October 10 th 2007Nupur Hetamsaria & Mithun Maity Application of ARIMA and GARCH Models to forecast the Gold Futures Prices Dr. Nupur Hetamsaria (ICFAI.

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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

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

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

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

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

October 10 th 2007Nupur Hetamsaria & Mithun Maity Dickey Fuller TestPhilip Peron Test Intercept ADF Test Statistic % Critical Value* PP Test Statistic % Critical Value* Akaike info criterion Akaike info criterion Schwarz criterion Schwarz criterion Trend and Intercept ADF Test Statistic % Critical Value* PP Test Statistic % Critical Value* Akaike info criterion Akaike info criterion Schwarz criterion Schwarz criterion None ADF Test Statistic % Critical Value* PP Test Statistic % Critical Value* Akaike info criterion Akaike info criterion Schwarz criterion Schwarz criterion

October 10 th 2007Nupur Hetamsaria & Mithun Maity

October 10 th 2007Nupur Hetamsaria & Mithun Maity Normality Mean Median0 Skewness Kurtosis Jarque Barra Probability0 Kurtosis high, indicating a fat tail distribution or a leptokurtic distribution.

October 10 th 2007Nupur Hetamsaria & Mithun Maity Correlogram VariableCoefficientStd. Errort-StatisticProb. AR(1) AR(3) AR(6) AR(11) AR(17) AR(21) AR(28) MA(1) MA(3) MA(6) MA(11) MA(17) MA(21)

October 10 th 2007Nupur Hetamsaria & Mithun Maity

October 10 th 2007Nupur Hetamsaria & Mithun Maity Heteroscedasticity ARCH Test: F-statistic Probability0 Obs*R-squared Probability0

October 10 th 2007Nupur Hetamsaria & Mithun Maity GARCH: Mean equation GARCH(1,1) Mean Equation CoefficientStd. Errorz-StatisticProb. AR(6) AR(12) AR(45) AR(79) AR(89)

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

October 10 th 2007Nupur Hetamsaria & Mithun Maity ARCH Test: F-statistic Probability Obs*R-squared Probability

October 10 th 2007Nupur Hetamsaria & Mithun Maity Performance of In sample forecast Root Mean Squared Error Theil Inequality Coefficient Bias proportion Variance proportion covariance proportion

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

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