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. Copyright © 2001 Biometrika Trust.
CitationWong, C. S., & Li, W. K. (2001). On a logistic mixture autoregressive model. Biometrika, 88(3), 833-846. doi: 10.1093/biomet/88.3.833
- EM algorithm
- Mixture mode
- Model selection