Higher-order asymptotic theory for discriminant analysis of Gaussian ARMA processes
This paper develops a higher-order asymptotic theory for discriminant analysis in time series. Higher-order asymptotic analysis may be necessary if the sample size is not large. Two discriminant statistics for Gaussian autoregressive processes are given. Then the asymptotic approximations of misclassification probabilities are derived -- the second-order one for Gaussian ARMA processes and the third-order one for Gaussian AR(1) processes. A numerical simulation study for the Gaussian ARMA(1,1) process with small samples is performed using the above two discriminant statistics, and the results are both close to the theoretical detection probabilities of the log-likelihood ratio.
scientific article; zbMATH DE number 633495