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


  • Hyndman, R.J.
  • Grunwald, G.K.


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.

Suggested Citation

  • Hyndman, R.J. & Grunwald, G.K., 1999. "Generalized Additive Modelling of Mixed Distribution Markov Models with Application to Melbourne's Rainfall," Monash Econometrics and Business Statistics Working Papers 2/99, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:1999-2

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    References listed on IDEAS

    1. Hyndman, R.J. & Yao, Q., 1998. "Nonparametric Estimation and Symmetry Tests for Conditional Density Functions," Monash Econometrics and Business Statistics Working Papers 17/98, Monash University, Department of Econometrics and Business Statistics.
    2. Grunwald, Gary K. & Hyndman, Rob J., 1998. "Smoothing non-Gaussian time series with autoregressive structure," Computational Statistics & Data Analysis, Elsevier, vol. 28(2), pages 171-191, August.
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    Cited by:

    1. 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.
    2. 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.

    More about this item


    Time Series ; Econometric Models ; Mixed Distribution Markov Models;

    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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