%0 Journal Article %1 doi:10.1080/00401706.1981.10486293 %A Katz, Richard W. %D 1981 %J Technometrics %K dfg_seq %N 3 %P 243-249 %R 10.1080/00401706.1981.10486293 %T On Some Criteria for Estimating the Order of a Markov Chain %U http://amstat.tandfonline.com/doi/abs/10.1080/00401706.1981.10486293 %V 23 %X Tong (1975) has proposed a procedure for estimating the order of a Markov chain based on Akaike's information criterion (AIC). In this paper, the asymptotic distribution of the AIC estimator is derived and it is shown that the estimator is inconsistent. As an alternative to the AIC procedure, the Bayesian information criterion (BIC) proposed by Schwarz (1978) is shown to be consistent. These two procedures yield different estimated orders when applied to specific samples of meteorological observations. For parameters based on these meteorological examples, the AIC and BIC procedures are compared by means of simulation for finite samples. The results obtained have practical implications concerning whether, in the routine fitting of precipitation data, it is necessary to consider higher than first-order Markov chains.

@article{doi:10.1080/00401706.1981.10486293, abstract = { Tong (1975) has proposed a procedure for estimating the order of a Markov chain based on Akaike's information criterion (AIC). In this paper, the asymptotic distribution of the AIC estimator is derived and it is shown that the estimator is inconsistent. As an alternative to the AIC procedure, the Bayesian information criterion (BIC) proposed by Schwarz (1978) is shown to be consistent. These two procedures yield different estimated orders when applied to specific samples of meteorological observations. For parameters based on these meteorological examples, the AIC and BIC procedures are compared by means of simulation for finite samples. The results obtained have practical implications concerning whether, in the routine fitting of precipitation data, it is necessary to consider higher than first-order Markov chains. }, added-at = {2017-04-25T11:21:57.000+0200}, author = {Katz, Richard W.}, biburl = {https://www.bibsonomy.org/bibtex/24bd42baf7b0c3f294b9df5162c4787ef/lemmi}, doi = {10.1080/00401706.1981.10486293}, eprint = {http://amstat.tandfonline.com/doi/pdf/10.1080/00401706.1981.10486293}, interhash = {e9154b7dc9b979b0868a81addf419172}, intrahash = {4bd42baf7b0c3f294b9df5162c4787ef}, journal = {Technometrics}, keywords = {dfg_seq}, number = 3, pages = {243-249}, timestamp = {2017-04-25T11:21:57.000+0200}, title = {On Some Criteria for Estimating the Order of a Markov Chain}, url = {http://amstat.tandfonline.com/doi/abs/10.1080/00401706.1981.10486293}, volume = 23, year = 1981 }