Time Series Mixtures of Generalized t Experts: ML Estimation and an Application to Stock Return Density Forecasting

We propose and analyze a new nonlinear time series model based on local mixtures of linear regressions, referred to as experts, with thick-tailed disturbances. The mean function of each expert is an affine function of covariates that may include lags of the dependent variable and/or lags of external predictors. The mixing of the experts is determined by a latent variable, the distribution of which depends on the same covariates used in the regressions. The expert error terms are assumed to follow the generalized t distribution, a rather flexible parametric form encompassing the standard t and normal distributions as special cases and allowing separate modeling of scale and kurtosis. We show consistency and asymptotic normality of the maximum likelihood estimator, for correctly specified and for misspecified models, and provide Monte Carlo evidence on the performance of standard model selection criteria in selecting the number of experts. We further employ the model to obtain density forecasts for daily stock returns and find evidence to support the model.