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...

A robust estimation procedure for periodic autoregressive (PAR) time series is introduced. The asymptotic properties and the asymptotic relative efficiency are discussed by the estimating equation approach. The performance of the robust estimators for PAR time-series models with order one 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...

A changepoint in a time series is a time of change in the marginal distribution, autocovariance, or any other distributional structure of the series. Examples include mean level shifts and volatility (variance) changes. Climate data, for example, is replete with mean shift changepoints,...

This paper quantifies the form of the asymptotic covariance matrix of the sample autocovariances in a multivariate stationary time series—the classic Bartlett formula. Such quantification is useful in many statistical inferences involving autocovariances. While joint asymptotic normality of...

This article studies tests for assessing whether two stationary and independent time series have the same dynamics - specifically, whether the autocovariances of both series coincide at all lags. Frequency domain statistics previously proposed for this purpose are reviewed. A time domain...