Non-Linear Time Series Modeling of Volatile Onion Price Data Using AR(p )-ARCH( q)-In-Mean

Abstract

Onion prices have been in the headline since 1998 for its tear jerking effect on consumers, farmers and Government alike. Present paper attempts to develop a realistic time-series model to explain the behaviour of monthly onion price data during April, 1996 to October, 2001 collected from National Agricultmal Cooperative Marketing Federation (NAFED), New Delhi. In the first step, attempts are made to apply Seasonal Autoregressive (SAR) model to the detrended data. However, residual analysis reveals that assumption of constant one-period ahead forecast variance does not hold true. Accordingly, a new class of stochastic processes, called Autoregressive Conditional Heterosqedastic (ARCH) process, is studied to model the residual series. To this end, computer programs are written in EViews and package, Version 4.0 and IML in SAS, Version 8e to perform Lagrange-Multiplier test for possible presence of ARCH, to fit the AR(p )- ARCH( q) model, and to carry out residual analysis after fitting ARCH model. It is shown that ARCH model provides a good description of the data under consideration. Finally, the identified model is employed for forecasting purposes.