Higher order asymptotic theory for time series analysis.

This study explores higher order asymptotic results in time series analysis, particularly the higher order asymptotic optimality of estimators and the power comparison of tests for ARMA processes. It covers the higher order asymptotics of statistics of multivariate stationary processes. Numerical studies are given, which demonstrate that the higher order asymptotic theory is useful and important for time series analysis. Also, the validities of Edgeworth expansions of some estimators are proved for dependent situations. It is hoped that the results of this text will serve as the basis for further theoretical development.