Parameter estimation for nearly nonstationary AR(1) processes

Abstract

In this paper, we consider parameter estimation problems in the first order nearly nonstationary autoregression AR(l) model, which is described by formula (2.1). By allowing the most general class of innovations, we extend the result of Chan and Wei [1]. Moreover, we discuss a sequential procedure for estimating the parameter, extending the result of Lai and Siegmund [2] and Greenwood and Shiryaev [3] to the nearly nonstationa.ry model. The results are essentially based on the preliminary Theorems 1 and 2, stating the weak convergence, as the sample size grows, of an observed nearly nonstationa.ry AR(l) process to a corresponding AR(l) process in continuous time.

ASYMPTOTIC INFERENCE FOR NEARLY UNSTABLE AR(p) PROCESSES

“…. , r j of the model (9) we introduce another two other systems of parameters, which both tend to the limit c j,k , j = 1, . .…”

“…see, for example, Phillips [18], Jeganathan [10], Dzhaparidze, Kormos, van der Meer and van Zuijlen [9]. (The above model is called also near integrated and is applied often in economic theory; see Phillips [18].)…”

“…One of the aims of the present paper is to find a simpler explanation for the asymptotic behaviour of the least-squares estimators in the nearly unstable AR(p) model (9). The starting point of our investigation is the following equivalent formulation of (8).…”

Asymptotic accuracy of the least-squares estimates in nearly nonstationary autoregressive models

“…Suppose that for each n /> 1, ( In recent years there has been considerable interest shown to the asymptotic properties of the estimates of parameters of nearly nonstationary AR models (e.g., Bobkoski [3], Chan and Wei [5], Phillips [15], Tsay and Tiao [16], Jeganathan [9], Cox and Llatas [7], Cox [7], Dzaparidze et al [8], Kormos et al [1 1], Pap and van Zuijlen [13]). …”

Asymptotic inference for nearly unstable multidimensional AR processes

“…see, for example, [18], [9], [7]. (The above model is called also near integrated and is applied often in economic theory; see [18].)…”