On the use of autoregressive order determination criteria in univariate white noise tests

Several tests of white noise are suggested, all of which are based on the application of known autoregressive order determination criteria or their modifications. Some of the proposed tests have, among other things, the property that their significance level approaches zero as the number of observations increases. This means that testing whether the residual series of a fitted model is white noise, the testing leads to a consistent order-selection method in the case in which the true order exists. The purpose of the white noise tests presented is to provide a method for selecting the order of an autoregressive moving-average model. The performance of the order-selection method is compared by simulation to the traditional autoregression order-selection criterion BIC