Common factor detection and estimation (Q1360497)

The authors consider the greatest common factor detection and estimation (CODE) of two polynomials of degrees \(n\alpha\) and \(n\beta\) respectively, the coefficients of which are assumed to have a normal distribution with a consistently estimable covariance matrix. First, using a large-sample maximum likelihood approach the common factor test criterion is obtained. Then, under setting \(\widehat{nc}=\min(n\alpha, n\beta)\), the minimization of the criterion is carried out with respect to the coefficients of the common factor and the deflated polynomials. Then, a \(\chi^2\)-based detection procedure is performed. If it fails then retry the procedure with setting \(\widehat{nc}= \widehat{nc}-1\) until success. This noniterative CODE-algorithm can also be used for estimating the orders and parameters of the ARMAX models. Numerical examples are included to indicate that the performance of the proposed methodology is rather good.