A new order determination technique for ARMA processes

It is generally recognized that when performing spectral estimation via the modeling approach, autoregressive moving average (ARMA) models can provide estimates of higher resolution than auto-gressive models alone [1], [2]. However, there is lacking a systematic method for determining the orders of an ARMA process from its output. Of the very few order determination techniques in existence, most are trial and error based. The Akaike information criterion for ARMA processes is one such example. This paper presents a new method that determines the ARMA orders in one pass. It is a modification of the method of Chow [6] and uses the Gram-Schmidt orthonormalization procedure to determine linear dependency of the columns in an order determination. The theoretical development is verified by simulation, which also includes results on order determination from output sequences alone.