On a logistic mixture autoregressive model

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.