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October 10 th 2007Nupur Hetamsaria & Mithun Maity Application of ARIMA and GARCH Models to forecast the Gold Futures Prices Dr. Nupur Hetamsaria (ICFAI Business School, Hyderabad) & Mithun Maity (Karvy Comtrade, Hyderabad) NICR Workshop, October 10 th 2007

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October 10 th 2007Nupur Hetamsaria & Mithun Maity Gold: An Investment Tool Equities and Commodities Gold forms 45% of total futures trading globally An effective hedging tool Higher liquidity than other real assets Oil price impact on Gold Resale value of Gold Forecasting the future Gold prices

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October 10 th 2007Nupur Hetamsaria & Mithun Maity Data and Methodology Daily prices from NYMEX and COMEX 14 years, appx. 3500 data points ARIMA GARCH

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October 10 th 2007Nupur Hetamsaria & Mithun Maity Price Graph of Gold Prices

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October 10 th 2007Nupur Hetamsaria & Mithun Maity Stationarity ADF Test Statistic0.3133241% Critical Value*-3.43532 PP Test Statistic0.4397371% Critical Value* -3.4353 Gold Price series is not stationary. First Difference of the price series.

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October 10 th 2007Nupur Hetamsaria & Mithun Maity Dickey Fuller TestPhilip Peron Test Intercept ADF Test Statistic-23.863 1% Critical Value*-3.4353 PP Test Statistic-60.86858 1% Critical Value*-3.4353 Akaike info criterion5.482112 Akaike info criterion5.485396 Schwarz criterion5.492703 Schwarz criterion5.488923 Trend and Intercept ADF Test Statistic-23.9215 1% Critical Value*-3.9662 PP Test Statistic-60.9116 1% Critical Value*-3.9662 Akaike info criterion5.481955 Akaike info criterion5.485005 Schwarz criterion5.494311 Schwarz criterion5.490296 None ADF Test Statistic-23.8299 1% Critical Value*-2.5664 PP Test Statistic-60.84753 1% Critical Value*-2.5664 Akaike info criterion5.481968 Akaike info criterion5.485379 Schwarz criterion5.490794 Schwarz criterion5.487142

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October 10 th 2007Nupur Hetamsaria & Mithun Maity

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October 10 th 2007Nupur Hetamsaria & Mithun Maity Normality Mean0.086144 Median0 Skewness-0.74033 Kurtosis18.11785 Jarque Barra33582.55 Probability0 Kurtosis high, indicating a fat tail distribution or a leptokurtic distribution.

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October 10 th 2007Nupur Hetamsaria & Mithun Maity Correlogram VariableCoefficientStd. Errort-StatisticProb. AR(1)0.6213010.05615711.063710 AR(3)-0.1343980.032265-4.1653870 AR(6)0.2076760.0611523.3960520.0007 AR(11)0.3974220.0493148.0589820 AR(17)-0.1161560.055514-2.092390.0365 AR(21)-0.2493670.024521-10.169530 AR(28)-0.0507720.015572-3.2605150.0011 MA(1)-0.6412570.05479-11.703850 MA(3)0.1744630.032615.3500720 MA(6)-0.2453220.056933-4.3089680 MA(11)-0.4351560.046657-9.3267470 MA(17)0.1710750.0583232.9332330.0034 MA(21)0.2368520.02338310.129330

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October 10 th 2007Nupur Hetamsaria & Mithun Maity

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October 10 th 2007Nupur Hetamsaria & Mithun Maity Heteroscedasticity ARCH Test: F-statistic74.38698 Probability0 Obs*R-squared72.86433 Probability0

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October 10 th 2007Nupur Hetamsaria & Mithun Maity GARCH: Mean equation GARCH(1,1) Mean Equation CoefficientStd. Errorz-StatisticProb. AR(6)-0.039030.018965-2.057780.0396 AR(12)-0.044920.018417-2.438810.0147 AR(45)-0.045220.017644-2.562660.0104 AR(79)0.0493380.018432.6770980.0074 AR(89)-0.033710.017259-1.953140.0508

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October 10 th 2007Nupur Hetamsaria & Mithun Maity Variance Equation C9.54E-089.48E-081.006210.3143 ARCH(1)0.041620.013393.108260.0019 GARCH(1)0.9604880.01269875.641370 GARCH (1,1)

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October 10 th 2007Nupur Hetamsaria & Mithun Maity ARCH Test: F-statistic1.513348 Probability0.218712 Obs*R-squared1.513561 Probability0.218597

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October 10 th 2007Nupur Hetamsaria & Mithun Maity Performance of In sample forecast Root Mean Squared Error7.622201 Theil Inequality Coefficient0.006179 Bias proportion0.000069 Variance proportion0.000121 covariance proportion0.99981

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October 10 th 2007Nupur Hetamsaria & Mithun Maity Performance of out of sample forecast

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