type="main" xml:id="jtsa12070-abs-0001"A two-step estimation method is proposed for periodic autoregressive parameters via residuals when the observations contain trend and periodic autoregressive time series. The oracle efficiency of the proposed Yule–Walker-type estimator is established. The...

The periodic correlation exists throughout the whole process in a analysis of variance (ANOVA) type model where the error terms consist of a periodic autoregressive time series. This paper studies the asymptotic property of least-squares estimators and linear testable hypotheses with a modified...

Mixture periodic autoregressive models are introduced to fit periodic time series with asymmetric or multimodal distributions. The stationary conditions of such series are derived, the asymptotic property of maximum likelihood estimators is obtained, and the application of EM algorithm is...

Time series often contain unknown trend functions and unobservable error terms. As is known, Yule–Walker estimators are asymptotically efficient for autoregressive time series. The focus of this article is the Yule–Walker estimators for time series with trends. A nonparametric detrending...