Statistical modelling of precipitation data in Canadian Prairies with a dynamic mixture structure

Abstract The present paper aims to model statistical structure of heavy-tailed precipitation data. In particular for agricultural purposes in Canadian Prairies, this is essential in many aspects such as assessing and managing risks resulting from the occurrence of unexpected precipitation events. Daily (or weekly) precipitation time series often contain many zeros (on dry days) and also exhibit important characteristics such as heavy-tailedness and volatility clustering. These features make it challenging to develop an effective model from both theoretical and practical viewpoints. In this paper, we propose a dynamic mixture model constructed based on a generalized Gaussian crack distribution with a GARCH specification to take into account the full range of precipitation measurements with a sufficient flexibility to fit both thin and heavy-tailed data, and stochastic volatility. The method of maximum likelihood estimation with the profile log-likelihood algorithm is illustrated with some simulation studies. The model fitting results on a historical data set from twelve stations in Canadian prairies show the applicability of the proposed model.