On a logistic mixture autoregressive model
C. S. Wong · Biometrika · 2001
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.