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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 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 Statistic % Critical Value* PP Test Statistic % Critical Value* 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 % 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

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October 10 th 2007Nupur Hetamsaria & Mithun Maity

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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.

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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)

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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-statistic Probability0 Obs*R-squared 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) AR(12) AR(45) AR(79) AR(89)

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

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

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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

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

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