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Mixture nonlinear time-series analysis: modelling and forecasting. (English) Zbl 1170.62364

Summary: 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 the Box-Jenkins airline model to residual series. To this end, the null hypothesis of presence of nonseasonal and seasonal stochastic trends is tested by using the D. R. Osborn, A. P. L. Chui, J. P. Smith and C. R. Birchenhall (OCSB) auxiliary regression [Oxf. Bull. Econ. Stat. 50, 361–377 (1988)]. Subsequently, appropriate filters in the airline model for seasonal fluctuations are selected. Presence of autoregressive conditional heteroscedasticity (ARCH) is tested by the naive Lagrange multiplier (Naive-LM) test. Estimation of the parameters is carried out using the Expectation-Maximization (EM) algorithm and the best model is selected on the basis of the Bayesian information criterion (BIC). Out-of-sample forecasting is performed for one-step and two-step ahead prediction by the naive approach, proposed by C. S. Wong and W. K. Li [J. R. Stat. Soc., Ser. B, Stat. Methodol. 62, No. 1, 95–115 (2000; Zbl 0941.62095)]. It is concluded that, for data under consideration, a three-component MAR model performs the best.

MSC:

62M20 Inference from stochastic processes and prediction
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62J02 General nonlinear regression
91B24 Microeconomic theory (price theory and economic markets)

Citations:

Zbl 0941.62095
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