Generalized additive modelling of mixed distribution Markov models with application to Melbourne’s rainfall

We consider modelling time series using a generalized additive model with first-order Markov structure and mixed transition density having a discrete component at zero and a continuous component with positive sample space. Such models have application, for example, in modelling daily occurrence and intensity of rainfall, and in modelling the number and size of insurance claims. We show how these methods extend the usual sinusoidal seasonal assumption in standard chain-dependent models by assuming a general smooth pattern of occurrence and intensity over time. These models can be fitted using standard statistical software. The methods of Grunwald & Jones (1998) can be used to combine these separate occurrence and intensity models into a single model for amount. We use 36 years of rainfall data from Melbourne, Australia, as a vehicle of illustration, and use the models to investigate the relationship between the Southern Oscillation Index and Melbourne’s rainfall. Department of Econometrics and Business Statistics, Monash University, Clayton VIC 3168, Australia. Department of Preventive Medicine and Biometrics, University of Colorado Health Sciences Center, Denver, CO 80262, USA.