Stochastic Modelling of Heavy-Tailed Precipitations in Canadian Prairies

Abstract

The statistical modelling of extreme precipitation structures is essential in many aspects such as assessing and managing risks resulting from the occurrence of such extreme events for agricultural purposes, in particular. Typically, daily precipitation time series with many zero (on dry days) and positive (on wet days) observations exhibits characteristics such as heavy-tailedness and volatility clustering (i.e., some periods of high and some periods of low volatility) which make it challenging to develop an effective model for both the theoretical and observations viewpoints. The main goal of this study is to introduce a model capable of describing structure of precipitation data and apply it to a historical data set from twelve stations in Canadian prairies where precipitation is a crucial factor in agriculture. In this thesis, the three main important characteristic of a precipitation based data set, as mentioned above, have been described through a dynamic mixture model. Firstly, in order to study the full range of precipitation measurements, we have assigned probabilities to zero and positive observations. Then, positive observations have been assumed to be drawn from a generalized Gaussian crack (GGCR) distribution which has exibility to fit heavy-tailed observations. In addition, a specification of a GARCH type model for the scale parameter of the GGCR distribution has been considered to capture the time-varying volatility. Meanwhile, for a model fitting method, the maximum likelihood estimation has been utilized with the profile log-likelihood algorithm. Furthermore, in order to con- firm the performance of the proposed model, simulation studies are performed. For the application purpose, the dynamic mixture model has been fitted to the Canadian prairies precipitation data set and the dependence structure of the residuals has been studied through Archimedean copulas.