Forecasting Wholesale Price of Pigeon Pea Using Long Memory Time-Series Models

Abstract

The fractional integration is a generalization of integer integration, under which time-series are usually presumed to be integrated of order zero or one. In this regard, the autoregressive fractionally integrated moving-average (ARFIMA) model along with its estimation procedure is investigated. ARFIMA model searches for a non-integer differencing parameter d to difference the data to capture long memory. The model has been applied for modelling and forecasting of daily wholesale price of pigeon pea (Cajanas cajan) in the Amritsar and Bhatinda markets and the all-India maximum, minimum and modal prices of pigeon pea. Augmented Dickey-Fuller (ADF) test and Philips Perron (PP) test have been used for testing the stationarity of the series. Autocorrelation (ACF) and partial autocorrelation (PACF) functions have shown a slow hyperbolic decay indicating the presence of long memory. In all the five price series, long memory parameters are found to be significant. On the basis of minimum AIC values, the best model was identified for each series. To this end, evaluation of forecasting was carried out with root mean squares prediction error (RMSPE), mean absolute prediction error (MAPE) and relative mean absolute prediction error (RMAPE). The residuals of the fitted models have been used for diagnostic checking. Out-of sample forecast of wholesale prices of pigeon pea has been computed up to February, 2014. The R software package has been used for data analysis.