Hurdle GARCH models for nonnegative time series

Abstract

The studied semi‐continuous time series contains a nonnegligible portion of observations equal to a single value (typically zero), whereas the remaining outcomes are strictly positive. A novel class of hurdle GARCH models having dependent zero occurrences is considered and the classical maximum likelihood estimation is employed. However, a distribution of the underlying time series innovations does not belong into the exponential family, which together with the dependence of innovations makes the whole inference nonstandard. Consistency and asymptotic normality of the estimator are derived. Efficiency of the estimation is elaborated and compared with the alternative quasi‐likelihood approach. A bootstrap prediction is also discussed. An analysis of sparse nonlife insurance claims is performed.