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THE ESTIMATION OF THE ORDER OF AN AUTOREGRESSION USING RECURSIVE RESIDUALS AND CROSS‐VALIDATION
Author(s) -
Kavalieris L.
Publication year - 1989
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/j.1467-9892.1989.tb00028.x
Subject(s) - akaike information criterion , autoregressive model , mathematics , representation (politics) , equivalence (formal languages) , star model , cross validation , information criteria , vector autoregression , nonlinear autoregressive exogenous model , bayesian information criterion , autoregressive integrated moving average , series (stratigraphy) , econometrics , statistics , time series , model selection , paleontology , discrete mathematics , politics , biology , political science , law
. Several criteria for the estimation of the order of an autoregressive representation of a stationary time series are examined. There need not be a true finite‐order autoregression model for the data, so that the purpose of model identification is to obtain an adequate representation of the data. It is proved that minimizing the sum of squares of recursive residuals (the ‘predictive minimizing description length’) is equivalent to minimizing BIC. The equivalence between the cross‐validation and Akaike information criterion methods of autoregressive modelling is also established.