What determines the gold spot price?
An APGARCH approach with daily data
By Mark Kruidhof*
Abstract:
This study is an attempt to uncover the short-term determinants of the gold price. With daily figures of an extensive time period (1986-2008) and by using a recently introduced (APGARCH) estimation method, several conclusions can be drawn. It appears that the USD exchange rate is the most important determinant of the short-run gold price. Furthermore, we find evidence for the “safe haven” or “flight to quality” theory of the gold price. Visual examination reveals a break in the time series of the gold price around 2003, which is confirmed by a Quandt-Andrews test. Two separate regressions (one for the period before and one for the period after the break) show a significant change in the estimated parameters of the determinants of the gold price. Finally, the APGARCH method is compared with more conventional estimation methods by evaluating an out-of-sample rolling window forecasting method. (JEL C22, G12, Q30)
For more than five millennia gold has been a commodity of great importance. The oldest pieces of gold jewellery were found in Egypt three thousand years BC and even in those days gold represented wealth and power. At that time gold was mainly used in artworks and jewellery, but soon thereafter gold became also important as medium of exchange. Properties like the stable demand and supply, the everlasting feature of this metal and the global dispersion of resources are the basic pillars of adopting gold as medium of exchange; see Wijnholds (1968).
The monetary function of gold was formalized in 1821 when Britain adopted the gold
* e-mail: j.m.kruidhof@dnb.nl
standard. Soon thereafter, other European countries followed and the gold standard was in place until the First World War. In 1944 the Bretton Woods system was created, which fixed the value of the US dollar to gold and the value of other currencies to the US dollar. This system was abandoned in the early seventies when flexible exchange rates were implemented; Cooper et al. (1982).
Although gold has lost its official role as medium of exchange and its function as formal international trade standard, it is still of great importance in today’s financial markets. Besides the use of gold for jewellery and industrial applications, it is an important investment object. Investors use gold as a hedge against exchange rate risk and inflation and also as a safe haven in times of financial uncertainty; Baur and Lucey (2006) and Capie et al. (2005). Furthermore, for many countries gold serves as a reserve asset, and the total amount of gold which is in the hands of central banks and international organizations accounts to more than a fifth of the total worldwide gold stock.1
Putting this altogether, getting more insight into the behaviour of the gold price is interesting for many agents. Although there are a lot of studies which tackle exclusively the long-run price developments of gold - with monthly, yearly or quarterly gold price figures -, there is less evidence on short-run price dynamics. This study is a useful contribution to the existing literature on the gold market in the sense that it adds new information about the short-term deshort-terminants of the gold price. The focus on high frequency data makes this paper different from most other gold price studies and also the extensive data set distinguishes this research from previous studies. The sample period contains daily figures of a long and interesting period (1986-2008), which include several economical downturns as well as periods with high growth levels.
With today’s highly flexible and international financial markets, a focus on short-term price dynamics in the gold market is very interesting. Investors become increasingly aware of the valuable investment properties of gold. Besides the interests of investors, there is another reason to study gold price dynamics with short-run figures. Increasing the frequency of data points can give interesting results as some functions of gold are more significant in the short-run than in the long short-run. For instance, some studies show that the function of gold as a safe haven is only very timely and to capture this effect, high-frequency data is necessary; see Baur and Lucey (2006).
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Earlier research has resulted in a list of several potential determinants of the short-term gold price (see section I). We apply a recently developed estimation method which belongs to the extended ARCH family to learn more about the short-run determinants of the gold price and to explore whether safe haven and hedge properties of gold change over time. The estimation method allows for clustered volatility, which is typical for high-frequency time series of prices of financial assets.
To prevent this study from having a too broad scope certain restrictions have to be made. The most important limitation is that this study considers only the spot market for gold. As in many other asset markets there is also a wide range of derivativeproducts for the gold market, but these are neglected in this research.2 Furthermore, the focus on short-run price dynamics in the gold market inherently requires the use of high frequency data which is unfortunately not available for the supply side of the gold market. Hence, the assumption is made that supply of gold is fixed in the short-run which is certainly not unrealistic on a day-to-day basis.
The structure of this paper is as follows. The next section starts with an overview of the demand determinants of the gold price. Section II contains a model of the short-run dynamics of the gold market and gives a summary of the used data in the model. In section III the estimation results are discussed and the main conclusions are drawn in the final section.
I. Demand determinants of Gold
Demand for gold can be roughly classified in “asset demand” for gold and “use demand” for gold, a distinction which is also used in a paper of Ghosh et al. (2004). Asset demand for gold comes mainly from investors, government agencies, and institutions, while use demand comes from jewellery, dental markets and industrial markets.
Besides the division between “use demand” and “asset demand” it is also possible to distinguish between long- and short-term driven demand. Use demand for gold is changing gradually over time due to income effects and consumer preferences and it is unlikely that this type of demand has a large influence on daily price changes. Central bank reserves are as well relatively stable over time and cannot explain short-term price changes in the gold market. Furthermore, investors, who hold gold as a hedge against inflation, are as well more long term
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oriented due to the long-term relationship between inflation and gold prices (which is explained in more detail further on).
Contrary, the remaining asset demand driven forces are highly short-term oriented. Investors who hold gold for portfolio diversification, as an exchange rate hedge or as safe haven, change their holdings constantly and also speculators are mostly interested in short-term profits. Consequently, a distinction between short-term and long-term price setting in the gold market is justified, due to the different actors and mechanisms underlying the system. The following subsections provide more detail on several demand categories. Due to the short-term approach of this study, the main focus is on the “asset demand” categories for gold. The long-term delong-terminants in the “use demand” category are combined and are only discussed very briefly.
A. Use demand for Gold
The use demand for gold is by far the largest demand factor in the gold market. Statistics obtained from the world gold council reveal that demand for jewellery in 2007 amounts to approximately 54.2 billion dollar while industrial and dental demand amounts to 10.4 billion dollar. Taken together, use demand for gold is roughly 64.6 billion dollar which accounts for more than 80% of total demand in the gold market. The remaining 20% of demand for gold comes from net retail investments, demand for Exchange Traded Funds (ETFs) en similar investment products which all belong to the asset demand class for gold.
B. Gold as a hedge against inflation
Their theoretical representation of the gold market has a specific set of conditions which have to be satisfied for the gold price to increase over time at the same growth rate as the general price level.
Figure 1: US Dollar price of gold required for gold to be a(n) (long term) inflation hedge in the United States in the period 1914-2007.
Long-term Inflation Hedge
$0 $200 $400 $600 $800 1914 1924 1934 1944 1954 1964 1974 1984 1994 2004 Year N o m in a l D o ll a rs
Inflation Hedge Gold Price Nominal Gold Price
Source: U.S. Department of Labor, Bureau of Labor Statistics, London Gold Bullion Market.
With monthly data of the period 1976-1999 they conclude that empirical evidence confirms their central hypothesis of gold as a hedge against inflation in the long run but they also find that this equilibrium can be seriously disturbed in the short run. This point is illustrated in Figure 1 as well where it can be seen that in the short-run nominal gold prices can show large deviations from the inflation hedge price and short-term gold holdings can be subjected to serious value depreciations.
An interesting point which can be seen from Figure 1 is that these short-term deviations did not exist in the first half of the 20th century. The relation between the general price level and the gold price is quite stable at that time but is changing rapidly thereafter. This has mainly to do with the volatile gold prices of the last three decades which are a result of the abolition of the gold standard and the adoption of a free gold market.
Thus, gold is an effective long-term hedge against inflation and does indeed have long-run store of value properties. In the short-run however, the gold price can substantially deviate from its long-term (equilibrium) value and holding gold is no guarantee for sustaining purchasing power.
C. Gold as reserve asset
Apart from asset demand for gold from institutional investors and commercial parties, gold has also always had close attention from official authorities like governments and central banks. Henderson et al. (2007) list three possible motives for such authorities to hold gold: (1) gold reserves would be necessary if gold ever again played an important role in international monetary arrangements; (2) gold is an important part of a “war chest” for times of international crisis; and (3) gold is irreplaceable in certain strategic uses. For those reasons gold was used as the main reserve asset of these authorities and throughout history central banks did acquire large physical gold stocks.
reserves is still substantial above 50%.3 Furthermore, the BIS report discusses the relative share of gold in the total reserves which does not tell much about the absolute quantities of gold possessions of authorities. The decline of the percentage gold in total foreign reserves of the last three decades is accompanied with an increase in the amount of official reserves; hence the absolute quantity of gold reserves does not automatically has to change.
Nevertheless, from the perspective of the gold market, central banks and other official authorities possess a large part of the above ground stock of physical gold. The total stock of official authorities is a fifth of all gold which is ever mined. Consequently, central banks with a large stock of gold can have an influence on the gold price. There is a possibility that an unexpected sale (purchase) of gold results in a downward (upward) correction of the spot gold price. Due to the unavailability of precise data of official gold purchases this impact on the spot gold price cannot be incorporated in the empirical model. Furthermore, a number of countries participate in the Central Bank Gold Agreement (CBGA) which is established in 1999 and which limits sales on the gold market. During the first agreement all the central banks of the EU and Switzerland participated, excluding Denmark and Greece. The USA, IMF and BIS promised to recognize this agreement and to postpone large purchases and sales of gold as well. As a result of the agreement and the commitment of the other large parties, 85% of all reserves in gold were covered. In 2004 this agreement is renewed for another five year period and taken this into account, supply of gold from official authorities is rather stable.
D. Gold for portfolio diversification
Another reason for demanding gold as investment object is its diversification property. Characterizing for today’s investment portfolio is its large spread of securities by type of issuer, geographical location, ownership rights, industrial sector, and so on. Professional investors try to reduce as much risk as is possible within a certain required yield range and adding commodities to an investment portfolio is a common method to achieve this.
Hillier et al. (2006) study the investment role of precious metals in financial markets. With daily data of gold, platinum and silver of the period 1976-2004 they find that all three precious metals have low correlations with the stock index return (they use the S&P 500 index as proxy for stock index return), which is a signal for diversification possibilities. They
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conclude that an investment portfolio which contains precious metals performs considerably better than more standard equity portfolios.
Almost two decades earlier, Chua et al. (1990) analyzed the diversification properties of gold stocks and gold bullion for which they used the capital asset pricing model. Risk in their model is composed of portfolio risk and systematic risk which is measured by the portfolio’s beta. Chua et al. examine the correlation between gold returns and common stocks in the portfolio, for the 1970’s and 1980’s. Their findings are that during this period the beta for gold stocks is more than doubled while the beta for gold bullion has remained the same, close to zero.
A very recent study of the World Gold Council (by Dempster (2008)) shows that the portfolio diversification possibilities of gold still exist nowadays. The correlation coefficients between gold and a range of US assets like the 3-month T-bill yields, the S&P 500, the DJ Industrial average and others have been close to zero for the last 5 years. Investors are increasingly aware of this advantage of holding gold and in today’s asset portfolios the amount of gold holdings is growing over time.4
Especially so called Exchange Traded Funds (ETF’s) which were established in 2004 are growing rapidly during the recent years. These are passively managed funds which are developed to track the returns of physical gold prices. Advantages of holding ETF’s instead of holding physical gold are the absence of costs of insurance, transportation and storage and in addition the market for Exchange Traded Funds is far more liquid than the physical gold market. Since the start of the first ETF fund in 2003 this market has shown substantial growth in terms of physical gold holdings as well as the amount of transactions. However, the market is still immature and it is difficult to address the impact of these funds on the actual gold price. Figure 2 shows the physical gold demand of SPDR Gold shares (worldwide one of the largest gold ETF funds settled on the New York Stock Exchange) and the nominal gold price in USD. The picture suggests that, to some extent, there is a relation between gold purchases of this ETF fund and the development of the nominal gold price. During periods of stock buildings the actual gold price seems to rise and when large quantities of physical gold are sold the gold price tends to decrease but a formal analysis of this is beyond the scope of this paper.
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Figure 2: Gold purchases and gold price 1/3/2008 – 6/10/2008
Exchange Traded Funds physical gold demand and the Gold Price
$750.00 $800.00 $850.00 $900.00 $950.00 $1'000.00 $1'050.00 1/3/ 2008 1/17 /200 8 1/31 /200 8 2/14 /200 8 2/28 /200 8 3/13 /200 8 3/27 /200 8 4/10 /200 8 4/24 /200 8 5/8/ 2008 5/22 /200 8 6/5/ 2008 6/19 /200 8 Date G o ld P ri ce -25 -20 -15 -10 -5 0 5 10 15 20 T o n n es ETF ounces Gold Price
Source: State Street Global Markets, SPDR Gold Share (www.SPDRGoldShares.com).
To summarize; several studies point at the role of holding gold in an investment portfolio for diversification purposes and due to more awareness of the benefits of gold holdings and due to recent financial innovations like ETF funds, the share of investment demand for gold has recently increased.
E. Gold as an exchange rate hedge
value of 1 means that a currency block completely dominates the gold market and depreciation effects are entirely passed trough in the price of gold in other currencies. With monthly observations of the period 1982-1990 they find that the gold market seems to be dominated by the European currency block which possesses about two-thirds of the ‘market power’ of all participants in that market. Furthermore, they find that floating exchange rates among the major currencies have contributed substantially to the high volatility in the gold price. Also, they find evidence for the inflation hedge property of gold. They estimated that the real price of gold rises by approximately three-quarters of 1% in response to a one point increase in the world inflation rate.
Figure 3: Exchange rates vs Gold price
Exchange Rate Hedge
0 50 100 150 200 250 300 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 Time In d ex GBP/USD DM and EUR/USD YEN/USD Gold price Source: DataStream
Figure 3 illustrates this relationship. Three exchange rates (respectively GBP/USD, YEN/USD and DM,EUR/USA) and the nominal gold price are been indexed. The Figure shows a plain negative relation between the gold price and the different exchange rates. What is most remarkable in Figure 3 is that there seems to be a structural break in this relationship somewhere near 2003/2004. Although the strength of the relation between the exchange rates and the gold price is somewhat fluctuating, it is quit stable in the period 1986-2003, which is in accordance with the findings of Capie et al. From 2003 onwards the price of gold increases considerably faster than the exchange rates depreciate. This recent development seems to be out of the ordinary which makes it very interesting to examine a bit more closely. Possible explanations for this recent trend are provided in the results section.
F. Gold as safe haven
relative high financial or political uncertainty investors flee away from normal investment products and take refuge by gold holdings.
Bauer and Lucey (2006) have studied whether gold is a hedge or a safe haven for stocks and bonds. Their main empirical result is that gold is a hedge as well as a safe haven for stocks for the entire sample period. However, gold is not a hedge or a safe haven for bonds in any market. Furthermore they find a distinction between the safe haven property in the long and short run. In the long run gold does not offer a flight to quality while it does offer this protection in the short-run. Bauer and Lucey (2006) have estimated that investors which keep their gold holdings for more than 15 days after an extreme financial shock occurs loose money. Furthermore their results also show that there is a large difference in investors which already possess gold stocks and investors which buy gold stocks when a financial shock occurs. Figure 5 in the estimation results section illustrates this phenomenon.
G. Gold for speculation
Just as other assets, gold can be subjected to speculation of investors. A study of Koutsoyiannis (1983) performed more than two decades ago discusses this type of demand already. She developed a theoretical model with adaptive expectations which tries to capture the price dynamics of the short-term gold market. With daily data of the period January 1980 to March 1981 she finds that speculation in the gold bullion market seems to be inefficient in the very short-run. Rational speculators dealing in assets like gold, from which the prices are highly volatile and which involve a large amount of funds, do not react immediately and prefer to wait and see whether changing conditions are more permanent of nature. Furthermore she included several macroeconomic variables in her model which explain a large share of total gold price variation.
Bertus and Stanhouse (2001) show more recently empirical research on speculation in the gold market. They employed a dynamic factor analysis to test whether there are rational bubbles in the gold futures market. With normal significance levels they cannot prove the existence of rational speculative bubbles in the gold future market. Because the focus of this paper is on the gold spot market I will not go into more detail with respect to the paper of Bertus and Stanhouse.
transportation costs, storage costs and more inconveniences, ETF’s have also lead to more liquidity in the gold market. Taking in mind these developments and the increased interests from investors for gold in general, it is likely that also speculation demand for gold has expanded lately.
II. Empirical short-run gold price model
This section provides the steps toward an empirical model which is able to capture the short-run fluctuations of the gold price. The absence of high-frequency data and the relative stability of the supply side in the gold market are the reasons why supply side forces are kept out. Included in the model are all macroeconomic variables with high frequent arrival rates and which potentially can have an influence on short-term gold price movements.
The explanatory variables are included for the lagged time period as well as for the current time period which result in a causality problem. One of the solutions to cope with this is to estimate a Vector Auto Regression model, which is beyond the scope of this paper. However, by analyzing the explanatory variables and the gold price, it is reasonable to assume that the causality runs from the exogenous variables to the gold price and not the other way around. Moreover, in the literature there is no evidence for feedback effects from the gold price on for instance the exchange rate or other variables. Simple Granger causality tests support this assumption, as for each variable (except the Industrial Metals index) the causality runs towards the gold price and not in the opposite direction. Table 12 in the appendix provides the results of the Granger causality tests.
Table 1 Macroeconomic determinants1
Determinant: Definition: Expected Sign:
Gold price Gold Bullion LBM U$/Troy Ounce
Exchange rate The GBP/USD exchange rate (-)2
Oil price Crude Oil-WTI Spot Cushing U$/BBL (+)
Industrial Metals index S&P GSCI Industrial Metals Spot Price Index (+)3 Stock market More than one definition is used, f.e. S&P 500
price index, FTSE 100 price index, NYSE price index
(-)
Interest rate UK Interbank 3 month – Middle Rate4 (-)
Food index S&P GSCI Agricultural Spot – price index (+) Stress dummy Dummy variable for financial instability5 (+)
ETF Gold ounces of the SPDR Gold Shares Exchange
Traded Fund6
(+)
Notes: 1 All variables except the ETF statistics are obtained from DataStream. 2 An appreciation of the US dollar is expected to lower the gold price. 3 The GSCI Industrial Metals index include Aluminium, Copper, Lead, Nickel and Zinc. 4 Regressions with the USA Effective Federal Funds Rate were also made but using the UK Interbank 3 month rate give better results. 5 The financial instability dummy or
stress dummy is constructed as the maximum of the squared negative returns of either the FTSE 100
index or the S&P 500 composite index with a threshold of 1%. If both returns are above -1% the value of the stress dummy is 0. 6 Data is used of the SPDR Gold Shares fund which is located on the New York Stock Exchange index and is one of the biggest ETF’s.
The exchange rate is defined as foreign currency GBP per USD5. An increase in the exchange rate corresponds thus with an appreciation of the USD. Therefore, considering the exchange rate hedge theory in Section I, the expected sign is negative. The food index is an indicator of short-term inflation expectations and consequently, a positive correlation between this variable and the gold price is expected. The industrial metals index reflects demand for raw materials in the industrial sector. Taking into account the industrial
use properties for gold, the industrial metals index should have a positive correlation with the gold price. The stock market and the interest rate should have a negative relation with the gold price as they are both alternative investments for gold. The correlation between the gold price and the financial instability indicator is expected to be positive. The “safe haven” or “flight to quality” function of gold predicts an increasing gold price during financial disturbances. The “flight to quality” or “safe haven” property of gold can also be analyzed by looking at the correlation of gold and the oil price. This is because oil prices tend to increase during political and social unrest. Finally, the ETF variable is used in an additional regression which measures the impact of purchases and sales of physical gold by an exchange traded fund. A positive relation between the amount of purchased gold and the actual price of gold is
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expected. To exclude causality problems for this variable, the additional model which measures the effect of ETF’s on the gold price include the lagged changes in ETF holdings.
An ordinary least square regression of the gold price against the macroeconomic variables
is given in model (1), where α is the intercept, Pt-1 is the lagged gold price, e is an error t
term and the vector X’ contains all exogenous macroeconomic variables.
t i t i t P X e P =α +β
∑
−1 +ψ∑
'+ (1)Evaluating the time series reveals non-stationarity in levels for all variables except the dummy for financial instability.6 Consequently, the equation incorporates the percentage daily change in each variable to avoid a spurious correlation (unit root tests on the first differences show that these are released from non-stationarity; see the appendix for more details).
The distribution of financial asset returns is typically non-normal. Particularly empirical models which are tested with high frequency data show often heteroskedasticity in the errors. Mills (2004) analyzed the statistical properties of daily gold prices in the period 1970-2002 and he concludes that daily returns are indeed highly leptokurtic. Besides the large amount of information in the tails, he finds also correlations in the lagged volatilities. Testing for the statistical properties of the empirical model in equation (1) confirms that the residuals of the regression are non-normally distributed. Figure 4 is a graphical representation of the residuals and it can be clearly seen that volatility in the errors seems to cluster around certain moments in time.
To incorporate this non-normality in the error terms, Engle (1982) developed a so called ARCH model where ARCH stands for autoregressive conditional heteroskedasticity. This model was intent to take into account the clustering of volatility during turbulent periods and became very popular in measuring economic time series. Within a short time period, several slightly modified types of the standard ARCH model were developed, of which the most important is the generalized ARCH (GARCH) model (Bollerslev, 1986). To estimate the short-run gold price model, I use the so called Asymmetric Power GARCH (APGARCH) model introduced by Ding et al. (1993).
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Figure 4: Residuals of OLS regression -8 -6 -4 -2 0 2 4 6 8 86 88 90 92 94 96 98 00 02 04
GOLDPRICE Res iduals
The APGARCH model can be described by equations (2), (3) and (4) where equation (2) is normally referred to as the mean equation, equation (3) gives the distribution of the errors and equation (4) describes the variance of the error term and is usually called the variance equation. t i t i t P X e P =α +β
∑
−1 +ψ∑
'+ (2) ) , 0 ( ~ td t N e σ (3)∑
∑
∑
= − − = − + + + + + = q j t i d j t d i t p i i t i d t c e e X 1 1 ' ) ( λ βσ ρ ξ θ σ (4)The mean equation includes an interceptα, a lagged vector of gold prices Pt-1 and a vector with exogenous macroeconomic variables X’. The error equation has a standard expected value of 0 and a variance which is described by the variance equation. Equation (4) captures the special characteristics of the APGARCH specification and each parameter will be separately tackled. First, the equation contains an intercept c and an innovation term ξt where
are d and λ where d is the parameter for the power term and λ is the leverage or asymmetry parameter.
The main advantage of these innovations is that it does not impose a stringent structure on the data but allows for an endogenous determination of the model parameters. Research on US stock market data by Ding et al. (1993) and Hentschel (1995) reveals that the standard ARCH en GARCH specifications where the power term is fixed at 2 does not necessarily give the best fit for the model. Their estimations of US stock market returns show optimal power terms of 1.43 and 1.52.
Furthermore earlier research on the stock market shows that positive and negative shocks do not bring forth equal responses. This fact is normally referred to as the leverage effect or asymmetry effect, see Black (1976). As mentioned above in equation (4) the leverage effect is measured by λ. If there is no leverage or asymmetry effect at all this parameter is close to zero and the equation transforms in a more normal GARCH equation. On the other hand, if λ is not equal to zero the financial time series include asymmetry effects which mean that there is a difference between positive and negative shocks. To conclude that leverage effects exist in the model λ have to be significantly negative. With leverage effects, the impact of previous negative shocks is a more than normal increase in current volatility. This can be seen from equation (4). When λ is negative and the shock in et-1 is negative as well, the product of these two terms is positive which results in a larger variance of the current period error. If a positive shock occurs the term in brackets will be adjusted downwards and the variance in the current period will be lower. In the case that λ is equal to zero, the asymmetry effect disappears and the term in brackets is just equal to past errors.
Table 2: Nested ARCH model specifications
Model d θ β λ
ARCH 2 free 0 0
GARCH 2 free free 0
Leverage ARCH 2 free 0 | λ | ≤ 1
Leverage GARCH 2 free free | λ | ≤ 1
Taylor ARCH 1 free 0 0
Taylor GARCH 1 free free 0
TARCH 1 free 0 | λ | ≤ 1
Generalized TARCH 1 free free | λ | ≤ 1
NARCH free free 0 0
Power GARCH free free free 0
Asymmetric PARCH free free 0 | λ | ≤ 1
Asymmetric PGARCH free free free | λ | ≤ 1
The application of this APGARCH model is therefore an easy way to test the different (G)ARCH specifications by changing the parameters. In the next section there is a comparison between the fit of the different models on daily gold price data.
The final step to complete the empirical model is to determine the lag length of each variable in equation (1). There is a trade-off between more explanatory power and more degrees of freedom in the model and selection methods like the Schwarz Information Criterion and the Akaike Information Criterion can be used to determine the optimal configuration. Both criteria work in the same way where the optimal lag length is the model with the lowest information criterion value. Tests are performed with a number of lags (L) 0, 1 and 2 and it is assumed that within each model the variables have the same lag length. All available data points over the entire period 1986-2008 are used to select the lag length of each variable. Table 3 contains the results.
Table 3: Test results for lagged variables
R-Squared Adj. R-Squared Schwarz I.C. Akaike I.C.
Model : L=0 0.0780 0.0752 2.2867 2.2650
Model : L=1 0.0905 0.0865 2.2874 2.2566
Model : L=2 0.0916 0.0863 2.2977 2.2577
III. Estimation Results
In this section the results of the empirical configurations are provided. First the outcome of the APGARCH model over the entire period is examined. Next, a breakpoint test is executed which shows that there seems to be a break in the model in the beginning of 2003. With this knowledge two new estimation rounds are performed, one for each period, 1986-2003 and 1986-2003-2008. Furthermore I provide a comparison of the APGARCH model and the other models of the GARCH family.
Table 4: Estimation results of the APGARCH model
Table 4 shows the result of the APGARCH regression for the period 1986-2008. As mentioned in the previous section, each variable is included for the current and the preceding time period. The lagged gold price has a significant negative influence on the current gold price which points to a kind of correction of previous price rises. The current and lagged Mean equation: Pt = iPt− + i
∑
Xt't− +et1 , 1 ψ
β
P is the gold price and X’ contains the exogenous variables Period: 1/7/1986-6/10/2008
Mean Equation Coefficient Std. Error
GOLD PRICE (-1) -0.0331 0.0129
EXCHANGE RATE -0.1654 0.0126
EXCHANGE RATE (-1) -0.0467 0.0138
STRESS DUMMY 0.0090 0.0016
STRESS DUMMY (-1) -0.0073 0.0012
CRUDE OIL PRICE 0.0187 0.0034
CRUDE OIL PRICE (-1) 0.0164 0.0035
INDUSTRIAL METALS INDEX 0.0775 0.0064
INDUSTRIAL METALS INDEX (-1) 0.0248 0.0069
exchange rate coefficients also have a significant negative effect on the gold price which is in line with theory. In terms of the US dollar it means that a devaluation of the US dollar results in an increase of the gold price and visa versa. The dummy which measures financial disturbances has a positive effect in the current period but a negative in the lagged time period. The positive sign of the current period supports the “flight to quality” or “safe haven” properties of gold but the negative lagged effect is a bit more difficult to explain. One explanation can be that investors overreact to financial distress by demanding more gold than
Figure 5: Short-term behaviour of gold price after a shock occurred
Gold Price Change
-8.00 -6.00 -4.00 -2.00 0.00 2.00 4.00 6.00 8.00 10.00 0 1 2 3 4 5 6 7 8 9 10 Time P e rc e n ta g e c h a n g e 9/28/1999 2/7/2000 9/11/2001 10/5/1999 2/9/2000 8/11/1986 1/16/1986
Source: London Gold Bullion market
significantly positive. The next variable in the APGARCH model is the food index. Both the coefficients of the current as well as the lagged variable are both significant and positive as expected. The food price variable can be seen as a short-term indicator of inflation and due to the positive relation between inflation and the gold price (gold as inflation hedge) the positive sign of the coefficients makes sense. The industrial metals index does to some extent also give an indication about short-term inflation, but it is even more an indicator for industrial gold demand.7 An increase in the index signals for increased industrial activity which in turn does have its demand impact on gold as a raw material. The positive estimated parameters for the industrial metals index in the current and preceding period is therefore in line with the expectation. The following variable is the stock market index which is an alternative for investing in gold. For that reason, a bullish stock market normally results in a redistribution of investments from gold towards equity, the so called search for yield which corresponds with the sign of the coefficient. The lagged coefficient for the stock market is not significant and therefore the sign of the lagged variable is rather meaningless. The same holds for current and lagged interest rate coefficients which are both not significant at the 5% level. Despite the coefficient of the lagged interest rate is not unambiguously defined, the sign of it is in the right direction. As mentioned in section I, the interest rate acts as an opportunity costs for holding gold investments and rising interest rates lead to a lower gold price and visa versa.
Besides the results of the mean equation, Table 4 contains also the outcomes of the variance equation. The explanatory variables were in a first attempt also incorporated in the variance equation, however it turned out that these were all insignificant and to keep the model simple they are removed from the equation. What is left are the parameters of the APGARCH model. All parameters are highly significant with p-values approaching zero. The theta and beta are the ARCH and GARCH parameters which are respectively 0.0418 and 0.9576. The more interesting parameters are the lambda and d where lambda accounts for leverage effects and d is the power term in the APGARCH configuration. Table 4 shows that lambda is -0.4198 which indicates that there are indeed leverage effects. This means that a negative shock on the gold price returns has a larger impact on volatility than a positive shock of the same magnitude. The power term of the APGARCH model (d) also has a significant impact on the variance equation. The magnitude of d which is 1.5921 is less than the ordinary GARCH equation where d is fixed at 2. The power term can freely adapt to the best fitting of the model so apparently a value of 1.5921 provide better results compared with the standard
7
GARCH specification. Wald tests on the power term with null hypothesis d=2 and d=1 can both be rejected which supports the conclusion that the APGARCH specification gives additional explanatory power. Table 5 gives an overview of Wald-tests performed on the other (G)ARCH models. The Chi-square test-statistics show that all models which fix one or more parameters are rejected. The APGARCH model is the only model in which the parameters are entirely endogenously determined and which does have no restrictions. Putting this altogether, the APGARCH specification describes the short-term movements of daily gold prices quite well in the period 1986-2008.
Table 5: Wald tests on the different (G)ARCH models
Model Restrictions Chi-square P-value
ARCH d=2, β=0, λ=0 384346.10 0.00 GARCH d=2, λ=0 125.40 0.00 Leverage ARCH d=2, β=0 295021.50 0.00 Leverage GARCH d=2 40.68 0.00 Taylor ARCH d=1, β=0, λ=0 377092.90 0.00 Taylor GARCH d=1, λ=0 275.94 0.00 TARCH d=1, β=0 292184.00 0.00 Generalized TARCH d=1 68.74 0.00 NARCH β=0,λ=0 333363.90 0.00 Power GARCH λ=0 116.74 0.00 Asymmetric PARCH β=0 284487.30 0.00
Asymmetric PGARCH free - -
Nevertheless it is probably not realistic that the dynamics in the gold markets are entirely constant over time. Figure 3 of section I shows that there seems to be a break in the behavior of the gold price around the start of the new century. Since the start of the data series, gold shows a clear negative correlation with the exchange rate but visual inspection shows that this relation approximately holds until 2003. From that point, a rapid rise in the gold price pops up which is not accompanied with a dollar devaluation of the same magnitude. Next we perform a test on the gold price model to look at break points.
A test for a possible break in a time series without knowing the exact date is the so called Quandt-Andrews test.8 This test is not applicable on (G)ARCH specifications and for that reason the ordinary least square method is used. Table 6 gives the results of the Quandt-Andrews test with the null hypothesis of no breakpoints in the time period. The results of the test show that the null hypothesis of no breakpoints within the time period can be clearly rejected. All test statistics are highly significant and the most likely breakpoint is located at date 2/6/2003. This seems to correspond with the visual observations made earlier. To
8
optimize the empirical APGARCH model, the dataset is divided in two periods conform the breakpoint test. The first period contains the observations 1/3/1986 till 2/5/2003 while the second period starts at 2/6/2003 and ends at 6/10/2008. Table 7 shows the results of the APGARCH model in the new time periods.9 Comparing the outcomes reveals that the impact of oil price changes and financial disturbances on gold prices are more or less the same in both periods. The significance of the coefficients of the interest rate has not changed either and is still insignificant in both periods.
Table 6: Break-point test results
H0: No Breakpoints within the trimmed data
Varying Regressors: Exchange Rate, Stress Dummy, Crude Oil Price, Industrial Metals Index, Food Index, Stock Market, Interest Rate
Quandt-Andrews test is conducted with 5% trimming.
Value P-value
Maximum LR F-statistic (2/6/2003) 40.35 0.00
Maximum Wald F-statistic (2/6/2003) 40.35 0.00
Exp LR F-statistic 17.34 0.00
Exp Wald F-statistic 17.34 0.00
Ave LR F-statistic 25.81 0.00
Ave Wald F-statistic 25.81 0.00
Note: probabilities calculated using Hansen's (1997) method.
More remarkable is the difference in the p-values of the stock market coefficients. In the period before the break the stock market has a clear negative impact on the gold price in both the current period and the lagged period. This seems to correspond with theory, which, as mentioned before, predicts that the stock market is an alternative investment opportunity for gold and therefore, bullish stock markets result in lower gold prices. After the break however, the stock market coefficients have become highly insignificant and this relationship seems not to hold anymore. It is difficult to interpret this difference between both periods. It can be the case that the length and timing of the period is one of the main causes of the difference. The period after the break is rather short and during this period the gold price has only increased.
9
Table 7: Estimation results of the APGARCH model for both sub samples Mean equation: Pt = iPt− + i
∑
Xt't− +et 1 , 1 ψ βP is the gold price and X’ contains the exogenous variables
Period 1:
1/7/1986-2/5/2003
Period 2:
2/6/2003-6/10/2008
Mean Equation Coefficient Std. Error Coefficient Std. Error
GOLD PRICE (-1) -0.0317 0.0146 -0.0915 0.0294
EXCHANGE RATE -0.1097 0.0133 -0.5776 0.0407
EXCHANGE RATE (-1) -0.0334 0.0142 -0.1657 0.0439
STRESS DUMMY 0.0074 0.0019 0.0230 0.0113
STRESS DUMMY (-1) -0.0076 0.0010 -0.0251 0.0109
CRUDE OIL PRICE 0.0142 0.0035 0.0200 0.0104
CRUDE OIL PRICE (-1) 0.0125 0.0037 0.0322 0.0112
INDUSTRIAL METALS INDEX 0.0447 0.0069 0.1995 0.0147
INDUSTRIAL METALS INDEX (-1) 0.0168 0.0074 0.0561 0.0161
FOOD INDEX 0.0306 0.0103 0.0868 0.0190 FOOD INDEX (-1) 0.0212 0.0104 0.0446 0.0196 STOCK MARKET -0.0391 0.0095 0.0058 0.0284 STOCK MARKET (-1) -0.0403 0.0093 0.0331 0.0298 INTEREST RATE -0.0113 0.0067 0.0502 0.0280 INTEREST RATE (-1) -0.0153 0.0092 -0.0232 0.0343 Variance equation:
∑
∑
∑
= − − = − + + + + + = q j t i d j t d i t p i i t i d t c e e X 1 1 ' ) ( λ βσ ρ ξ θ σ et ~N(0,σtd) Variance Equation CONSTANT 0.0048 0.0006 0.0026 0.0016 THETA 0.0514 0.0032 0.0217 0.0091 LAMBDA -0.3778 0.0385 -0.3573 0.0978 BETA 0.9505 0.0022 0.9689 0.0056 D 1.5200 0.0743 2.2491 0.5804This one-sidedly development could be the cause of the insignificant relation between the stock market and the gold price.10 Another explanation can be the rise of Exchange Traded Funds during this period. This new financial product, which is already described in section I D, can be seen as an alternative investment for physical gold, just like the stock market. Although Exchange Traded Funds have to acquire physical gold holdings to satisfy increased investment demand, they do not influence the gold price on a day to day basis. Therefore, it is reasonable that this has an impact on the role of the stock market as an alternative for gold holdings.
Another difference between the two periods is the correction mechanism of previous gold price changes. Where in the first period the coefficient for the lagged gold price is -0.0321, in the second period this coefficients is almost three times larger in absolute terms and accounts
10
-0.0915. Even more interesting are the coefficients of the exchange rate, industrial metal index and food index. For these variables the coefficients are highly significant and there impact on gold prices has shown a major increase. Especially the relation between gold prices and the exchange rate has changed dramatically from the first to the second period. The sign of the exchange rate parameter has not changed but its absolute magnitude is in the second period substantially larger than the first period. The impact of the exchange rate on gold prices is in the second period almost 6 times larger than in the first period. In the time period 2/6/2003 – 6/10/2008 an appreciation of the USD of 1% in the current period reduces the gold price with almost 0.6% while an appreciation in the previous period reduces the gold price by 0.17%.
Another striking result is the change in the coefficient of industrial metals. The sign of this coefficient has also stayed the same but the magnitude in the second period is much larger than the first period. Finally, the impact of the food index has increased from the first period to the second. Figure 6 provides an overview of the magnitude of the coefficients in both periods were the dots represent the coefficient values for the first and the second period, which are in between a confidence interval of two times the standard deviation. The confidence intervals for the exchange rate, the industrial metal index and the food index do not overlap each other which is even more evidence for a structural break.
Figure 6: Coefficients APGARCH model in period 1 and period 2
Besides the variables in the mean equation there are also differences between the variance equations of both periods. The magnitude of the intercept is nearly the same in both periods and the value of theta slightly differs. More interesting however is that the leverage effect which showed up in the APGARCH model of the entire period, also exist in both sub sample periods by almost the same magnitude. The variable which has experienced the largest change is the power term (d). Where the power term in the first period had a magnitude which differed significantly from 2 (the standard (G)ARCH model), in the second period the power term converges more toward the ordinary (G)ARCH models. Consequently, a Wald test where the null hypothesis is d=2 cannot be rejected.
Now we have discussed the variations of all the variables in isolation, it is interesting to analyze the roots of the break in a more general way. Gold demand for consumption and gold supply effects which are both long-term oriented can be potential sources of the recently increased gold price. Our short-term model does not incorporate such effects however and therefore we try to look at another cause for the breakpoint in the model which is the establishment of exchange traded funds. The characteristics of this new way of investing are already described in section I D and are left out in this section. As mentioned before, the first exchange traded funds were founded in the beginning of 2003 which is almost at the same time of the break point. The rapid growth of these funds (during the first five years the average year-on-year growth was more than 150%) is a first signal for their increased importance in the gold market. The characteristics of these funds are another aspect which can explain a break in the gold price model. In the past, holding gold as an investment asset came together with some obstacles like storage costs, transportation costs and insurance costs which made the gold market more difficult to approach compared to other asset classed. With the arrival of ETF’s these problems were solved and investing in gold became more simple and accessible for all type of investors; see the speech of Nedeljkovic (2005). To test the effects of exchange traded funds on the short-run gold price, the APGARCH model is estimated one more time with lagged ETF holdings as an additional explanatory variable.11 The results of this alternative model are provided in Table 15 of the appendix. The ETF variable, in which we are mainly interested, appears to be significantly positive which means that lagged physical gold purchases push current spot prices upwards. Although the degree to which these funds have altered the gold market is difficult to estimate, the regression outcome support, at
11
least to some extent, the idea that the introduction of exchange traded funds has changed the short-term gold market.
just looking in a more straightforward way, these theories seem to be in line with actual gold price behavior.
The fact that the APGARCH estimation method is different compared to the regular models makes it interesting to look at its forecasting ability, and compare this with other models. We have used data from the start of the second period (2/6/2003) up to the end of 2007 (12/29/2007) to estimate the model once again. Subsequently, we have made several forecasts for different time spans in the remaining period (1/1/2008 – 6/10/2008). These periods are out-of-sample, are arbitrary defined and exist out of one week ahead (starting at 6/3/2008), one month ahead, 3 months ahead and 6 months ahead. Actual observations are inserted for the explanatory variables in the out-of-sample observation period and the forecasting method is dynamic. Table 15 in the appendix provides an overview of the root mean squared errors (RMSE) and the mean absolute errors (MAE) of the APGARCH model as well as for the more common OLS and GARCH(1,1) models. It appears that the forecasting abilities of the different models depend strongly on the selected time period but are not very different within a certain period.
Figure 7: Forecast ability of the APGARCH model
Forecast Ability -6.5 -4.5 -2.5 -0.5 1.5 3.5 P er c e n ta g e C h a n g e Lower Bound Upper bound Forecast Price Actual Price
model. Figure 7 shows that the forecast price approaches the actual gold price quit well. Although the magnitude of the predicted gold price changes does not exactly matches the actual price movement, the direction is most of the time correct. Furthermore, it can be seen that the actual gold price only occasional passes the upper or lower confidence interval bounds.
To limit the impact of a specific time period on the forecasting results, another out-of-sample forecast is performed which uses a rolling window estimation. More specific, for each type of (G)ARCH model, out-of-sample forecasts are performed with a changing sample period. The first period which is used to estimate the parameters of the model is 2/6/2003-12/29/2006 and these parameters are used to forecast the gold price for the period 1/1/2007-1/7/2007. Thereafter the sample period which is used to obtain the parameters of the model as well as the out-of-sample forecasting period, shift each time with a week, until the end of the data series which is 6/10/2008. Finally, the complete vector of forecasted gold prices is compared with the actual gold prices of the out-of-sample period and the RMSE and mean absolute percentage error (MAPE) are calculated.
Table 8: Forecast evaluation of nonlinear (G)ARCH models, as compared to the ARCH model.
RMSE MAPE OLS 1.0004 1.0080 GARCH 1.0084 0.9254 Power ARCH 1.0044 0.9964 Leverage ARCH 1.0000 1.0000 Leverage GARCH 1.0084 0.9254 No-change model 1.6055 2.1306
Assymetric Power GARCH 1.0135 0.9080
The MAPE signals for more difference between the (G)ARCH specifications although the OLS, the Power ARCH and the Leverage ARCH models seem to behave nearly the same as the ARCH model. The GARCH, Leverage GARCH and APGARCH models perform substantial better. Following the MAPE, the APGARCH model has the lowest number and the forecast results appears to be almost 10% better compared to the standard ARCH specification. The differences between the two forecast evaluation statistics rise from the fact that the RMSE gives more weight to extreme outliers due to the non-linear configuration. When we mitigate these outliers, the APGARCH method seems to provide better forecasting results. Overall however, there is not enough ground to conclude that there are substantial differences between the (G)ARCH models.
IV. Summary and Conclusions
Generally, previous empirical research on the gold market is performed over long time periods with monthly, quarterly or yearly data. This study is an attempt to discover more details about the short-term determinants in the gold market. With daily figures of an extensive time period and by using a recently introduced (APGARCH) estimation method, several conclusions can be drawn.
First, empirical evidence underscores the role of gold as an exchange rate hedge. While the strength of the correlation between gold and the USD exchange rate is changing over time, the direction of this relation is clearly negative. To be more specific, a devaluation (appreciation) of the dollar results in an increase (decrease) of the gold price.
Two other determinants which have an impact on the gold price are the oil price and the food price index. These two variables can be seen as proxies for short-term inflation (expectations) and both figures have a positive correlation with the gold price. The use of proxies for inflation due to the unavailability of high frequency general price levels however, is a serious limitation. Therefore the positive correlation between the oil and food price, and the gold price, is not unambiguous evidence for the inflation hedge theory.
In addition to the examination of the several theories about the determinants in the gold market, this study has also observed developments in these determinants of gold in time. A break point test provides evidence for a structural break in the short-term gold market around the beginning of 2003. Consequently, the overall estimation period is divided in two periods, namely 1986-2003 and 2003-2008. Two separate regressions show that the determinants of the short-term gold market behave different in both periods where the most striking result is the increased correlation between the gold price and the exchange rate.
Another remarkable development in the gold market, which is worth to be mentioned, is the rise of Exchange Traded Funds. These funds provide new opportunities to invest in physical gold without bearing the disadvantages like insurance and storage costs. The first ETF’s are established in 2003 and since then this market has experienced a tremendous growth which could be one of the explanations for the structural break in the time series.
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Appendix
Table 9: Unit Root tests 1/7/1986-6/10/2008
Variable Levels First Differences
Gold price t-statistic a)
Intercept included Trend included Lag length b) 0.74 Yes Yes 0 -76,54** Yes No 0 Exchange Rate: GBP/USD t-statistic a) Intercept included Trend included Lag length b) -2.41 Yes No 0 -77.11** No No 0 YEN/USD t-statistic a) Intercept included Trend included Lag length b) -4.36** Yes No 0 EUR/USD t-statistic a) Intercept included Trend included Lag length b) -3.02 Yes Yes 1 -52.81** Yes Yes 0
Stress dummy t-statistic a)
Intercept included Trend included Lag length b) -16.88** Yes Yes 8
Crude Oil Price t-statistic a)
Intercept included Trend included Lag length b) 3.56 No No 3 -48.45** Yes Yes 2 S&P GSCI
Industrial Metals Spot
t-statistic a) Intercept included Trend included Lag length b) -1.16* Yes Yes 0 -79.26** Yes Yes 0 S&P GSCI Agricultural Spot t-statistic a) Intercept included Trend included Lag length b) 1.26 No No 2 -54.28** Yes Yes 1 Stock market: NYSE COMPOSITE t-statistic a) Intercept included Trend included Lag length b) -2.54 Yes Yes 0 -78.27** Yes No 0 S&P500 COMPOSITE t-statistic a) Intercept included Trend included Lag length b) -2.13 Yes Yes 0 -79.27** Yes No 0 FTSE 100 t-statistic a) Intercept included Trend included Lag length b) -1.90 Yes Yes 3 -48.40** Yes No 2 Interest rate: UK INTERBANK 3M. t-statistic a) Intercept included Trend included Lag length b) -1.48 No No 3 -65.30** Yes Yes 1
Table 10: Unit Root tests 1/7/1986-2/5/2003
Variable Levels First Differences
Gold price t-statistic a)
Intercept included Trend included Lag length b) -2.75 Yes Yes 0 -68.85** No No 0 Exchange Rate: GBP/USD t-statistic a) Intercept included Trend included Lag length b) -3.22 Yes Yes 0 -67.09** No No 0 YEN/USD t-statistic a) Intercept included Trend included Lag length b) -3.98** Yes No 0 EUR/USD t-statistic a) Intercept included Trend included Lag length b) -2.06 Yes No 0 -34.87** Yes Yes 0
Stress dummy t-statistic a)
Intercept included Trend included Lag length b) -14.70** Yes Yes 8
Crude Oil Price t-statistic a)
Intercept included Trend included Lag length b) -3.68* Yes Yes 3 -48.45** Yes Yes 2 S&P GSCI
Industrial Metals Spot
t-statistic a) Intercept included Trend included Lag length b) -2.91* Yes No 1 -63.12** No No 0 S&P GSCI Agricultural Spot t-statistic a) Intercept included Trend included Lag length b) -2.02 Yes Yes 1 -63.11** No No 0 Stock market: NYSE COMPOSITE t-statistic a) Intercept included Trend included Lag length b) -1.33 Yes Yes 1 -63.81** Yes No 0 S&P500 COMPOSITE t-statistic a) Intercept included Trend included Lag length b) -1.15 Yes No 0 -66.84** Yes Yes 0 FTSE 100 t-statistic a) Intercept included Trend included Lag length b) -1.41 Yes No 3 -42.29** Yes Yes 2 Interest rate: UK INTERBANK 3M. t-statistic a) Intercept included Trend included Lag length b) -1.56 No No 2 -57.54** Yes No 1
Table 11: Unit Root tests 2/5/2003-6/10/2008
Variable Levels First Differences
Gold price t-statistic a)
Intercept included Trend included Lag length b) -2.46 Yes Yes 0 -36.82** Yes Yes 0 Exchange Rate: GBP/USD t-statistic a) Intercept included Trend included Lag length b) -2.34 Yes Yes 0 -38.30** Yes No 0 YEN/USD t-statistic a) Intercept included Trend included Lag length b) -2.19 Yes Yes 0 -39.24** No No 0 EUR/USD t-statistic a) Intercept included Trend included Lag length b) -2.32 Yes Yes 0 -39.67** Yes No 0
Stress dummy t-statistic a)
Intercept included Trend included Lag length b) -5.86** Yes Yes 12
Crude Oil Price t-statistic a)
Intercept included Trend included Lag length b) -2.31 No No 0 -39.60** Yes Yes 0 S&P GSCI
Industrial Metals Spot
t-statistic a) Intercept included Trend included Lag length b) -2.39 Yes Yes 0 -40.27** Yes No 0 S&P GSCI Agricultural Spot t-statistic a) Intercept included Trend included Lag length b) 1.78 Yes No 1 -33.73** Yes Yes 0 Stock market: NYSE COMPOSITE t-statistic a) Intercept included Trend included Lag length b) -2.63 Yes Yes 1 -41.43** Yes Yes 0 S&P500 COMPOSITE t-statistic a) Intercept included Trend included Lag length b) -2.73 Yes Yes 1 -42.05** Yes Yes 0 FTSE 100 t-statistic a) Intercept included Trend included Lag length b) -2.20 Yes Yes 1 -42.53** Yes Yes 0 Interest rate: UK INTERBANK 3M. t-statistic a) Intercept included Trend included Lag length b) -1.84 Yes Yes 6 -13.77** Yes No 5
Table 12: Granger Causality tests
H0: Explanatory variable does not Granger Cause Gold Price
F-Statistic Prob.
Exchange rate 5.4267 0.0002
Oil price 7.4165 0.0000
Industrial Metals index 7.3054 0.0000
Stock market 2.7641 0.0260
Interest rate 0.4115 0.8005
Food index 7.0231 0.0000
Stress dummy 2.7297 0.0276
H0: Gold Price does not Granger Cause Explanatory variable
F-Statistic Prob.
Exchange rate 1.0904 0.3594
Oil price 0.4157 0.7974
Industrial Metals index 2.7982 0.0246
Stock market 1.7964 0.1266
Interest rate 0.5086 0.7294
Food index 0.2261 0.9239
Stress dummy 0.7908 0.5309
Table 13: Estimation results for the APGARCH model with an intercept
Mean equation: Pt =c+ iPt− + i
∑
Xtt− +et ' 1 , 1 ψ βP is the gold price and X’ contains the exogenous variables and c is an intercept
Period 1:
1/7/1986-2/5/2003
Period 2:
2/6/2003-6/10/2008
Mean Equation Coefficient Std. Error Coefficient Std. Error
C 0.0046 0.0100 0.0312 0.0248 GOLD PRICE (-1) -0.0319 0.0144 -0.0924 0.0294 EXCHANGE RATE -0.1091 0.0133 -0.5796 0.0409 EXCHANGE RATE (-1) -0.0348 0.0143 -0.1703 0.0441 STRESS DUMMY 0.0133 0.0013 0.0135 0.0122 STRESS DUMMY (-1) -0.0160 0.0014 -0.0336 0.0116
CRUDE OIL PRICE 0.0140 0.0036 0.0198 0.0104
CRUDE OIL PRICE (-1) 0.0125 0.0037 0.0311 0.0113
INDUSTRIAL METALS INDEX 0.0492 0.0072 0.1980 0.0149
INDUSTRIAL METALS INDEX (-1) 0.0151 0.0079 0.0532 0.0163
Table 14: Estimation results for the APGARCH model with ETF included
Table 15: Forecast abilities of three different models
APGARCH OLS GARCH(1,1)
Period: RMSE MAE RMSE MAE RMSE MAE
6 months 1.3452 1.0095 1.3274 0.9981 1.3407 1.0068 3 months 1.4869 1.1149 1.4785 1.1045 1.4844 1.1139 1 month 1.1425 0.9583 1.1126 0.9245 1.1336 0.9514 1 week 1.4297 1.1699 1.3718 1.0985 1.4076 1.1460 Mean equation: Pt = iPt− + i
∑
Xtt− +et ' 1 , 1 ψ βP is the gold price and X’ contains the exogenous variables Period: 2/6/2003-6/10/2008
Mean Equation Coefficient Std. Error
ETF 0.0166 0.0033 GOLD PRICE (-1) -0.0331 0.0364 EXCHANGE RATE -0.1654 0.0569 EXCHANGE RATE (-1) -0.0467 0.0647 STRESS DUMMY 0.0090 0.0144 STRESS DUMMY (-1) -0.0073 0.0173
CRUDE OIL PRICE 0.0187 0.0132
CRUDE OIL PRICE (-1) 0.0164 0.0126
INDUSTRIAL METALS INDEX 0.0775 0.0182
INDUSTRIAL METALS INDEX (-1) 0.0248 0.0220
