Mixture Nonlinear Time-Series Analysis : Modelling and Forecasting

Abstract

Gaussian mixture transition distribution (GMTD) models and mixture autoregressive (MAR) models are generally employed to describe those data sets that depict sudden bursts, outliers and flat stretches at irregular time epochs. In this paper , these two approaches are compared by considering weekly wholesale onion price data during April, 1998 to November, 2001. After eliminating trend, seasonal fluctuations are studied by fitting Box­Jenkins airline model to residual series. To this end, null hypothesis of presence of nonseasonal and seasonal stochastic trends is tested by using Osboru­Chui­Smith­Birchenhall (OCSB) auxiliary regression. Subsequently, appropriate filters in airline model for seasonal fluctuations are selected. Presence of autoregressive co nditional heteroscedasticity (ARCH) is tested by Naive Lagrange multiplier (Nave­ LM) test. Estimation of parameters is carric~d out using Expectation­Maximization (EM) algorithm and the best model is selected on the basis of Bayesian information criterion (BIC). Out­of­sample forecasting is performed for one­step and two­step ahead prediction by uaive approach, proposed by Wong and Li (2000). It is concluded that, for data under consideration, a three­component MAR model performs the best.