Discriminant Analysis for ARMA Models Based on Divergency Criterion: A Frequency Domain Approach

The extension of classical analysis to time series data is the basic problem faced in many fields, such as engineering, economic and medicine. The main objective of discriminant time series analysis is to examine how far it is possible to distinguish between various groups. There are two situations to be considered in the linear time series models. Firstly when the main discriminatory information contained in mean function and secnodly when the mean functions are equal and discriminotary information is in the autocovariance functions. The latter case is more interested because the the first case is well documnted. The classical method for discrimation of time series is based on likelihood ratio approach. Using this approach the vector x has to be allocated to H1 or H2 leads to the discriminant function dQ(x)=x-prim(R2-1 -R1-1)x Shumway and Stoffer, 2006) in where x is the the R1 and R2  are the covariance matrices under  H1 and H2  models, respectively. Another approach is based on assessing distance between models. Two important and common distance measuers, Kullback-Leibler information measure, KL, and Chernoff information measure, CH. In this case x is allocated to  H1 or H2 or  depending on disparity measure between the sample spectrum of x and two models (  H1 or H2 ), (see Kakizawa et al., 1998). In this article KL and CH have been adopted to both autoregressive models and moving average models. Three methods, classical method (call Shumway method) has been compared with KL and CH criterions. The peformance of method has been carried out using a numerical study. One hundred time series each of length two hundred points simulated from the first model, say  H1 , and subjected to the discrimination criterion obtained from Kullback-Leibler, KL, and Chernoff, CH, crierions. The number of series that were misclassified out of hundred was noted. The results showed that three method work well for both autoregressive or order of one and moving average order of one models. The miscllasifican rate decreases when the distance between two populations increases. However, the performance of KL method is superior than both CH and Shumway methods.