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Parameter values of ARMA models minimising the one-step-ahead prediction error when the true system is not in the model set

Published online by Cambridge University Press:  14 July 2016

Paul Kabaila
Paul Kabaila*
Affiliation:
CSIRO Division of Mathematics and Statistics
*
∗ Postal address: CSIRO Division of Mathematics and Statistics, P.O. Box 310, South Melbourne, VIC 3205, Australia.
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Abstract

In This paper we answer the following question. Is there any a priori reason for supposing that there is no more than one set of ARMA model parameters minimising the one-step-ahead prediction error when the true system is not in the model set?

Keywords

AUTOREGRESSIVE MOVING AVERAGE MODELSINCORRECT PARAMETRIC MODEL FITTING
Type
Short Communications
Information
Journal of Applied Probability , Volume 20 , Issue 2 , June 1983 , pp. 405 - 408
Copyright
Copyright © Applied Probability Trust 1983 

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References

[1] Bloomfield, P. (1972) On the error of prediction of a time series. Biometrika 59, 501–507.Google Scholar
[2] Davies, N. and Newbold, P. (1980) Forecasting with misspecified models. Appl. Statist. 29, 87–92.Google Scholar
[3] Dieudonne, J. (1969) Foundations of Modern Analysis. Academic Press, New York.Google Scholar
[4] Kabaila, P. and Goodwin, G. C. (1980) On the estimation of the parameter of an optimal interpolator when the class of interpolators is restricted. SIAM J. Control and Optimisation 18, 121–144.Google Scholar
[5] Ogata, Y. (1980) Maximum likelihood estimates of incorrect Markov models for time series and the derivation of the AIC. J. Appl. Prob. 17, 59–72.Google Scholar
[6] Titchmarsh, E. C. (1939) The Theory of Functions. Clarendon Press, Oxford.Google Scholar