Estimation of the order of an auto-regressive model

There are no definitive solutions available for the order estimation of the auto-regressive process. First, the performance of the three criteria, namely FPE, AIC and MDL is illustrated. Next, it is indicated that there are possibilities of their performance being improved. The algorithm tri proposed here utilizes three minimum values of any of the conventional loss functions in the FPE, AIC and MDL methods. It also uses three statistics derived from these three minimum values. The estimated order is a rounded weighted average of these six statistics. The algorithm is found to do better in a qualified sense of yielding peakier distribution of the estimated orders when tested for 1000 synthetic models of orders 3, 5 and 7 each. The conclusion drawn is that there are open possibilities of improving upon the conventional order estimators for auto-regressive processes. This means that till axiologically sounder estimators are available one should be ready to use heuristic estimators proposed here.