On the efficiency of the global gold markets

ﬁ (RWS) and martingale difference sequence (MDS) hypotheses, and consequently, investigates the extent to whichpredictabilityornon-predictability ofglobaldailyspotgoldpricereturnseriesbehaviourcanbeexplained byvolatilitiesinmacroeconomicfundamentals.Weapplytraditionalparametricvariance-ratiotestsandtheirre- centnon-parametricmodi ﬁ cationsbasedonranksandsignstooneofthelargestdatasetsonworldgoldmarkets to-date,consistingofdailyspotpriceseriesof28emerginganddevelopedgoldmarketsfromJanuary1968toAu- gust 2014. First, our results show that gold markets in Egypt, Indonesia, Mexico, Nepal, Pakistan, Russia, Saudi Arabia, UAE and Vietnam are not weak-form ef ﬁ cient neither from the perspective of the strict RWS nor in the relaxed MDS sense. By contrast, RWS and MDS hypotheses cannot be rejected for gold markets in Hong Kong, Japan, Switzerland, UK and US at the conventional rejection levels. Results for gold markets in Australia, Bahrain, Brazil, Canada, China, Germany, India, Malaysia, Singapore, South Africa, South Korea, Taiwan, Thailand and Turkey are, however, mixed. Second, our ﬁ ndings show that greater changes in economic funda- mentals are associated with lower levels of rejecting the RWS and MDS hypotheses. Third, our evidence shows that the probability of rejecting the weak-form ef ﬁ ciency is higher in emerging gold markets than developed ones. Fourth, our results show that the RWS hypothesis is rejected more frequently than its MDS alternative, and thereby justifying our decision to conduct an explicit test of the RWS and MDS hypotheses. Our results are robusttoestimatingsubsamples,overlappingrollingwindowsandendogeneitycorrectedmodels,aswellascon-trolling for a number of country-speci ﬁ c institutional and trading factors. Our ﬁ ndings have crucial implications for global portfolio managers, investors, poly-makers and regulatory authorities.


Introduction
In this paper, we seek to contribute to the extant international finance and financial markets literature in two main waysby examining the: (i) weak-form efficiency of daily gold spot price return series of a large number of global gold markets with particular focus on testing the random walks (RWS) and martingales difference sequence (MDS) hypotheses; and (ii) extent to which gold price returns predictability or non-predictability can be explained by volatilities in macroeconomic fundamentals. Specifically, and to the best of our knowledge, we provide evidence for the first time in 17 gold markets (i.e., Bahrain, Brazil, Egypt, Indonesia, Malaysia, Mexico, Nepal, Pakistan, Russia, Saudi Arabia, Singapore, South Africa, South Korea, Taiwan, Thailand, UAE and Vietnam) and extend prior findings in 11 gold markets (i.e., Australia, Canada, China, Germany, Hong Kong, India, Japan, Switzerland, Turkey, UK and US) relating to the efficiency and determinants of gold price return series behaviour.
There are, however, a number of observable weaknesses within the current literature, especially with respect to studies that focus on the efficiency of gold prices. First, the findings of previous studies that explicitly examine the weak-form efficiency of gold returns are widely mixed, even within the same study. For example, evidence by Tschoegl (1978Tschoegl ( , 1980, Ball et al. (1985), Beckers (1984), Ho (1985) and Pierdzioch et al. (2014) suggests that gold price returns are weakform efficient. By contrast, the findings of Solt and Swanson (1981), Ball et al. (1982), Basu and Clouse (1993), Narayan et al. (2010), Shafiee and Topal (2010), Baur (2013), and Blose and Gondhalekar (2013) suggest that gold prices are predictable, whilst those of Monroe and Cohn (1986), Smith (2002), Parisi et al. (2008), Wang, Wei, et al. (2011),  are mixed. Second, despite the conflicting findings, existing studies have mostly simply focused on testing rather than explaining efficiency, and in particular, the extent to which predictability or non-predictability of gold price returns can be explained by observable changes in the underlying macroeconomic variables.
Third, the existing weak-form efficiency studies on gold prices have tested mostly the RWS hypothesis with virtually no study providing explicit test of its MDS alternative. However, unlike the RWS, the MDS has the unique capacity to relax the strict gaussian-random variable assumption underlying the RWS hypothesis to permit for the possible existence of time-varying volatilities in an asset's return series like conditional-heteroscedasticity, which though expecting successive residual increments to be independent, does not necessarily require it to be identically distributed (iid), and thereby permitting a more powerful test of gold price return efficiency. Finally, despite the rapid growth and expansion in the size and number of global gold markets with gold being currently traded in organised futures, exchange traded funds (ETFs) and other derivative markets in about 40 countries (O'Callaghan, 1991;WGC, 2011WGC, , 2014a, existing studies have focused mostly on the Western European, Japanese, UK and US markets to the neglect of a relatively small, but rapidly growing emerging gold markets in Africa and Middle East, Asia-Pacific, Eastern-Europe and South America. This limits opportunities for comparative analysis of the findings between developed markets (matured and large) and emerging markets (new and small) gold markets, and thereby arguably impairing a more complete international understanding of the gold price return behaviour.
Consequently, the current study seeks to address the limitations of prior studies on the weak-form efficiency of gold price returns, and thereby extending, as well as making a number of new contributions to the extant international finance literature. First, we contribute to the literature by testing the weak-form efficiency in the price series of the global gold markets. However, rather than simply testing for weak-form efficiency of gold price returns, we take a different approach from prior studies by simultaneously examining the extent to which volatilities in the underlying macroeconomic fundamentals (e.g., exchange, inflation, and interbank rates) can explain observable efficiencies and inefficiencies in the gold returns series. As prior studies suggest that macroeconomic variables drive gold prices (Apergis, 2014;Batten, Ciner, & Lucey, 2010;Christie-David et al., 2000;Feldstein, 1980;Lili & Chengmei, 2013;Narayan et al., 2010;Shafiee & Topal, 2010;Tully & Lucey, 2007), we conjecture that increased volatilities in such fundamentals may equally be associated with rapid changes in the efficiency of gold price returns series and vice-versa. Second, we contribute to the literature by explicitly offering evidence on the RWS and MDS hypotheses, and thereby allowing us to provide a more robust test of the weak-form efficiency for gold prices and markets. Third, to the best of our knowledge, we employ for the first time the Wright's (2000) non-parametric variance-ratio tests based on ranks and signs alongside its MacKinlay (1988, 1989) parametric alternative. In several Monte Carlo tests, Wright shows that his non-parametric alternative is better specified, and thereby permitting us to provide a more robust tests of the RWS and MDS. Finally, we employ daily gold spot price return series between 1968 and 2014 from organised markets in 28 countries with developed and emerging gold markets spanning over every continent. This is by far one of the most extensive and up-to-date gold price returns datasets to be used to-date. This allows us not only to shed new insights on gold price return behaviour around the world, but also conduct a comparative analysis between developed and emerging gold markets over a relatively long period of time (i.e., 46 year-period).
Our results contribute to the literature in several ways. First, our findings show that gold markets in Egypt, Indonesia, Mexico, Nepal, Pakistan, Russia, Saudi Arabia, UAE and Vietnam are not weak-form efficient neither from the perspective of the strict RWS nor in the relaxed MDS sense, but both hypotheses cannot be rejected for gold markets in Hong Kong, Japan, Switzerland, UK and US. We, however, find mixed results for gold markets in Australia, Bahrain, Brazil, Canada, China, Germany, India, Malaysia, Singapore, South Africa, South Korea, Taiwan, Thailand and Turkey. Second, our findings show that higher volatilities in macroeconomic variables (i.e., crude oil price, inflation rate, interbank rate, multilateral exchange rate and share price) are associated with lower levels of rejecting the RWS and MDS hypotheses. Third, our results show that the RWS hypothesis is rejected more frequently than its MDS alternative with the nonparametric variance-ratio tests producing more consistent findings compared with the parametric tests. Fourth, our evidence shows that the probability of rejecting the weak-form efficiency is higher in emerging gold markets than developed ones. Our results are robust to estimating subsamples, overlapping rolling windows and endogeneity consistent models, as well as controlling for a number of countryspecific institutional and trading factors. Our findings have crucial implications for global portfolio managers, investors, poly-makers and regulatory authorities.
The remainder of the paper is organised as follows. Section 2 reviews the prior empirical literature on the efficiency of gold markets. Section 3 provides an overview of the global gold market. Section 4 describes data and research methodology. Section 5 presents empirical results and discussion, whilst Section 6 concludes.
With specific reference to the behaviour of gold prices, Tschoegl (1978Tschoegl ( , 1980, Booth and Kaen (1979), and Solt and Swanson (1981) are amongst the pioneers to explicitly investigate the weak-form efficiency of the gold market, although they report mixed findings. Whereas the findings of Tschoegl (1978Tschoegl ( , 1980 suggest that the null hypothesis that information contained in the sequences of successive price changes cannot be forecasted is not rejected in daily and monthly return series of London morning (AM) and afternoon (PM) 'fixing' gold prices from January 1975 to June 1977, those of Solt and Swanson (1981) reject the notion of random walks in monthly, quarterly and yearly return series of London Friday closing (PM) gold prices from 1971 to 1979. The results of Booth and Kaen (1979) based on daily changes in US spot gold prices from January 1972 to June 1977 also rejected the RWS hypothesis, implying that US gold prices were predictable. Similarly, Ball et al. (1982) report evidence of a weekend effect in daily AM and PM London 'fixing' gold price series using data from 1975 to 1979, suggesting that gold price returns are significantly different during weekends than weekdays. Additionally, Beckers (1984) and Ho (1985) have independently examined the weak-form efficiency in the daily gold price return series of the Dutch (i.e., daily gold options prices on the European Options Exchange from January to December 1981) and UK (i.e., daily closing/'fixing' prices on the London gold market from 1979 to 1980) gold markets, respectively. The results of both studies fail to reject the notion of weak-form efficiency in both gold markets. The findings of Beckers (1984) have been supported by those of Ball et al. (1985), which also failed to reject the RWS hypothesis in daily gold option prices of the same Dutch-based European Options Exchange from April 1981 to June 1982. However, the results of Monroe and Cohn (1986) using monthly price series of gold futures traded on the Chicago Mercantile Exchange from 1976 to 1982 are mixed. Specifically, their findings suggest that the RWS hypothesis is rejected for the Chicago gold futures market in some periods, but not for other periods, implying that gold futures price series' weak-form efficiency changes over-time.
It is worth noting that mixed evidence relating to the random walk behaviour in gold price series reported by these studies are largely consistent with those of similar earlier indirect tests that sought to detect random gold price movements by Lipschitz and Otani (1977), McDonald and Solnik (1977) and Abken (1980). Equally important, however, is that most of the studies conducted in this era are discernibly based on the application of simple traditional statistical techniques (e.g., autocorrelation, runs, and unit root tests) (Beckers, 1984;Booth & Kaen, 1979;Ho, 1985;Monroe & Cohn, 1986;Solt & Swanson, 1981;Tschoegl, 1978Tschoegl, , 1980. A major weakness of all these simple techniques is that they assume linearity in financial asset price return series (Ntim, 2012;Ntim et al., 2007Ntim et al., , 2011Savit, 1988), often leading to spurious rejection or acceptance of the RWS hypothesis (Chow & Denning, 1993;Hsieh, 1991;Luger, 2003;Wright, 2000).
Consequently, and with the availability of more powerful computers coupled with advances in econometric and mathematical modelling (Belaire-Franch & Opong, 2005a,b, 2010, recent studies examining whether gold prices follow random walk behaviour mainly employ powerful and sophisticated statistical techniques (e.g., chaos, fractals, neural networks, variance-ratios, and ARCH-GARCH models) (Parisi et al., 2008;Pierdzioch et al., 2014;Shafiee & Topal, 2010;Wang, Wei, et al., 2011). These advanced mathematical techniques are generally capable of dealing with security return series with non-linear distributions, and thereby providing a more precise test of the RWS hypothesis. However, the findings of recent studies employing more sophisticated statistical techniques are still generally mixed (Basu & Clouse, 1993;Christie-David et al., 2000;Mills, 2004;Narayan et al., 2010;Yu & Shih, 2011;Baur, 2013;Blose & Gondhalekar, 2013). For example, using real-time forecasting approach and London monthly PM 'fixing' gold prices between 2000 and 2010, the findings of Pierdzioch et al. (2014) suggest that the London gold market is weak-form efficient. By contrast, utilising long-term trend reverting jump and dip diffusion model to monthly spot gold prices from 1968 to 2008, the results of Shafiee and Topal (2010) reject the RWS hypothesis in the UK gold markets. Similarly, Baur (2013) and Blose and Gondhalekar (2013) document evidence of an existence of significant autumn and weekend effects in UK and US gold returns, respectively, suggesting that UK and US gold markets are weak-form inefficient. The findings of Smith (2002) for the UK gold market, Parisi et al. (2008) for the US gold market, and Wang, Wei et al. (2011 for the US gold market, who employed variance-ratio, neural networks, and multifractals statistical techniques, respectively, are rather mixed. For example, Smith (2002) examines the RWS hypothesis for daily London AM, PM and over-the-counter (OTC) or 'closing' gold prices from January 1990 to September 2001 by employing Chow and Denning's (1993) multiple variance-ratio tests, with his findings suggesting that London AM and PM return series are not weak-form efficient, whilst that of the OTC market appears to be randomly generated.
Thus, it is evident from above that the current literature seems to suffer from a number of weaknesses. First, despite the apparent conflicting findings, existing studies simply test rather than seek to identify factors that may explain consistencies or deviations from the RWS hypothesis. However, past studies suggest that gold prices are determined by a number of macroeconomic factors (Batten et al., 2010;Davidson et al., 2003;Tully & Lucey, 2007;Wang, Wei et al., 2011). For example, and briefly, high levels of inflationary pressures can render local currencies less attractive and increase the demand for gold, and thus increased gold price volatility (e.g., Wang, Wei, et al., 2011), and vice-versa. Similar theoretical arguments can be made for other macroeconomic variables, such as exchanges rates, interest rates, crude oil price, money supply and property prices (e.g., Blose, 1996;Capie et al., 2005;Baur & McDermott, 2010). Hence, we depart from most prior studies to not just simply test the weak-form efficiency, but also attempt to ascertain whether the degree of efficiency may be influenced by the extent of volatilities in the underlying macroeconomic fundamentals. Second, despite the development and expansion in formally organised gold markets worldwide primarily through gold futures, ETFs and other gold derivatives (Fuangkasem, Chunhachinda, & Nathaphan, 2012;O'Callaghan, 1991;Tully & Lucey, 2007;WGC, 2014a,b), existing studies on the behaviour of gold price series are concentrated in a few developed gold markets, especially UK and US, with emerging gold market studies by Rockerbie (1999) on South Africa, Muradoglu et al. (1998) and Kutan and Aksoy (2004) on Turkey, Mani and Vuyyuri (2003) and Fuangkasem et al. (2012) on India, Baur and McDermott (2010) and Lucey et al. (2014) that include a number of emerging gold markets, such as Brazil, China, and India, and Apergis (2014) on Australia being rare exceptions. Even amongst these limited studies on emerging gold markets, only Muradoglu et al. (1998), and Kutan and Aksoy (2004) directly examine the efficiency of gold price return series. Arguably, this limits opportunities for comparative analysis relating to the predictability of gold prices in developed and emerging gold markets. We, therefore, address this weakness by conducting our tests in both developed and emerging gold markets. Third, existing studies examining whether gold prices are predictable have focused mostly on testing the RWS hypothesis compared with its MDS alternative. However, as the MDS is able to relax the strict independent and identically distributed (iid) returns assumption implies that it is better able to provide a more conclusive weak-form efficiency test. Hence, we explicitly develop and test both the RWS and MDS hypotheses. Finally, to the best of our knowledge, we employ for the first time Wright's (2000) nonparametric tests based on ranks and signs to the weak-form efficiency in gold price return series, which are known to be robust even in the presence of conditional heteroscedasticity.

An overview of the global gold market
Unlike markets for other modern financial assets, the gold market has ancient origins. However, a truly 'free' market for gold did not emerge until the dissolution of the Bretton Woods gold standard monetary system between 1968 and 1973 (i.e., a system in which the standard unit of exchange was determined by a specified quantity of gold, originally pegged at US$35 or GBP£12.50 to a quantity of 1 oz of gold). Thus, the introduction of a 'free' gold market transformed gold trading in that it allowed gold to be officially traded widely around the globe. Nevertheless, the current global gold market can narrowly be classified into two, namely in: (i) London's OTC (24 h) cash (spot) centred bullion market; and (ii) gold futures, ETFs and other gold derivative markets worldwide (Lucey et al., 2013(Lucey et al., , 2014. A closer examination, however, reveals a slightly more broad and complex picture than this simple two-tier or 'bipolar' classification of the global gold market. In particular, O'Callaghan (1991) offers a detailed historical overview of the structure, operation and market microstructure of the global gold market. Thus, we draw from the prior literature, especially O'Callaghan (1991) in classifying the global gold market as follows: (i). UKthe oldest, largest, most liquid and influential organised market. (ii). A group of matured and large organised markets, consisting of Hong Kong, Singapore and Switzerland that have become global trading, storage and distribution centres ('transit markets') of physical gold bullion bars. (iii). A group of matured and large organised markets, consisting of Brazil, Canada, Japan, Netherlands and US who are pioneers of high frequency exchange-based trading of financial gold products (i.e., ETFs, futures, and other gold derivatives). (iv). A group of medium-sized markets, including Australia, the mainland European market (e.g., Belgium, France, Germany, Italy, and Luxembourg), South Africa, and Turkey. (v). A group of small, but rapidly growing markets in Asia-Pacific (e.g., China, India, Indonesia, Malaysia, Philippines, South Korea, Taiwan, Thailand and Vietnam), Eastern Europe (e.g., Russia), and Middle East (e.g., Bahrain, Jordan, Kuwait, Saudi Arabia and UAE). (vi). Finally, a group of very small (frontier) markets that are struggling to take-off in Africa and Middle East (e.g., Egypt, Kenya and Israel), Asia-Pacific (e.g., Nepal and Pakistan), and the Americas (e.g., Mexico). Table 1 summarises some of the trading arrangements (i.e., formal trading date, days, hours, system, cash/physical settlement, contract specifications, clearing and settlement days, markets and cities) of the sampled gold markets, whilst Table 2 reports some descriptive statistics, primarily relating to gold and other financial market development indicators (i.e., number of commodity futures/options, gold in tonnes, gold in US$m, total foreign exchange reserves excluding gold in US$m, total reserves in US$m, gold as a % of total reserves, equity market capitalisation as a % of GDP, and total number of equity listed) as at the end of the sampled period. As Table 1 shows, the UK (London) is the oldest known organised gold market, having started around 1800, but has observably experienced a chequered history (closed and re-opened several times, for example, in 1840, 1919, 1939, 1954 and 1968) (see O'Callaghan, 1991, p. 19). The London market started with its five original brokers, who informally traded in gold bullions with mining companies and refineries until 1919, where the market was officially established. It gained further prominence in 1987 when its membership was expanded through the formation of the London Bullion Market Association (LBMA), which currently has 53 full members (dealers), including the five London gold price 'fix' members and 33 associate members (see Table 1) and loosely supervised by the Bank of England. London is by far the biggest gold market in the world both in size and volume. For example, on average, 18.3 m ounces of gold worth US$13.9bn were reportedly cleared daily by the LBMA in 2008. Similarly, London as a gold trading centre accounted for about 86% of the total global volume traded in 2011 (Lucey et al., 2013, p. 813). As Table 1 shows, the London gold market is essentially an OTC cash centred spot pricing of gold bullion (i.e., gold bars) market, and thereby guaranteeing continuous (24 h) trading of gold bullions   worldwide. Usually the gold bars must be 99.5% purity or fineness in gold content of 400 ounces (400 oz) in size per contract, although other contract specifications, such as 99.95% or 99.99% with 100 oz are available. The London market opens formally for trading between 8 am and 5 pm from Monday to Friday and similar to most markets around the world, trades are normally quoted in US$ (this is explained by the fact that gold was valued mainly in US dollars during the international gold standard monetary system period), which are settled in cash over 2 trading days.
Although primarily a spot market, in April 1982, the London gold futures market was opened and the London Stock Exchange (LSE) also trades in gold futures, options, ETFs and other derivatives with minimum price movement of US$0.10 per gramme (within a 5% initial margin trading) and no maximum price movement limit with opportunities for both cash and physical settlement. However, what makes London the most liquid and influential market in the world is arguably its twice-daily (morning/AM -10.30 am and afternoon/PM -3 pm) spot price 'fixings' (O'Callaghan, 1991). The price is famously 'fixed' by the influential five ('quintupoly') LBMA gold 'fix' members, currently consisting of Barclays Capital, HSBC, Societe Generale, Bank of Nova Scotia (current chair), and Rothschild & Sons. The 'fix' typically begins with the chairman suggesting a starting price with each participant linked to its trading room via a telephone in which each firm is regularly updated by the chairman as to whether it is a net seller or buyer at a particular price. The price is altered until equilibrium price is reached and subsequently the 'fix' is declared and announced immediately. The 'fix' price then becomes the reference point or benchmark for all gold markets around the world and thus, almost every other gold market in the world quotes the London (loco-London) AM and PM 'fix' prices, as well as its own local market price. In fact, the importance of the London 'fix' has been summed up by Smith (1981, p. 77) as follows: "Because of its format and the expertise of its members, and the communication from London, I believe that the fixings are trulythe trulygenuine open outcry market, where real volume can be moved at one pricea price at which anyone in the world can participate in directly, or through some else, and it is a price that is published for all people to see (cited in O'Callaghan, 1991, p. 20)". The 'fix' used to be conducted once daily (10.30 am), but the 3 pm 'fix' was introduced in the 1960s to allow US investors to participate in the trading. A notable downside of the London spot gold 'fix' pricing system is that because each participant in the market communicates its net position, it is difficult to determine the actual volume of gold transacted at any 'fix'.
Apart from London, trading in Hong Kong, Singapore and Switzerland together constitutes the next biggest physical gold bullion market in the world. A common characteristic of these three markets is that they are large centres for the trading, storage and distribution ('transit markets') of gold bullion bars with Hong Kong and Singapore serving the Asia-Pacific market (e.g., China and India), whilst Switzerland serving the European market. These markets are also relatively old, large and matured. For example, and as Table 1 shows, the Hong Kong market (Chinese Gold and Silver Exchange Society -CGSE) has informally existed since 1910, officially growing rapidly from 1974. Daily trading takes place from Monday to Saturday with trading typically settled over 2 days with both cash and physical settlements possible. Unlike London, but similar to New York, a small number of trading is still conducted in the open outcry market with a daily price 'fixing' at 11.30 am, but trading is mainly electronic-based with prices quoted in both London prices (loco-London) and Hong Kong dollars (loco-Hong Kong) in traditional 100 Chinese tael per contract of 99% fineness. Any transaction of 35 kg attracts no initial trading margins, but any trading above 35 kg attracts an initial margin of HKD140,000 for each 5 kg of additional trading with a minimum price movement of HKD0.50 per tael and no maximum price movement limit.
The Singapore gold market was officially set up in 1969primarily a cash-based market with 5 days trading between 8.3 am and 11.25 am of 25 kg per contract of 99.99% purity. There is a 10% initial margin requirement with a minimum price movement of SGD0.005 per gramme and no maximum price movement limit with settlement over 2 trading days. Unlike the Hong Kong and Singapore markets, the Switzerland gold market (Zurich) was established in 1961 following the closure of the London market in 1939 for trading, storage and distribution of physical gold bullion bars. In fact, it is the largest physical gold bullion market after London. Popularly known as the Zurich 'Gold Pool', the market is distinctively informal and unregulated, remaining a loose co-operation amongst the three Swiss major banks -Credit Suisse, Union Bank, and Swiss Bank. Unlike London and Hong Kong, however, there is no price fixing system in the Zurich market. Instead, at any given time of each trading day (i.e., Monday to Friday between 8 am and 5 pm of 100 oz per contract with 99.95% fineness and settled within 2 trading days), the price is set based on the interplay of demand and supply forces. Hence, the market encourages direct competition amongst its participants, which has a minimum price movement of CHF0.10 per ounce and no maximum price limits or restrictions within an electronic trading platform.
In contrast to the large physical gold bullion markets in Hong Kong, Singapore, Switzerland and UK, Brazil, Canada, Japan, Netherlands and US were amongst the pioneers who helped in developing the financial gold products market (i.e., futures, options, ETFs and other derivatives) in organised exchanges often set-up in a high frequency electronic trading environment. According to O'Callaghan (1991), the first gold futures contract was launched in the Canadian Winnipeg Commodity Exchange (WCE) in 1972. This was followed by the launching of gold futures contracts on a number of commodity exchanges, including the New York Mercantile Exchange (NYMEX), especially its commodity division (COMEX) and Chicago Mercantile Exchange (CME) in 1974, the European Options Exchange (EOE) in Amsterdam in 1978, Tokyo Commodity Exchange (TOCOM) in 1982 and Brazilian Mercantile and Futures Exchange (BM&F) in Sao Paulo in 1986. This development sparked rapid development of, and expansion in, the trading of financial gold products and markets around the globe. 1 In fact, most of the remaining gold markets 2 in Table 1 are gold futures market offering varying choices in terms of products, contract specifications and other trading arrangements.
Additionally, and as Table 2 shows, the past decades have witnessed rapid development of relatively large financial markets outside those of traditional countries with advanced financial markets, such as Japan, UK and US. For example, equity market capitalisation as a percentage of GDP, one measure of financial development for India in 2013 was 130%, comparing favourably with that of the US of about 111%. Similarly, the number of commodity futures and options contracts traded in 2013 in China was the highest in the world at about 142 m. India has the highest number of listed firms, and although US is a dominant player in terms of total global gold reserves market (i.e., in terms of tonnes, US$m, FX reserves in US$m, total reserves in US$m and gold as a % of total reserves), Table 2 shows that a clear majority is held outside the traditional markets of Japan, UK and US. However, and notwithstanding the existence of a large and diverse global gold market, prior studies on the efficiency of the gold markets are concentrated mainly in a few matured gold markets, especially UK and UK, and thereby arguably limiting the current understanding of the price behaviour of the global gold markets. The current study, therefore, seeks to extend, as well as provide new insights on the efficiency of both emerging and developed gold markets.

Data
We employ two main types of datasets in testing our hypotheses. First, we use daily spot gold price return series of gold markets in 28 countries from four major continents (i.e., Africa and Middle East, Americas, Asia-Pacific, and Europe) form January 1968 to August 2014. All the daily spot gold prices are quoted in the relevant local currencies. Thus, our returns series span over 46 years, ranging from the longest period of 3 January 1968 to 13 August 2014 for the UK (12,162 daily observations) to the shortest period of 24 June 2010 to 13 August 2014 for Taiwan (1080 daily observations). The data was collected from two main sources, namely the: (i) World Gold Council (WGC) website; and (ii) DataStream database. The data begins from January 1968 because it was the first year in which the gold price was 'freely' set by market forces around the world, and ends in August 2014 because it was the latest year for which data was available in the WGC and DataStream databases at the time of data collection. Second, we collect data on macroeconomic fundamentals, including broad money (M2+) supply, crude oil price, inflation (consumer price index -CPI) rate, interbank (overnight) borrowing rate, interest (3-month treasury-bill ratet-bill), multilateral exchange rate, residential property price and share price. Macroeconomic data on multilateral (effective) exchange rate and residential property prices were collected from the Bank for International Settlement (BIS) website, whilst the data on broad money supply, inflation (CPI) rate, interbank rate, interest (t-bill) rate, and share price were collected from DataStream. Twentyeight gold markets were included in the sample because they were the countries for which data was available on them in the BIS, WGC and/or DataStream databases. For brevity, Tables 3 and 7 provide additional detailed descriptions of the dataset used.

The RWS and MDS hypotheses
The strict RWS and the relaxed MDS hypotheses of the weak-form market efficiency are explicitly tested. The RWS hypothesis indicates Notes: A-D and K-S represent Anderson-Darling and Kolmogorov-Smirnov goodness-of-fit absolute values with *** and ** means that the log-normality assumption is rejected at the 1% and 5% levels, respectively. Panels A, B, C, and D present descriptive statistics and diagnostics of the daily spot gold price return series of African and Middle Eastern, the Americas, Asian-Pacific, and European gold markets, respectively. Volatility is the standard deviation (SD) of the spot gold price return series, whilst N refers to the number of time series observations. The daily gold spot prices were collected from two main sources: (i) DataStream and ( that in an efficient market, successive price changes follow that of a gaussian-random variable (iid). This means that future price changes cannot be predicted based on past price history. In line with Campbell et al. (1997), a financial asset's price series (P t ) is said to follow a random walk, if: P t = μ + P t − 1 + ε t , ε t~I DD N(0, ∂ 2 ), where (P t ) refers to the log of the asset's return series under consideration (i.e., the daily gold spot price return series) at time (day) t; μ is an arbitrary drift parameter; and the error term ε t~I DD N(0, ∂ 2 ) is independently and identically distributed (iid) with zero mean and unit variance (∂ 2 ). Thus, the strict RWS hypothesis to be tested is as follows: H1. The global daily spot gold price return series follow a random walk.
On the other hand, an asset's price series (P t ) is said to follow a martingale difference sequence (MDS) if it meets the following condition: E[P t + 1 − P t |P t , P t − 1 , …] = 0, where (P t ) is the log of the asset's price series under consideration (i.e., the global gold price return series) at time (day) t. This implies that the gold's price is equally likely to increase, as it is to decrease, and thus renders it difficult to forecast. However, a major distinction between the RWS and the MDS hypotheses is that the latter relaxes the strict iid assumption to allow for the possible existence of time-varying volatilities in the gold's price return series, such as conditional-heteroscedasticity, which though expecting successive residual changes to be independent, does not necessarily need it to be identically distributed. Hence, the relaxed MDS hypothesis to be tested is as follows: H2. The global daily spot gold price return series follow a martingale difference sequence.

Research methodology
The weak-form efficiency is tested by first applying the MacKinlay (1988, 1989) parametric variance-ratios tests, then, followed by the implementation of its recent non-parametric modification suggested by Wright (2000) based in ranks and signs. The Lo and MacKinlay (1988) (hereafter LM) variance-ratio test assumes that if a natural logarithm of a time series (p t ) follows a pure random walk, then the variance of its k-differences in a finite sample increases proportionally with the difference, k, where k refers to the number days interval, such as 15, 20, 25 and 30 days. Following LM (1988), let (p t ) denote a time series consisting of T observations p 1 ,p 2 ,…,p T of asset returns. Then, the variance-ratio of the k-th difference, VR(k), is defined as: where, VR(k) is the variance-ratio of a gold's price return series k-th difference; ∂ 2 (k) is the unbiased estimator of 1/k of the variance of an index k difference, under the null hypothesis; ∂ 2 (1) is the variance of the first-difference of a gold price returns series, and k is the number of days of base observations intervals or lags, 3 where k = 15, 20, 25 and 30 days with regard to this study. The estimated variance, VR(k) values for all k-th lags, under the null hypothesis, are expected to be equal to unity if the observed series truly follow a random walk.
Following LM (1988), the estimator of the k-period difference, ∂ 2 (k), is calculated as: whereμ is the estimated arbitrary drift parameter defined as:μ ¼ 1 T ∑ T t¼1 p t ; and the unbiased estimator of the variance of the first difference, ∂ 2 (1), is computed as: The LM (1988) test statistic is implemented in two specifications. The first test statistic, which is considered as a test for the strict RWS hypothesis with reference to this study, M 1 (k) is given by: which, under the assumption of homoscedasticity, is normally distributed with zero mean, and unit variance, i.e.,N(0,1). The homoscedasticconsistent asymptotic variance of the variance ratio, ϕ(k), is given by: The heteroscedasticity-consistent test statistic, which is understood as a test for the relaxed MDS hypothesis with respect to this study, M 2 (k), is given by: LM (1988) show that, unlike the M 1 , the M 2 test statistic under the null hypothesis is robust to many forms of heteroscedasticities. A corresponding heteroscedasticity-consistent asymptotic variance for the M 2 test statistic is defined as: Non-parametric tests are widely regarded to be robust even in the presence of non-normalities (e.g., Luger, 2003). Informed by this idea, Wright (2000) modifies LM's (1988) parametric variance-ratio test to a non-parametric variance-ratio test. A major distinction is that Wright's (2000) non-parametric variance-ratio test statistics substitute the return differences used in LM (1988) with return ranks and signs. Following Wright (2000), let r(p t ) be the rank of p t among p 1 ,p 2 ,…,p T . Then, r 1t and r 2t are the ranks of the returns p 1 and p 2 respectively, defined as: According to Wright (2000), the rank series r 1t is a simple linear transformation of the ranks, standardised to have zero sample mean and a unit variance. Similarly, the rank series r 2t , where Φ −1 is the inverse of the standard normal cumulative distribution function, also has zero sample mean and variance approximately equal to one. The rank series r 1t and r 2t are put in place of p t in the definition of LM (1988) test statistics, which is written as R 1 and R 2 , where: where ϕ(k) is defined in Eq. (3). 3 According to Lo and MacKinlay (1988, p. 46), the arbitrary base lag (k) selected, must be any equally spaced integer, which is greater than one. Similarly, the daily base intervals, where k = 15, 20, 25 and 30 days have been chosen on that basis. Additionally, we employ different testing intervals, such as where k = 2, 4, 8 and 16 days or 5, 10, 15 and 20 days, as part of our robustness checks. Wright (2000) demonstrates that the distribution of the test statistics is generated under the assumption that the rank r(p t ) is a random permutation of the numbers 1,2,…,T, with each having equal probability. Therefore, the exact sampling distribution of R 1 and R 2 can be simulated to an arbitrary degree of accuracy, for given choices of T and k. Due to this, the distribution does not suffer from disturbance parameters; hence, it can be used to construct a test with exact power. By contrast, the test statistic based on the signs of returns rather than ranks, S 1 and S 2 , is given by: In several Monte-Carlo tests, Wright (2000) shows that the ranks (R 1 and R 2 ) are well-specified under the assumption of homoscedasticity (RWS hypothesis), whereas the signs (S 1 and S 2 ) are exact under heteroscedastic conditions (MDS hypothesis). We, therefore, employ them in conducting an explicit test of the RWS and MDS hypotheses. Table 3 reports the summary descriptive statistics and diagnostics of naturally logged computed daily spot gold price return series for all 28 gold markets examined. Panels A, B, C, and D report descriptive statistics and diagnostics of gold returns for gold markets in Africa and Middle East, Americas, Asia-Pacific and Europe, respectively. In line with the findings of past studies (Tschoegl, 1978(Tschoegl, , 1980Beckers, 1984;Muradoglu et al., 1998;Smith, 2002;Wang, Wei, et al., 2011;, the table indicates that daily average returns for all the 28 gold return series examined are small, ranging from a minimum of −0.0487% for Taiwan to a maximum of 0.235% for Brazil. Noticeably, all the sampled gold markets depict positive mean returns behaviour apart from Pakistan and Taiwan in Panel C. The volatility or standard deviation (SD) suggests that daily gold price volatilities are fairly large, ranging from a maximum of 3.189% for Taiwan to a minimum of 1.561% for the UK. For symmetry, the standard normal distribution should have zero skewness, whilst the kurtosis test statistic should not exceed the absolute figure of 3. The findings contained in the table indicate that symmetry and mesokurtic distribution are consistently rejected by the skewness and kurtosis tests statistics at the 1% significance level for the return series for all 28 gold markets examined.

5.2.
Empirical results and discussion: The efficiency of global gold markets Table 4 reports the findings of the variance-ratio tests for the naturally logged calculated daily gold return series for gold markets in Africa and Middle East, and the Americas. Column 1 indicates the specific time period, k, which is the number of interval days, where k = 15, 20, 25 and 30 days for each of the eight gold return series. Columns 2 to 7 present the test statistics for M 1 , M 2 , R 1 , R 2 , S 1 and S 2 for each gold market's return series investigated. M 1 reports the Lo and MacKinlay (LM) (1988) tests statistics under the null hypothesis of homoscedasticity (RWS), whereas M 2 presents similar test statistics under the assumption of heteroscedasticity (MDS hypothesis). The ranks (R 1 and R 2 ) and signs (S 1 and S 2 ) refer to Wright (2000) non-parametric alternative variance-ratio tests. A number of interesting findings emerge from Table 4. First, the findings indicate that both the RWS (M 1 , R 1 and R 2 ) and MDS (M 2 , S 1 and S 2 ) hypotheses are consistently rejected at the 1% significance level for the gold return series for all intervals of k for the gold markets in Egypt, Saudi Arabia, and UAE in Africa and Middle East, and Mexico in the Americas, implying that these gold markets are not efficient in the weak-from, neither from the perspective of the strict RWS nor in the relaxed MDS sense. Noticeably, all rejections with respect to LM's test statistics for the gold markets in Mexico, Saudi Arabia and UAE are in the lower tail (have negative signs) of the distribution, suggesting that any serial dependence is negative, whereas the opposite evidence is observed for the Egyptian market.
Second, applying the M 1 test statistic, the RWS hypothesis cannot be rejected for the US except when k = 15 at the unconventional 10% significance level. Similarly, the M 2 test statistic indicates that the MDS hypothesis cannot be rejected for the US gold market at any reasonable significance level. The implication is that the RWS and MDS are supported for the US gold market based on LM's test statistics. However, Wright (2000) demonstrates that LM's variance-ratio tests statistics are not robust to heteroscedasticity, and thus, we investigate the RWS and MDS for the US gold market by applying his robust ranks (R 1 and R 2 ) and signs (M 2 , S 1 and S 2 ) alternative, respectively. Discernibly, Table 4 shows that the RWS cannot be rejected for the US market except when k = 25 and 30 at the unconventional 10% significance level when R 1 and R 2 are implemented, respectively. Similarly, employing the S 1 and S 2 test statistics indicate that MDS hypothesis cannot be rejected for the US gold market at any reasonable significance level, suggesting that the acceptance of the RWS and MDS hypotheses by LM's M 1 and M 2 test statistics are robust to heteroscedasticity.
Third, the findings relating to the weak-from efficiency for Bahrain, South Africa and Turkey (Africa and Middle East) and Brazil and Canada (the Americas), as contained in Table 4 are, however, mixed. For Brazil, Canada and Turkey, the RWS and MDS cannot be rejected when the M 1 and M 2 are applied (except when k = 15 and 20 for Brazil and Turkey, and when k = 15 for Canada for the M 1 test statistic). However, when the robust R 1 and R 2 are implemented, the RWS is rejected for all three gold markets (except when k = 15 for R 1 for Canada), implying that the acceptance of the RWS hypothesis by the M 1 appears to be spurious. In contrast, the MDS hypothesis cannot be rejected for all three gold markets when the S 1 and S 2 test statistics are employed (except when k = 15 and 20 for S 1 for Brazil and when k = 30 for S 2 for Canada), meaning that the acceptance of the MDS hypothesis by the M 2 test statistic is insensitive to the presence of heteroscedasticity. For the South African gold market, the RWS and MDS hypotheses cannot be rejected when M 1 and M 2 are applied (except when k = 15 for the M 1 and when k = 15 and 20 for the M 2 ), but when the robust ranks and signs alternative are employed, the RWS and MDS hypotheses are consistently rejected at the 1% significance level, suggesting that the acceptance of the RWS and MDS hypotheses by the M 1 and M 2 are not robust to heteroscedasticity. A similar evidence is observed for the gold market in Bahrain in which the MDS hypothesis cannot be rejected when the M 2 test statistic is implemented (except when k = 25 and 30), but its heteroscedasticity consistent S 1 and S 2 consistently reject the MDS hypothesis at the 1% significance level. Observably, both the LM's M 1 and Wright's robust ranks (R 1 and R 2 ) consistently reject the RWS hypothesis for the Bahrain gold market.
Overall, the evidence from Table 4 is that the daily gold price return series of the US gold market are weak-form efficient both from the RWS and MDS perspectives, whilst the opposite evidence holds for the gold markets in Egypt, Mexico, Saudi Arabia and UAE. The Brazilian, Canadian and Turkish gold markets are efficient in the relaxed MDS sense, but not from the perspective of the strict RWS. For the gold markets in Bahrain and South Africa, whilst the results obtained by implementing LM's test statistics are mixed, that of Wright's signs and ranks consistently reject the RWS and MDS hypotheses for both gold markets, implying that both gold markets are not efficient in the weak-form. Table 5 presents the findings relating to the gold markets in the Asia-Pacific region. First, the results indicate the RWS and MDS hypotheses are rejected for gold markets in Indonesia, Nepal and Pakistan irrespective of the test statistic used, implying that these gold markets are conclusively not efficient in the weak-form. Second, the RWS and MDS cannot be rejected for gold markets in Hong Kong and Japan (except when k = 15 for M 1 , when k = 30 for R 1 , and when k = 15 and 30 for S 1 in the case of Hong Kong; and when k = 15 for M 1 and R 1 , and when k = 15 and 20 for R 2 in the case of Japan, mainly at the unconventional 10% significance level), implying that their gold return series are largely weak-form efficient. Third, the results relating to the gold markets in Australia, China, India, Malaysia and Singapore are mixed. Specifically, whereas the MDS hypothesis cannot be rejected for the 4 gold markets irrespective of the test statistic that is applied (except when k = 15 and 20 for M 2 , when k = 25 and 30 for S 1 , and when k = 30 for S 2 in the case of China; when k = 15 and 20 for S 1 in the case of India; when k = 15 for M 2 , when k = 25 and 30 for S 1 , and when k = 30 for S 2 in the case of Malaysia; and when k = 15 for S 1 in the case of Singapore, primarily at the unconventional 10% significance level), the RWS hypothesis is consistently rejected for all 4 gold markets irrespective of the test statistic that is implemented, although the LM's M 1 test statistic appears to lack power (i.e., rejections are visibly weakmostly at the 10% significance level). In sum, the main evidence that emerges from examining Table 5 is that gold markets in Indonesia, Nepal and Pakistan are not weak-form efficient both in the RWS and MDS sense, but the exact opposite evidence holds for gold markets in Hong Kong and Japan. Gold markets in Australia, China, Malaysia and Singapore are weak-form efficient in the sense of the relaxed MDS hypothesis, but not in the perspective of the strict RWS hypothesis. Table 6 reports the variance-ratio test results relating to gold markets in the Asia-Pacific and Europe. First, the findings indicate that the RWS and MDS hypotheses are conclusively rejected for the gold markets in Russia and Vietnam irrespective of the test statistic used, implying that daily spot gold return series from the two markets are not efficient in the work-form. Second, the RWS and MDS hypotheses cannot be rejected for the Swiss and UK gold markets irrespective of the test statistic used (except when k = 30 for M 1 , R 1 , R 2 , S 1 and S 2 in the case of Switzerland; and when k = 30 for M 1 and R 1 , and when k = 25 and 30 for R 2 in the case of the UK, notably at the unconventional 10% significance level), suggesting that the Swiss and UK gold markets are fairly efficient in the weak-form. Third, mixed results are observed for the gold markets in Germany, South Korea, Taiwan and Thailandthe MDS hypothesis cannot generally be rejected for these markets (except when k = 15 for M 2 and when k = 25 and 30 for S 2 in the case of South Korea), but the RWS hypothesis is rejected for the four gold markets. When k = 25 and 30 for M 1 in the case of Germany and when k = 30 for M 1 in the case of South Korea, are discernible exceptions. Fourth, the findings show that the RWS hypothesis is rejected more frequently than its MDS alternative, implying that most of the rejections of the weak-form efficiency in the global gold markets are due to heteroscedascity problems instead of simple autocorrelation ones. Finally, consistent with the findings of past studies (Belaire-Franch & Opong, 2005a,b, 2010Ntim, 2012;Ntim et al., 2007, 2011), LM's (1988 variance-ratio tests (M 1 and M 2 ) generally produce mixed results, whereas those of Wright's (2000) ranks (R 1 and R 2 ) and signs (S 1 and S 2 ) based alternatives are fairly consistent.
consistently reject the RWS and MDS hypotheses for both gold markets, implying that the failure of the parametric variance-ratio tests to reject the weak-form efficiency for both gold markets may be due to heteroscedasticity problems rather than autocorrelation ones. Overall, our results are generally in line with the findings of past studies on the efficiency of gold markets (Ball et al., 1982(Ball et al., , 1985Baur, 2013;Blose & Gondhalekar, 2013;Muradoglu et al., 1998;Narayan et al., 2010;Parisi et al., 2008;Pierdzioch et al., 2014;Shafiee & Topal, 2010;Yu & Shih, 2011). For example, our findings that suggest that the return series of the UK and US gold markets are weak-form efficient offer support for the similar findings of Tschoegl (1978Tschoegl ( , 1980, Monroe and Cohn (1986), Smith (2002) and Pierdzioch et al. (2014), but contradict those of Ball et al. (1982), Booth and Kaen (1979), Solt and Swanson (1981), Shafiee and Topal (2010), Baur (2013), and Blose and Gondhalekar (2013) that rejected the weak-form in both gold markets. Similarly, the findings of Muradoglu et al. (1998) rejected the notion of random walk in the Turkish gold market, and thus our evidence that the return series of the Turkish gold market do not follow random walk offers further support for their findings.

Empirical results and discussion: Global gold market efficiency and macroeconomic variables
In line with past studies that have examined the efficiency of gold markets (Basu & Clouse, 1993;Baur, 2013;Beckers, 1984;Blose & Gondhalekar, 2013;Christie-David et al., 2000;Ho, 1985;Mani & Vuyyuri, 2003;Mills, 2004;Narayan et al., 2010;Parisi et al., 2008;Pierdzioch et al., 2014;Yu & Shih, 2011), our findings are observably generally mixed. It is, however, not easily conceivable why some gold markets are efficient, whilst others are not. For example, whereas some developed global gold markets, such as Hong Kong, Japan, Switzerland, UK and US are weak-form efficient, the behaviour of daily gold price return series of other matured gold markets, such as Australia, Brazil, Canada, Germany, Singapore and Turkey do not follow random walk. However, the findings of past studies suggest that gold prices can be influenced by a number of macroeconomic fundamentals (Batten et al., 2010;Blose, 2010a,b;Christie-David et al., 2000;Pukthuanthong & Roll, 2011;Sjaastad, 2008;Zhang & Wei, 2010). For example, increased crude oil prices can lead to greater inflationary pressures, and thus, increased demand for gold as an alternative 'safe haven' investment (Baur & Lucey, 2010;Baur & McDermott, 2010;Ewing & Malik, 2013;Lili & Chengmei, 2013). Similarly, greater increases in broad money supply (M2+) (i.e., 'quantitative easing') without a corresponding increase in the production of goods and services can create inflationary pressures through rising prices, and thereby leading to greater demand for gold (Mahdavi & Zhou, 1997). Similar theoretical and empirical links have been made between gold prices and: (i) exchange rates (Sjaastad & Scacciavillani, 1996;Wang, Wei, et al., 2011); equity returns (Baur, 2013); and interest rates (Mani & Vuyyuri, 2003), amongst other macroeconomic variables. Consequently, we argue that one way of explaining the extent to which a gold market's return series are efficient or inefficient is to examine volatilities in the underlying macroeconomic fundamentals. Specifically, we conjecture that increased volatilities in the underlying macroeconomic variables are more likely to be associated with rapid changes in the efficiency of the gold market and vice-versa. Thus, we depart from previous studies from simply testing the efficiency of gold returns to examining the extent to which changes in the underlying macroeconomic fundamentals can explain predictability or non-predictability of such returns. Table 7 contains a logit regression results of the effect of changes in macroeconomic variables [(i.e., Δbroad money [M2+] supply, Δcrude oil price, Δinflation [CPI] rate, Δinterbank borrowing rate, Δinterest [3-month t-bill] rate, Δmultilateral exchange, Δresidential property prices and Δshare prices)] on the probability of rejecting the RWS (M 1 , R 1 and R 2 ) and MDS (M 1 , S 1 and S 2 ) hypotheses. The dependent variables (M 1 , M 1 , R 1 , R 2 , S 1 and S 2 ) are binary variables, which take the value of 1 if the RWS or MDS hypothesis is rejected at the 1%, 5% or 10% significance level. To ascertain whether the maturity of a gold market impacts on its efficiency, we include an emerging gold market dummy, 4 which takes a value of 1 if a country is classified as a developing/emerging country by the World Bank and five other reputable global rating agencies (Dow Jones, FTSE, MSCI, Russell and S&P), 0 otherwise.
A number of interesting findings are observable in Table 7. First, and consistent with our intuition, the findings generally indicate that changes in the underlying macroeconomic fundamentals are fairly capable of explaining the probability of rejecting the RWS and MDS hypotheses. Specifically, changes in crude oil price, inflation rate, interbank borrowing rate, multilateral exchange rate and share price are statistically significant and negatively related to the probability of rejecting the RWS (M 1 , R 1 and R 2 ) and MDS (M 1 , S 1 and S 2 ) hypotheses. This provides new evidence to suggest that the probability of rejecting the RWS and MDS hypotheses is significantly lower when there are greater changes (volatilities) in these five underlying macroeconomic variables. Second, and by contrast, we do not find any evidence to suggest that changes in broad money (M2+) supply, interest (t-bill) rate and residential property prices are associated with the probability of rejecting the RWS and MDS hypotheses, implying that not every underlying macroeconomic variable has the capacity to explain the probability of predicting gold returns. Third, the coefficient on the emerging gold markets dummy is discernibly significant and positively related to the probability of rejecting the RWS and MDS hypotheses. This also provides new evidence to suggest that the probability of rejecting the RWS and MDS hypotheses is higher in emerging gold markets than their developed counterparts. Overall, our findings have implications for international portfolio managers, investors, policy-makers and regulatory authorities.

Robustness analyses
We conduct a number of additional analyses as a way of ascertaining the robustness of our results. First, to address the potential endogenous association that may result from estimating contemporaneous link between probability of rejecting the RWS/MDS hypotheses and macroeconomic variables, we use one-year lagged explanatory variables as alternative to contemporaneous ones. Table 8 contains a logit regression of the effect of lagged changes in macroeconomic variables on the probability of rejecting the weak-form (RWS and MDS) hypotheses. Apart from minor sensitivities in terms of the magnitude of the coefficients, our previous evidence that increased changes in crude oil price, inflation rate, interbank borrowing rate, multilateral exchange rate and share price are associated with significantly lower probability of rejecting the RWS and MDS hypotheses remains fairly unchanged.
Second, it can be argued that gold price return predictability may not only be driven be macroeconomic variables, but also country-specific institutional (e.g., exchange rate regime, international accounting standards legal system, national gold regulations, and national governance quality) and trading (e.g., availability of gold ETFs, market liquidity and daily price movement restrictions) characteristics. 5 For example, the use of a de facto independent free floating exchange rate regime may lead to an increase in the volatility of exchanges rates and gold prices, and thereby a potential reduction in the predictability of gold prices. By contrast, reliance on a fixed or managed exchange rate regime may lead to exchange rates and gold prices not changing to reflect the 4 It should be noted that our classification is based on the 2008 list of developing/ emerging countries classified jointly by the World Bank and five other reputable global rating agencies (i.e., Dow Jones, FTSE, MSCI, Russell and S&P), whereby countries are classified based on six broad development factors: (i) per capital income; (i) maturity and effectiveness of market and regulatory environment; (iii) the speed of custody and settlement; (iv) development, maturity and sophistication of the derivatives markets; (v) the sophistication of the landscape for trading and market dealing; and (vi) the size and depth of the market. 5 We are grateful to an anonymous reviewer for this suggestion.
underlying macroeconomic conditions, and thus a potential increase in the ability to accurately predict gold price returns. National duties, regulations and restrictions relating to the importation and taxation of purchases (demand) and sales (supply) of specific quantities of gold may not only have significant effect on the price of gold in that country, but also the price of gold in neighbouring countries and the global gold market in general. Gold regulations in India, for example, limit the weight of all imported gold to 10 kg; as well as impose an import duty of 15% and additional special tax of 3% on all imported gold. In fact, a clear majority (20 out of 28) of the countries in our sample have some form of national regulations (e.g., quality, quantity and taxation) relating to the importation, sale and purchase of gold and its ornaments. Similarly, strong legal system, good national governance, and increased commitment towards accountability, transparency and disclosure through the full adoption of international accounting standards can improve pricing efficiency of financial assets, including gold through the attraction of foreign direct investments and international investors. In addition to the institutional factors, national trading conditions and environment can have an effect on the efficiency of gold price returns. For example, the availability of gold ETFs, greater stock market liquidity and removal of maximum daily gold price movements can improve the efficiency of gold prices. Thus, to ascertain the extent to which countryspecific institutional factors and trading characteristics drive our findings, we re-run our findings in Table 7 by including a number of institutional (exchange rate regime, international accounting standards legal system, national gold regulations, and national governance quality) and trading (gold ETFs, market liquidity and price movement restrictions). Observably, the findings reported in Table 9 are generally consistent with those reported in Table 7, suggesting that our previous results are fairly robust to the inclusion of the country-specific institutional factors and trading characteristics. Specifically, the findings contained in Table 9 indicate that changes in crude oil price, inflation rate, interbank borrowing rate, multilateral exchange rate and share price are Notes: This table reports the findings of a logit regression of the changes in macroeconomic variables on the probability of rejecting the weak-form efficiency in the daily spot gold price return series in 28 global gold markets. Specifically, it seeks to test the effect of changes in the underlying macroeconomic fundamentals on the probability of rejecting the random walk (RWS) and martingale difference sequence (MDS) hypotheses in the daily spot gold price returns series of the 28 global gold markets investigated. Macroeconomic data on multilateral (effective) exchange rate and residential property prices were collected from the Bank for International Settlement (BIS) website, whilst the data on broad money supply (M2+), inflation (consumer price index -CPI) rate, interbank (overnight/short-term) borrowing rate, interest (3-month government treasury-billt-bill) rate, and share price were collected from DataStream. ΔBroad money (i.e., notes, coins, and demand deposits) supply is measured as month-on-month naturally logged changes in reported broad money supply. ΔCrude oil price is operationalised as month-on-month naturally logged changes in Brent crude oil price. ΔInflation rate refers to the month-on-month naturally logged changes in the consumer price index. ΔInterbank borrowing rate is measured as month-on-month naturally logged changes in the short-term (overnight) interbank borrowing rate. Δinterest (t-bill) rate is operationalised as a quarter-on-quarter naturally logged changes in the interest (3-month government t-bill) rate. ΔMultilateral (effective) exchange rate is measured as month-onmonth naturally logged changes in the monthly trade weighted BIS multilateral exchange rate index series of a country's currency against a basket of currencies based on the relative strength or value of trade (exports and imports). ΔResidential property price refers to the quarter-on-quarter naturally logged changes in the quarterly residential BIS property price index series. ΔShare price is measured as the month-on-month naturally logged changes in the broad all share (equity) index series for each country. For example, the FTSE all share index is used for the UK, whilst the S&P 500 index is used for the US. Emerging gold market dummy is a binary variable that takes the value of 1 if a rejection is from a developing gold market [(i.e., based on the 2008 list of developing/emerging countries classified jointly by the World Bank and five other reputable global rating agencies (i.e., Dow Jones, FTSE, MSCI, Russell and S&P), whereby countries are classified based on six broad development factors: (i) per capital income; (i) maturity and effectiveness of market and regulatory environment; (iii) the speed of custody and settlement; (iv) development, maturity and sophistication of the derivatives markets; (v) the sophistication of the landscape for trading and market dealing; and (vi) the size and depth of the market)] (Bahrain, Brazil, China, Egypt, India, Indonesia, Malaysia, Mexico, Nepal, Pakistan, Russia, Saudi Arabia, South Africa, Taiwan, Thailand, Turkey, UAE and Vietnam), 0 otherwise (i.e., Australia, Canada, Germany, Hong Kong, Japan, Singapore, South Korea, Switzerland, UK, and US). Note that similar to the daily spot gold prices, all macroeconomic variables are in their respective local currencies and that the data is not always balanced for all countries and variables due to access limitations. For example, Bahrain, Nepal, Pakistan and Vietnam are not covered by the BIS multilateral exchange rates. Similarly, Bahrain, Nepal, Pakistan, Taiwan and Vietnam are not included in the BIS residential property index series. Share index return series are also short for some countries, such as Bahrain, China, Nepal, Russia, Saudi Arabia, UAE, and Vietnam with more recent stock market development and activity. The dependent variables (M 1 , M 2 , R 1 , R 2 , S 1 and S 2 ) are binary variables which take the value of 1 if the RWS and MDS hypotheses are rejected 1%, 5% or 10% level, 0 otherwise. M 1 and M 2 are based on the conventional Lo and MacKinlay's (1988) parametric variance-ratio tests, whilst R 1 , R 2 , S 1 and S 2 are based on the recent non-parametric (ranks and signs) modification proposed by Wright (2000). The M 1 is robust under the assumption of homoscedasticity (RWS), whilst the M 2 is more precise under heteroscedasticity (MDS) conditions. Similarly, the ranks (R 1 , R 2 ) are more powerful under homoscedasticity (RWS) conditions, whereas the signs (S 1 and S 2 ) are robust under the assumption of heteroscedasticity. Thus, the M 1 , R 1 , and R 2 explicitly test the RWS hypothesis, whilst the M 2 , S 1 and S 2 test the MDS hypothesis. Following Petersen (2009), the coefficients are estimated by using the robust Clustered Standard Errors technique along country and year dimensions. P-values are in parentheses. ***, **, and * denote significance at the 1%, 5% and 10% levels, respectively. statistically significant and negatively related to the probability of rejecting the RWS (M 1 , R 1 and R 2 ) and MDS (M 1 , S 1 and S 2 ) hypotheses.
With specific reference to the institutional factors and trading characteristics, the findings suggest that the quality of national governance, the use of independent floating exchange rate regime, and greater stock market liquidity are associated with lower levels of predicting gold price returns. By contrast, we do not find any evidence to suggest that the adoption of international accounting standards, legal system, national gold regulations, price movement restrictions and the availability of gold ETFs have a significant impact on the efficiency of gold price returns. Third, to ascertain whether efficiency changes over-time, we reimplement our test by conducting four separate ten-year sub-sample periods (1968 to 1977; 1978 to 1987; 1988 to 1997; and 1998 to 2014) and our results our reported in Table 10. As R 1 and S 1 are better specified and more powerful under the assumption of RWS and MDS hypotheses, respectively, we limit our analysis to them although the findings are essentially similar irrespective of the test statistic that is applied. Similarly, and for brevity, we report results for 10 of the gold markets (with at least one representation from each major continent) we examined, but the findings generally follow similar trend. The results contained in Table 10 suggest generally that gold return predictability reduces over-time. For example, daily spot gold price returns for Australia are reasonably predictable in the first two decades (Windows I and II), but follow RWS and MDS in the last two decades (Windows III and IV). Similar patterns can be observed for Canada, China, Germany and South Africa, and even for India and Saudi Arabia, where gold returns remain highly predictable, there are observable reductions in the levels of rejection of the RWS and MDS hypotheses over-time. Our mixed results for South Africa have been particularly surprising because as a major gold producer, one will expect gold price returns to be fairly efficient. Our additional analyses, thus, offer further insights on clarifying the mixed findings for South Africa in particular.
Fourth, we conduct a number of additional analyses, which for brevity are not reported, but available upon request. For example, to account for country-level effects over-time, we-run our logit model by including country and year dummies with the central tenor of our findings remaining essentially the same. Fifth, since rejections are usually at the conventional 1% and 5% significance levels, we re-estimate our logit model by excluding all rejections at the 10% significance level. We observe some improvements in the statistical significance and magnitude of the coefficients, as well as in the diagnostics and explanatory power of the model, but our main conclusions remain unaffected. Sixth, to further ascertain whether efficiency changes over-time, we carry additional analysis by estimating a five-year overlapping rolling window. Similar to the four separate ten-year subsamples, we do observe evidence of decreasing return predictability over-time irrespective of the variance-ratio test statistic that is applied, especially over the last decade and particularly for the matured gold markets. Finally, to determine whether our findings are sensitive to the testing interval (i.e., the lag of 'k') used, we repeat our analysis by employing two different intervals of k: (i) when k = 2, 4, 8, and 16 days; and (ii) when k = 5, 10, 15, and 20 days, with our findings suggesting that our central evidence is insensitive to the testing interval or the lag of k used. Overall, our robustness analyses make us fairly confident that our findings are not spuriously driven by any endogenous or unidentified heterogeneities.

Summary and conclusion
Although the number of formal gold markets in the world has increased rapidly, especially over the last decade, existing studies on Notes: This table reports the findings of a logit regression of one-year lagged changes in macroeconomic variables on the probability of rejecting the weak-form efficiency in the daily spot gold price return series in 28 global gold markets. Specifically, it seeks to test the effect of lagged changes in the underlying macroeconomic fundamentals on the probability of rejecting the random walk (RWS) and martingale difference sequence (MDS) hypotheses in the daily spot gold price returns series of the 28 global gold markets investigated. The variables are the same as defined under Table 7 except that we have introduced a year lag between the macroeconomic variables and the probability of rejection in order to avoid potential endogenous association that may arise due to simultaneity or contemporaneity. M 1 and M 2 are based on the conventional Lo and MacKinlay's (1988) parametric variance-ratio tests, whilst R 1 , R 2 , S 1 and S 2 are based on the recent non-parametric (ranks and signs) modification proposed by Wright (2000). The M 1 is robust under the assumption of homoscedasticity (RWS), whilst the M 2 is more precise under heteroscedasticity (MDS) conditions. Similarly, the ranks (R 1 , R 2 ) are more powerful under homoscedasticity (RWS) conditions, whereas the signs (S 1 and S 2 ) are robust under the assumption of heteroscedasticity. Thus, the M 1 , R 1 , and R 2 explicitly test the RWS hypothesis, whilst the M 2 , S 1 and S 2 test the MDS hypothesis. Following Petersen (2009), the coefficients are estimated by using the robust Clustered Standard Errors technique along country and year dimensions. P-values are in parentheses. ***, **, and * denote significance at the 1%, 5% and 10% levels, respectively.
the efficiency of gold markets are limited to a few developed markets, especially those in the UK and US, and thereby limiting current understanding of the return behaviour of global gold markets. Additionally, the few existing studies have also mainly merely tested the efficiency of gold markets with limited attempts at identifying the factors that may explain the degree of a gold market's efficiency. This paper has, therefore, examined the weak-form efficiency of global gold markets with specific focus on the random walks (RWS) and martingale difference sequence (MDS) hypotheses, and consequently, investigated the extent to which predictability or non-predictability of global daily spot gold price return series behaviour can be explained by volatilities in macroeconomic fundamentals.
Our findings contribute to the literature in a number of ways. First, our results indicate that gold markets in Egypt, Indonesia, Mexico, Nepal, Pakistan, Russia, Saudi Arabia, UAE and Vietnam are not weak-form efficient neither from the perspective of the strict RWS nor in the relaxed MDS sense, but both hypotheses cannot be rejected for gold markets in Hong Kong, Japan, Switzerland, UK and US. We, however, find conflicting findings for gold markets in Australia, Bahrain, Brazil, Canada, China, Germany, India, Malaysia, Singapore, South Africa, South Korea, Taiwan, Thailand and Turkey. Generally, our study contributes to the literature by providing new evidence on the gold return behaviour and efficiency in Bahrain, Brazil, Egypt, Indonesia, Malaysia, Mexico, Nepal, Pakistan, Russia, Saudi Arabia, Singapore, South Africa, South Korea, Taiwan, Thailand, UAE and Vietnam and extending prior findings in gold markets in Australia, Canada, China, Germany, Hong Kong, India, Japan, Switzerland, Turkey, UK and US.

Table 10
Variance-ratio test results for the daily spot gold price return series based on four separate ten-year windows. I: 1968II: 1978-1987III: 1988IV: 1998-2014  Note: A test statistic with ***, **, and * indicates significance at 1%, 5%, and 10% levels respectively. Figures in windows I to IV give the values of the test statistics for R 1 and S 1 for selected daily spot gold price return series over four ten-year windows, respectively. R 1 and S 1 are based on the recent non-parametric (ranks and signs) modification proposed by Wright (2000). The rank (R 2 ) is more powerful under homoscedasticity (RWS) conditions, whereas the sign (S 1 ) is robust under the assumption of heteroscedasticity. Thus, the R 1 explicitly tests the RWS hypothesis, whilst the S 1 tests the MDS hypothesis.

Windows period
Second, our results suggest that the higher the volatilities in macroeconomic variables (i.e., crude oil price, inflation rate, interbank rate, multilateral exchange rate and share price), the less likely it is to reject the RWS and MDS hypotheses. Third, our results show that the RWS hypothesis is rejected more frequently than its MDS alternative, and thereby justifying our decision to conduct an explicit test of the RWS and MDS hypotheses. Fourth, in line with the findings of prior studies, the results obtained by applying Wright's (2000) non-parametric variance-ratio tests are more consistent, whilst those of the MacKinlay's (1988, 1989) parametric alternatives are generally mixed. Finally, our evidence shows that the probability of rejecting the weakform efficiency is higher in emerging gold markets than developed ones. Our findings are fairly robust to estimating subsamples, overlapping rolling windows and endogeneity consistent models, as well as controlling for a number of country-specific institutional factors and trading characteristics.
Our findings have crucial implications for global portfolio managers, investors, poly-makers and regulatory authorities. For international portfolio managers and investors, our evidence of gold return predictability in some gold markets does not only offer opportunities for immediate exploitation, but also risk reduction through the formation of portfolio strategies that strike a fair balance between investments in efficient and inefficient gold markets. For policy-makers and regulatory authorities, our evidence offers a stronger impetus to strengthen market regulations, infrastructure, and microstructure. In particular, and as smaller and less matured markets are generally less efficient, policies that can encourage greater integration and co-operation, for example, through mergers and acquisitions both within and across continents may be a step in the right direction.
Finally, whilst the findings of our study are important and robust, its limitations need to be explicitly acknowledged. First, due to data limitations, we do not fully examine (we only investigate liquidity, price limits and availability of gold ETFs) how market trading and market microstructure (e.g., trading volume, system, frequency, margin requirements, settlement, contract size, and tick size, amongst others) impact of on the efficiency of gold market return series. Thus, future studies may enhance their findings by examining how these factors affect the efficiency of gold market returns. Second, we examine a limited number of macroeconomic variables and institutional factors that can potentially explain the predictability or non-predictability of global gold market returns, and thus future studies may improve their findings by exploring the effect of other factors, such as political instability and financial crisis, on gold market efficiency. Third, due to data limitations, our test is limited to 28 gold markets, and thus future studies may improve the insights that they may be able to offer by expanding their sample, especially to include gold markets with limited evidence, such as those in Belgium, France, Luxembourg, Israel, Kenya, Kuwait, Nigeria, and Philippines. Finally, although we find evidence of return predictability in some gold markets, it is not easily clear whether it will be economically profitable to be exploited taking into consideration inherent costs, such as transaction costs. Future studies may enhance their results by assessing economic feasibility of an investment strategy that may seek to exploit such predictability opportunities.