On the Median-Unbiased Estimation of the Periodically Correlated AR(1) Coefficients

In this paper we consider the periodically correlated first-order autoregressive (PCAR(1)) process with period T and periodic white noise. One problem in studying this model is to estimate periodic coefficients from an observed segment. For ordinary stationary AR(1) model, a median unbiased estimate of the coefficient is well-known. This paper is concerned with the median-unbiased (MU) estimation of the periodic coefficients of the PCAR(1) process with period T. Our median unbiased estimator is an adaptation with the periodic case of the well-known work of Zielinski. The method of estimation is illustrated by simulated data.