ON THE PROBABILITY OF ERROR WHEN USING A GENERAL AKAIKETYPE CRITERION TO ESTIMATE AUTOREGRESSION ORDER
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Abstract. A general Akaiketype procedure is studied where the additive penalty is proportional to the autoregression order but the constant of proportionality has a general value . For the procedure to be weakly consistent it is necessary and sufficient that 0 and n as n, where n denotes the sample size. If n1 for some >0 then the probability of erring when estimating the autoregression order converges to zero at a rate nc, for all c>0, as n. However, several procedures suggested for practical use have n10 for each >0; in particular, they have =n1 log n or =n1 log log n. To elucidate the properties of error probabilities in these circumstances we study the case of an AR(1) process. It is shown that in this case the probability of underestimating order is usually substantially less then the chance of overestimation, unless the autoregressive constant is particularly small (in fact, of size 21/2). Copyright 1993, Wiley Blackwell. All rights reserved