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An autoregressive model for multilag Markov chains

Published online by Cambridge University Press:  14 July 2016

G. G. S. Pegram
G. G. S. Pegram*
Affiliation:
University of Natal
*
∗Postal address: Department of Civil Engineering, University of Natal, King George V Avenue, Durban, Natal 4001, Republic of South Africa.
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Abstract

By assembling the transition matrix of a finite discrete Markov chain from overlays of matrices which are defined only by the serial correlation coefficients and marginal distribution of the chain to be modelled, a considerable saving is made in the number of parameters required to define a multilag Markov chain. This parsimony is achieved without detriment to the marginal distribution or serial correlation structure of the modelled chain. Applications to daily precipitation sequences and reservoir reliability are outlined to demonstrate the model's versatility.

Keywords

DISCRETE MARKOV CHAINSMODELLINGPARSIMONYPRECIPITATION MODELSSTOCHASTIC RESERVOIR THEORYSEASONAL MARKOV CHAINS
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 2 , June 1980 , pp. 350 - 362
Copyright
Copyright © Applied Probability Trust 1980 

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References

Chin, E. H. (1977) Modelling daily precipitation occurrence process with Markov chain. Water Resources Res. 13, 949–956.Google Scholar
Cox, D. R. and Miller, H. D. (1965) The Theory of Stochastic Processes. Methuen, London.Google Scholar
Gabriel, K. R. and Neumann, J. (1962) A Markov chain model for daily rainfall occurrences at Tel Aviv. Quart. J. R. Meteorol. Soc. 88, 90–95.Google Scholar
Gates, P. and Tong, H. (1976) On Markov chain modelling of some weather data. J. Appl. Meteorol. 15, 1145–1151.Google Scholar
Lloyd, E. H. (1977) Reservoirs with seasonally varying Markovian inflows, and their first passage times. Research Report RR–77–4, Internation Institute for Applied Systems Analysis, Laxenburg, Austria.Google Scholar
Odoom, S. and Lloyd, E. H. (1965) A note on the equilibrium distribution of levels in a semi-infinite reservoir subject to Markovian inputs and unit withdrawals. J. Appl. Prob. 2, 215–222.Google Scholar
Pegram, G. G. S. (1975) A multinomial model for transition probability matrices. J. Appl. Prob. 12, 498–506.Google Scholar
Pegram, G. G. S. (1978) Some simple expressions for the probability of failure of a finite reservoir with Markovian input. Geophys. Res. Letters 5, 13–15.Google Scholar
Tong, H. (1975) Determination of the order of a Markov chain by Akaike's information criterion. J. Appl. Prob. 12, 488–497.Google Scholar