Modeling Long Memory in Volatility for Spot Price of Lentil with Multi-step Ahead Out-of-sample Forecast Using AR-FIGARCH Model

The potential presence of long memory (LM) properties in return and volatility of the spot price of lentil in Indore market has been investigated. Geweke and Porter-Hudak (1983) (GPH) method has been applied to test for presence of long range dependence in the volatility processes for the series. Stationarity of the series has been tested using Augmented Dickey-Fuller (ADF) unit root test and Philips-Peron (PP) unit root test. It is observed that both the log returns as well as squared log returns series are stationary at level but there is a significant presence of long memory in squared log return series. Accordingly, AR-FIGARCH model was applied for forecasting the volatility of lentil price. To this end, window based evaluation of forecasting is carried out with the help of Mean squares prediction error (MSPE), Root MSPE (RMSPE), Mean absolute prediction error (MAPE) and Relative MAPE (RMAPE). The residuals of the fitted models were used for diagnostic checking. Out-of sample forecast of volatility has been computed for 1st June-31st July, 2015 along with the percentage deviation from the actual price. The maximum deviation has been found to be 2.55%. The R software package has been used for data analysis.