On Some Criteria for Estimating the Order of a Markov Chain

摘要: Tong (1975) has proposed a procedure for estimating the order of Markov chain based on Akaike's information criterion (AIC). In this paper, asymptotic distribution AIC estimator is derived and it shown that inconsistent. As an alternative to procedure, Bayesian (BIC) by Schwarz (1978) be consistent. These two procedures yield different estimated orders when applied specific samples meteorological observations. For parameters these examples, BIC are compared means simulation finite samples. The results obtained have practical implications concerning whether, in routine fitting precipitation data, necessary consider higher than first-order chains.