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Hypothesis testing in mixtures-of-experts of generalized linear time series

We consider a novel class of non-linear models based on mixtures of local generalized linear time series. In our models, at any given time point, we have a certain number of generalized linear models (GLM), denoted as experts, where the vector of covariates may include functions of lags of the dependent variable. Additionally, we have a latent variable, whose distribution depends on the same covariates as the experts, that determines which GLM is observed. This structure is considerably flexible, as was shown by Jiang and Tanner in a series of papers for mixtures of GLM with independent observations. Carvalho and Tanner (2002) show that the maximum likelihood estimator is consistent and asymptotically normal for correctly specified as well as misspecified models, under the appropriate regularity conditions. In this paper, we discuss the use of the Wald test for hypothesis testing and illustrate the theory with an example using financial time series.