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An Improvement of Akaike's FPE Criterion to Reduce its Variability
Author(s) -
De Luna Xavier
Publication year - 1998
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00103
Subject(s) - akaike information criterion , mathematics , statistics , inference , econometrics , sequence (biology) , bayesian information criterion , selection (genetic algorithm) , information criteria , mean squared error , mean squared prediction error , model selection , computer science , artificial intelligence , biology , genetics
The selection of the number of past observations to be included in a linear predictor (the order of the predictor) should be done with minimum variability, since it is not taken into account in the inference stage. For finite time series, there is a trade‐off between variability and optimality (in the sense of mean squared prediction error). The widely used Akaike criteria, FPE and AIC, lead to highly variable estimated orders, whereas consistent criteria are downward biased when the optimal order increases with the sample size. In this paper we propose the use of a sequence of tests to analyse the order selected with FPE. The result is a new identification criterion. In a simulation study, this criterion is shown to reach a compromise with respect to the above‐mentioned trade‐off. Some asymptotic properties are also derived.