Modeling nonlinearities with mixtures-of-experts of time series models

We discuss a class of nonlinear models based on mixtures-of-experts of regressions of exponential family time series models, where the covariates include functions of lags of the dependent variable as well as external covariates. The discussion covers results on model identifiability, stochastic stability, parameter estimation via maximum likelihood estimation, and model selection via standard information criteria. Applications using real and simulated data are presented to illustrate how mixtures-of-experts of time series models can be employed both for data description, where the usual mixture structure based on an unobserved latent variable may be particularly important, as well as for prediction, where only the mixtures-of-experts flexibility matters.