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Generalized Additive Modelling of Mixed Distribution Markov Models with Application to Melbourne's Rainfall

Rob Hyndman () and G.K. Grunwald

No 2/99, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: 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 and 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 effect of the El Nino phenomenon on Melbourne's rainfall.

Keywords: Time Series; Econometric Models; Mixed Distribution Markov Models (search for similar items in EconPapers)
JEL-codes: C32 C50 (search for similar items in EconPapers)
Date: 1999-01
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Published in Australian and New Zealand J. Statistics (2000), vol. 42, no. 2, pp.145-158

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