Forecasting of Long Memory Time-Series Paul Ranjit Kumar Indian Agricultural Statistics Research Institute, New Delhi-110 012 Online published on 10 September, 2013. Abstract Fractional integration is the primary conceptual framework for describing long memory in financial time-series. It 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 has been widely studied. It searches for a non-integer differencing parameter to differentiate the data to capture long memory. In the present investigation, this model has been applied for forecasting of daily wholesale price of pigeon pea (Cajanas cajan) in Amritsar and Bhatinda markets and the all-India maximum, minimum and modal price of pigeon pea. The data were collected from the Ministry of Consumer's Affairs, Government of India, New Delhi, for the period 1st January to 10th June, 2013. The Augmented Dickey-Fuller (ADF) test and Philips Peron (PP) test have been conducted to test the stationarity of 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 have been found to be significant. On the basis of minimum AIC values, the best model has been identified for each series. Finally, the evaluation of forecasting has been 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 were used for diagnostic checking. Top Keywords ADF test, ARFIMA model, long memory, PP test, stationarity. Top |