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

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  • Hyndman, R.J.
  • Grunwald, G.K.

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.

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File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/1999/wp2-99.pdf
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Bibliographic Info

Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 2/99.

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Length: 14 pages
Date of creation: Jan 1999
Date of revision:
Publication status: Published in Australian and New Zealand J. Statistics (2000), vol. 42, no. 2, pp.145-158
Handle: RePEc:msh:ebswps:1999-2

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Keywords: Time Series ; Econometric Models ; Mixed Distribution Markov Models;

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References

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  1. 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.
  2. 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.
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Cited by:
  1. Campbell, Sean D. & Diebold, Francis X., 2004. "Weather forecasting for weather derivatives," CFS Working Paper Series 2004/10, Center for Financial Studies (CFS).
  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.

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