * ) statistic is that it reveals the sign of overall autocorrelations of asset return. That is, the value of AV R(k * ) greater (less) than one indicates overall positive (negative) autocorrelations of asset return. This sign can be an important indicator to profit-seeking investors, as it provides a key signal to which trading strategies they should adopt (e.g., momentum vs. contrarian strategies).

Empirical Results

In this section, we present the data details and their descriptive properties. We also present the empirical results and discuss their implications.

Data and Computational Details

The sample data consists of daily closing spot prices and their log returns for gold, silver and platinum. The data spans from January 3, 1977 to October 23, 2013, with a total of 9,603 observations. The data are obtained from Thomson Financial Datastream. Figure 1 Similarly, the returns show high volatility in the early 1980's, followed by a long period of relative stability. From around 2005, the volatility becomes to a degree higher for all three metals. The period from 2005 represents the timing of US housing bubble, commodities boom, and the Global Financial Crisis, which have strong impact on the psychology of the markets for all financial assets including those of the precious metals.

We first present descriptive statistics for the return series calculated as the first logarithmic difference of the daily closing prices in Table 1 (see Figure 1). The results reveal that gold and platinum display higher mean returns than silver. In terms of standard deviation, gold exhibits the least volatility, while silver displays the highest volatility. All returns series display excess skewness, with negative skewness for gold and platinum and positive skewness for silver, indicating that the empirical distributions of the returns exhibit asymmetric shape (with longer left tail for gold and platinum). Excess kurtosis is observed for all return series, showing that their empirical distributions are leptokurtic, i.e. with substantially fatter tails (than the normal distribution). The Jarque-Bera test statistic is significant at the 1% level of significance for all series, indicating that the precious metal returns are highly non-normal. We also conduct the LM test for ARCH conditional heteroscedasticity 4 , with the strong evidence of conditional heteroscedasticity. Note that the tests for the MDH or return predictability presented in the previous section, which we employ for our empirical analysis, are found to show desirable size and power properties in small samples under non-normality and conditional heteroskedasticity (see [START_REF] Charles | Small sample properties of alternative tests for martingale difference hypothesis[END_REF]).

To evaluate time-varying return predictability, we use moving sub-sample window of 2 years, which consists of approximately 520 daily observations. This sample size is large enough to ensure desirable size and power properties of the tests employed (see [START_REF] Charles | Small sample properties of alternative tests for martingale difference hypothesis[END_REF]. The 2-year window is also suitable to capture the effects of changing market conditions. The first sub-sample window covers the period from January 1977 to December 1978. Then, the window moves forward by one month to cover the period of February 1977 to January 1979. The process continues to the end of data set. Through this process, we obtain monthly measures of time-varying return predictability. In this way, the periods or episodes of high degree of return predictability (with statistical significance) is identified, which in turn are related to the corresponding events and shocks. Note that the use of moving sub-sample window approach is not intended for multiple testing in this paper, but adopted as a means of measuring the degree of return predictability over time. It is also an effective guard against data snooping bias (see Hsu and Kuan, 2006). For the AVR tests, the AVR statistics are plotted along with their 95% confidence intervals under the null hypothesis. If an AVR value lies outside the confidence interval, the null hypothesis of MDH (no return predictability) is rejected at 5% level of significance, which is evidence against weak-from efficiency of the market.

Evaluating time-varying return predictability

As mentioned earlier, the AVR value less (greater) than 1 indicates the overall negative (positive) return autocorrelations.

The overall results indicate that all precious metals returns have been predictable in a number of periods. This means that the precious metals markets often show departure from market efficiency from time to time, which is consistent with the implications of the AMH. The gold market, however, has an extensive period of no return predictability in 2000's, while the silver and platinum markets have become mostly efficient from around 2005. All three returns have been showing predictable episodes depending on various economic events, with downward trend in return predictability. These findings are consistent with the prediction of the AMH of [START_REF] Lo | The adaptive markets hypothesis: Market efficiency from an evolutionary perspective[END_REF].

We also find strong evidence that the episodes of return predictability are closely related with the prevailing economic and market conditions. Table 2 provides a summary of the events that may have affected the precious metals markets in the chronological order.

Further Discussions

As observed above, the gold and silver markets exhibit a downward trend in return predictability. This feature is particularly clear in Figure 2, where the AQ statistics decline over time. This means that the degree of pricing efficiency has gradually improved from the late 1970's. This is consistent with the gradual improvement in the efficiency of the U.S. stock market from the early 1980's, reported in [START_REF] Gu | The evolution of market efficiency: 103 years daily data of Dow[END_REF] and [START_REF] Kim | Stock return predictability and the adaptive markets hypothesis: Evidence from century long U.S. Data[END_REF]. The latter authors attribute this to the technological innovations in financial markets and stability of U.S. macroeconomic fundamentals, which may also have influenced the precious metals markets. In contrast with the gold and silver markets, the platinum market does not exhibit such a downward trend of return predictability.

The higher degree of efficiency of gold market may be strongly related with the fact that it is the biggest market of all three metals, with an average of trading volume of US$32.5 billion for gold against US$4.5 billion and US$0. partly due to the fact that it was the first ETC to be created. 6 In addition, this provides easily accessible information for investors about the general market for gold to use in their decision making.

According to the AVR statistics reported in Figure 3 and Table 2, these metal returns are characterized by negative overall autocorrelations more often than positive ones. This feature is particulary strong for the silver market. In particular, for all markets, when the AVR statistics are statistically significant, they are mostly negative as evident from Table 2. The presence of negative autocorrelation can be explained by the overreaction hypothesis. The foundation of this hypothesis originated in applied psychology's overreaction hypothesis that predicts that people tend to overreact to dramatic news and events, regardless of whether these events are positive or negative in nature. This would lead to excessive optimism over good news and extreme pessimism over bad news (De Bondt andThaler, 1985, 1987).

As a result, prices tend to overshoot, causing mispricing to occur. Prices would deviate temporarily from their intrinsic values, originating in the medium-long term a mean-reverting effect. 7 A consequence of overreaction is the profitability of a contrarian portfolio strategy that exploits negative serial dependance. The defining characteristic of a contrarian strategy is the purchase of securities that have performed poorly in the past and the sale of assets that have performed well. Selling the winners and buying the losers will earn positive expected profits in the presence of negative serial correlation because current losers are likely to become winners and current winners are likely to become future loser. This feature may be of importance to profit-seeking investors. That is, the negative serial correlation could be evidence of price reversals, and would be consistent with a market where positive returns are more likely to follow negative returns and vice versa. Therefore, one implication of overreaction is positive expected profits from a contrarian investment rule [START_REF] Lo | When are contrarian profits due to stock market overreaction[END_REF]). There are thus reasons for contrarian investors to look favorably on precious metals.

Conclusion

Precious metals are important components of investment portfolios for individuals as well as for institutions, due mainly to their effectiveness as a hedge or safe haven.

A key question to many investors and traders is whether they should buy-and-hold these metals in their portfolio or actively trade them in order to gain extra profits. The question is closely related with the weak-form efficiency of these precious metals markets, which is a fundamental property of their return distributions over time. Given the accumulated evidence that these markets are heavily influenced by economic and political conditions, it is highly likely that the degree of market efficiency (or return predictability) change over time depending on such conditions This paper examined the weak-form efficiency of three precious metals (gold, silver, platinum) markets, in close association with [START_REF] Lo | The adaptive markets hypothesis: Market efficiency from an evolutionary perspective[END_REF] and their degree of predictability depends heavily on the prevailing economic and political conditions. This finding is consistent with the implications of the adaptive markets hypothesis. The degrees of return predictability of the gold and silver markets show a strong downward trend, which indicates that these markets have been gradually becoming more efficient over time. In particular, the gold market has been the most efficient, which may be strongly related with its attractiveness as an investible asset and its effectiveness as a vehicle for risk management.

The evidence obtained in this study points to a buy-and-hold strategy for precious metals, but profit opportunities may arise from time to time depending on prevailing economic and political conditions. We also observe that all three metals returns show strong tendency of negative autocorrelations, which is an important indicator to the investors and traders who may wish to exploit such profit opportunities. The corresponding 95% confidence intervals under the null of no return predictability are also plotted.

  al., 2001; Baur and McDermott, 2010; Daskalaki and Skiadopoulos, 2011; Batten et al., 2013). It has also been widely documented that gold protects investors' wealth against fluctuations in the foreign exchange value of the US dollar (Capie et al., 2005; Pukthuanthong and Roll, 2011; Reboredo, 2013; Ciner et al., 2013).

  , Christie-David, Chaudhry and Koch (2000), Ciner (2001), Batten, Ciner and Lucey (2010), Radetzki (1989), Riley (2010), Hood and Malik (2013), and Areal et al. (2014). 2 These events have strong implications to the psychology of market participants and the way the markets incorporate new information into the prices, which in turn may cause time variations in serial correlation of returns.

  displays the metal prices and their log returns. All three prices show instability around 1980, especially with the silver. All three prices are relatively stable until about 2005, where they all show clear upward trends.

Figures 1 -

 1 Figures 1-6 report the AQ and AVR test statistics obtained from moving sub-sample windows, monthly from January 1979 to November 2013. For the AQ statistic, the horizonal line indicate the 5% asymptotic critical value of 3.89. The AQ value greater than the critical value indicates the rejection of the null hypothesis of MDH.

  For gold, the AQ and AVR tests reject the MDH in 1982. The timing corresponds to the US tight monetary policy, leading to a recession and high interest rates in 1982, which also coincide with the timing of the intervention of the Reagan administration for concerted interventions with major central banks to slow down the appreciation of the dollar. As the sub-sample window moves to 1985, both tests reject the MDH for gold, which coincides with tensions in South African gold mines. For the silver market, both tests reject the MDH during the period 1978-1979 which can be explained by the silver manipulation due to the Hunt brothers to corner the silver market. 5 The rejection of the MDH by the AQ test at the end of 1984 coincides with the opening of the silver options market on the Commodity Exchange in October 1984, in which traders will be able to trade exchange-traded options on Comex's silver futures at prices determined by a continuing auction and not by dealer fiat. As the subsample window moves to 1989, the AQ and AVR tests reject the MDH with high level of dollar in 1989, the invasion of Kuwait by Iraq in August 1990, and the Operation Desert Storm in January 1991. Contraction in demand from jewelery, photographic and electronic industries, coupled with rising in supply from Mexico and Peru, may be closely related with the rejection of MDH for silver in the beginning of 2000s. The AQ and AVR tests reject the MDH for platinum at the end of 1984. The timing corresponds to the filing under Chapter 11 of the bankruptcy code in December 1984 of Deak & Company, one of the largest company of precious metal dealers. The MDH is rejected for the platinum market when the sub-sample window moves forward to the end of 1988 after Ford Motor Company announced a pilot program to eliminate the precious metal from catalytic converters. Both tests started to move to the rejection region in the beginning of 2000 for platinum with high demand from automotive and jewelery industries and the Russian restricting policy in delivery (exportation). The AQ test rejects the MDH from the mid 2002 with increasing automotive industrial demand and problems of production due to fear of tensions (strikes) in Russian and South African producers. The AVR test rejects the MDH from the beginning of 2007 with high demand from jewelery and automobile industries, and low level of the South African mining production. For all three precious metals, the AQ and AVR tests start to move to the rejection region from the end of 1992, indicating a strong deviation from the MDH with inflation fears and expectations for higher interest rates in the US, and the Mexican political assassination (presidential candidate Colosio). The MDH is rejected by both tests for gold and silver when the sub-sample window moves forward to 1997 with the Asian and Russian crises. The announcements of central banks to support the economy can explain the rejection of the MDH for platinum by the AVR test from the mid-2012. Further, the AVR test rejects the MDH for platinum in mid-2013 with possible changes in monetary policy announced by the Fed Chairman Ben Bernanke and fears of economic slowdown. The rejection of MDH from the AVR test for silver and platinum at the end of 2013 can be explained by bad news on US economy and the fall of the dollar.

Figure 2 : 23 Figure 3 :

 2233 Figure 2: Automatic Q statistics: 1979-2013

  Let Y t denote asset return at time t, where t = 1, ..., T . Under the null hypothesis of no asset return predictability, Y t is a strictly stationary and ergodic martingale difference sequence (MDS) with appropriate moment conditions (see Escanciano and Lobato, 2009; Assumption A1). The original portmanteau test statistic is written as

Table 1 :

 1 Descriptive statistics for daily returns

		Mean (×100) Std. dev. Skewness Kurtosis	JB	ARCH(10)
	Gold	0.024	0.012	-0.41 *	17.22 *	13980.7 *	1212.9 *
	Silver	0.017	0.024	0.05 *	37.96 *	39068.3 *	2823.2 *
	Platinum	0.024	0.017	-0.47 *	12.68 *	8339.1 *	1177.6

*

Note: * indicates statistical significance at the 5% level. JB and ARCH

[START_REF] Bauer | Is gold a safe haven? International evidence[END_REF]

are the Jarque-Bera test for normality and the LM test for conditional heteroscedasticity, respectively.

  [START_REF] Shafiee | An overview of global gold market and gold price forecasting[END_REF]. The gold ETFs have stimulated the demand side of gold because it has become as easy to trade as it is to trade any stock or share(World Gold Council, 2008). The gold demand for the ETFs was US$1.7 billion in 2004 and US$279 billion in 2012 (World Gold Council, 2013).

	8 billion for silver
	and platinum, respectively, on the 2006-2010 period (World Gold Council, 2011).
	It is also becoming an attractive and important investment product for a range of
	investors in the financial market for diversification and hedging purposes. Investing
	in gold is becoming easier via gold Exchange Traded Funds (ETFs) compared to
	other finance markets (Further, in 2008, 65% of all Exchange Traded Commodities (ETCs) are exposed to
	gold, with the remaining 35% exposed to other commodities. Gold's dominance is

  adaptive markets hypothesis. Using the daily data from 1977 to 2013, we calculate the monthly measures of return predictability and conduct the tests for no return predictability over time. For this purpose, we employ the automatic portmanteau test of Escanciano and Lobato (2009) and automatic variance ratio test of[START_REF] Kim | Automatic variance ratio test under conditional heteroskedasticty[END_REF], which possess desirable small sample properties (see[START_REF] Charles | Small sample properties of alternative tests for martingale difference hypothesis[END_REF]. The main finding of our study is that the three markets show time-varying return predictability over time,7 Recently,[START_REF] Aggarwal | Rationality in precious metals forward markets: Evidence of behavioural deviations in the gold markets[END_REF] document that gold forward markets overreact.

Table 2 :

 2 Major Events for the Eposiodes of High Return Predictability

	Period	Events	Autocorrelations
			Gold	Silver	Platinum
	1978-1979 Silver Thursday		negative
	1982	US tight monetary policy
		US$ Intervention	negative
	1984	Opening of Silvers Options Markets		negative
	1984	Deak & Company Bankrupt		negative
	1985	Tensions in South African mines	negative
	1989	High US dollar		negative
	1988	Ford Company Policy Change		negative
	1990-1991 Iraqi Invasion of Kuwait
		Operation Desert Storm		negative
	1992	Inflation fears and higher interest
		rates expectation in US
		Mexican assassination	negative negative	negative
	1997	Asian and Russian Crisis		negative
	2000	Contracting Demand
		and Rising Supply		negative
	2000	High Demand for Platinum
		and Russian Restricting policy		negative
	2002	Higher Demand from Automotive
		Industry and Tensions is Russian
		and South African Producers		positive
	2007	High Demand and low Production		negative

Note: Positive (negative) indicates overall positive (negative) autocorrelations as indicated by the AVR statistic.

The major demands in precious metals in

are: jewelry (58%), investment (22%) and electronics (7%) for gold; investment (23%), electrical and electronics (22%) and jewelry (18%) for silver; and autocatalyst (37%), jewelry (33%) and investment (9%) for platinum.

Overall, the findings on precious metals are consistent with the view ofErb and Harvey (2006, p. 69) who find that "commodity futures returns have been largely uncorrelated with one another " or that ofBatten et al. (2010, p. 65) who suggest that "individual commodities are too distinct to be considered a single asset class or represented by a single index ". Gold volatility is shown explained by monetary variables, but this is not true for silver. Silver volatility seems to respond strongly to the influences of the other precious metals. Platinum and palladium appear to more likely act as a financial market instrument than gold. Gold also seems to be highly sensitive to exchange rate and inflation, which implies that it is the best hedge during inflationary pressures and exchange fluctuations[START_REF] Batten | The macroeconomic determinants of volatility in precious metals markets[END_REF][START_REF] Arouri | Long memory and structural breaks in modeling the return and volatility dynamics of precious metals[END_REF].

[START_REF] Griffin | Do market efficiency measures yield correct inferences? A comparison of developed and emerging markets[END_REF] use the absolute value of V R(k) -1 as a measure of return predictability.

The LM test is applied on the residuals of the ARMA model, where the lag length is selected based on the Akaike information criterion.

The largest single day drop in the price of silver occurred on Silver Thursday (March 27, 1980), leading panic on commodity markets.

On March 28, 2003, the first gold-backed ETF, developed by ETF Securities, was launched. It trades on the Australian stock exchange as the ETFS Physical Gold. Globally, there are now 143 gold ETFs available. The first ETF for silver and platinum was launched in April 2006 and in April 2007, respectively.

* Olivier Darné gratefully acknowledge financial support from the Chaire Finance of the University of Nantes Research Foundation.