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

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.

[1]  Jan Beran,et al.  Statistics for long-memory processes , 1994 .

[2]  P. Phillips.  Testing for a Unit Root in Time Series Regression , 1988 .

[3]  Uwe Hassler,et al.  Long Memory in Inflation Rates: International Evidence , 1995 .

[4]  J. Geweke,et al.  THE ESTIMATION AND APPLICATION OF LONG MEMORY TIME SERIES MODELS , 1983 .

[5]  P. Robinson.  Time Series with Long Memory , 2003 .

[6]  D. Dickey,et al.  Testing for unit roots in autoregressive-moving average models of unknown order , 1984 .

[7]  R. Paul,et al.  STATISTICAL MODELLING OF INLAND FISH PRODUCTION IN INDIA , 2010 .

[8]  Jan Beran,et al.  Maximum Likelihood Estimation of the Differencing Parameter for Invertible Short and Long Memory Autoregressive Integrated Moving Average Models , 1995 .

[9]  W. Fuller,et al.  Distribution of the Estimators for Autoregressive Time Series with a Unit Root , 1979 .

[10]  F. Scacciavillani.  Long Memory Processes and Chronic Inflation , 1994 .

[11]  Ying-Wong Cheung,et al.  A search for long memory in international stock market returns , 1995 .

[12]  Modelling and Forecasting of Meat Exports from India , 2013 .

[13]  Katsuto Tanaka,et al.  THE NONSTATIONARY FRACTIONAL UNIT ROOT , 1999, Econometric Theory.

[14]  Examining the dependency in intra‐day stock index futures , 1994 .

[15]  Fred R. Kaen,et al.  Memory in commodity futures contracts , 1984 .

[16]  K. Denning,et al.  Long-term and short-term price memory in the stock market , 1995 .

[17]  Hyun Joung Jin,et al.  Fractional Integration in Agricultural Futures Price Volatilities , 2004 .

[18]  Rohit S. Deo,et al.  The mean squared error of Geweke and Porter‐Hudak's estimator of the memory parameter of a long‐memory time series , 1998 .

[19]  R. Baillie,et al.  Fractionally integrated generalized autoregressive conditional heteroskedasticity , 1996 .

[20]  Fred R. Kaen,et al.  R/S analysis of foreign exchange rates under two international monetary regimes , 1982 .

[21]  P. Robinson.  Log-Periodogram Regression of Time Series with Long Range Dependence , 1995 .