On a mixture autoregressive model

Chun Shan WONG, Wai Keung LI

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169 Citations (Scopus)

Abstract

We generalize the Gaussian mixture transition distribution (GMTD) model introduced by Le and co‐workers to the mixture autoregressive (MAR) model for the modelling of non‐linear time series. The models consist of a mixture of K stationary or non‐stationary AR components. The advantages of the MAR model over the GMTD model include a more full range of shape changing predictive distributions and the ability to handle cycles and conditional heteroscedasticity in the time series. The stationarity conditions and autocorrelation function are derived. The estimation is easily done via a simple EM algorithm and the model selection problem is addressed. The shape changing feature of the conditional distributions makes these models capable of modelling time series with multimodal conditional distributions and with heteroscedasticity. The models are applied to two real data sets and compared with other competing models. The MAR models appear to capture features of the data better than other competing models do. Copyright © 2000 Royal Statistical Society.
Original languageEnglish
Pages (from-to)95-115
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume62
Issue number1
DOIs
Publication statusPublished - 2000

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Autoregressive Model
Mixture Model
Gaussian Mixture
Conditional Distribution
Model
Conditional Heteroscedasticity
Time Series Modelling
Nonlinear Time Series
Predictive Distribution
Heteroscedasticity
Stationarity
Autocorrelation Function
EM Algorithm
Autoregressive model
Model Selection
Time series
Cycle
Generalise
Modeling
Range of data

Citation

Wong, C. S., & Li, W. K. (2000). On a mixture autoregressive model. Journal of the Royal Statistical Society, Series B: Statistical Methodology, 62(1), 95-115. doi: 10.1111/1467-9868.00222

Keywords

  • Autocorrelation
  • EM algorithm
  • Mixture autoregressive model
  • Model selection
  • Stationarity