Incorporating lag order selection uncertainty in parameter inference for AR models

Parameter inference on autoregressive models is usually carried out conditi onally on a previously selected lag order. In the majority of cases the lag order selection is carried out using information criteria and in particula r the Akaike [2nd International Symposium on Information Theory (1973) 267- 281], Schwarz [Annuls of Statistics (1978) 461-464] or Hannan and Quinn [Jo urnal of the Royal Statistical Society (Series B), 41 (1979) 190-195] crite ria. It is well known that the latter two criteria are consistent in lag or der selection in the sense of picking the true order of the system with pro bability one asymptotically. On the other hand, Akaike's criterion is known to overestimate the lag order in this sense. In this note we discuss the a symptotic distribution, of the parameter estimates without conditioning on the lag order selected. (C) 2001 Elsevier Science BN. All rights reserved.