The prediction error of autoregressive small sample models

Abstract

In order selection, one single realization of a stochastic process is used twice, for the estimation of parameters for different model orders and for the selection of the best model order. The purpose of order selection is to find the model order that gives the best fit to other realizations of the same stochastic process. This fit is expressed by the squared prediction error and it will increase if too many parameters are used. The weak parameter criterion (WPC) is an estimate for the squared prediction error, with the special feature that it is computed from the same observations that are used for the estimation of the parameters. A novel justification for the principle of the WPC is presented, which shows the correspondence between the WPC and the squared prediction error. Calibration formulas are presented that describe the averages over many simulation runs of WPC, the squared prediction error and residual variance all as a function of the order of the estimation model. >