© 2001 by Biometrika Trust
On a logistic mixture autoregressive model
1 Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kongchun-shan.wong{at}graduate.hku.hk hrntlwk{at}hku.hk
We generalise the mixture autoregressive, MAR, model to the logistic mixture autoregressive with exogenous variables, LMARX, model for the modelling of nonlinear time series.The models consist of a mixture of two Gaussian transfer function models with the mixing proportions changing over time. The model can also be considered as a generalisation of the self-exciting threshold autoregressive, SETAR, model and the open-loop threshold autoregressive, TARSO, model. The advantages of the LMARX model over other nonlinear time series models include a wider range of shape-changing predictive distributions, the ability to handle cycles and conditional heteroscedasticity in the time series and better point prediction. Estimation is easily done via a simple EM algorithm and the model selection problem is addressed. The models are applied to two real datasets and compared with other competing models.
Key Words: EM algorithm; Forecasting; Mixture model; Model selection
Received October 1999. Revised December 2000