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On the Likelihood of a Time Series Model

Hirotugu Akaike
Journal of the Royal Statistical Society. Series D (The Statistician)
Vol. 27, No. 3/4, Partial Proceedings of the 1978 I.O.S. Annual Conference on Time Series Analysis (and Forecasting) (Sep. - Dec., 1978), pp. 217-235
Published by: Wiley for the Royal Statistical Society
DOI: 10.2307/2988185
Stable URL: http://www.jstor.org/stable/2988185
Page Count: 19
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On the Likelihood of a Time Series Model
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Abstract

The conventional approach to parametric model fitting of time series is realized through the comparison of various competing models by some ad hoc criterion. Since each of the models is usually specified by the parameters determined by the information from the data, the extension of the classical concept of likelihood to this situation is not obvious. By asking the log likelihood of a model to be an unbiased estimate of the expected log likelihood of the model, a reasonable definition of the likelihood is obtained and this allows us to develop a systematic approach to parametric time series modelling. Practical utility of this approach is demonstrated by numerical examples.

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