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

Rob J. Hyndman, Gary K. Grunwald

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The paper considers the modelling of 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 numbers and sizes of insurance claims. The paper shows 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 (2000) can be used to combine these separate occurrence and intensity models into a single model for amount. The models are used to investigate the relationship between the Southern Oscillation Index and Melbourne's rainfall, illustrated with 36 years of rainfall data from Melbourne, Australia.

Original languageEnglish
Pages (from-to)145-158
Number of pages14
JournalAustralian & New Zealand Journal of Statistics
Issue number2
Publication statusPublished - 1 Jan 2000


  • Binary time series
  • Droughts
  • Dry spells
  • Gamma time series
  • Generalized additive model
  • Generalized linear model
  • Markov model
  • Mixture distribution
  • Non-Gaussian time series
  • Southern oscillation index

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