1. 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

2. 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

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

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

5. 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.

6. 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

7. October 10 th 2007Nupur Hetamsaria & Mithun Maity

8. 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.

9. 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

10. October 10 th 2007Nupur Hetamsaria & Mithun Maity

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

12. 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

13. 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)

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

15. 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

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