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

Author

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  • Hyndman, Rob J.
  • Grunwald, Gary K.

Abstract

We consider modelling time series using a generalized additive model with firstorder 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.

Suggested Citation

  • Hyndman, Rob J. & Grunwald, Gary K., "undated". "Generalized Additive Modelling of Mixed Distribution Markov Models with Application to Melbourne's Rainfall," Department of Econometrics and Business Statistics Working Papers 267393, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:ags:monebs:267393
    DOI: 10.22004/ag.econ.267393
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    Cited by:

    1. is not listed on IDEAS
    2. Sean D. Campbell & Francis X. Diebold, 2005. "Weather Forecasting for Weather Derivatives," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 6-16, March.
    3. Sharda, V.N. & Das, P.K., 2005. "Modelling weekly rainfall data for crop planning in a sub-humid climate of India," Agricultural Water Management, Elsevier, vol. 76(2), pages 120-138, August.

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    Keywords

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    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General

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