Estimating a gradual parameter change in an AR(1)-process - Kölner UniversitätsPublikationsServer

Huskova, Marie, Praskova, Zuzana ORCID: 0000-0003-1089-5541 and Steinebach, Josef G. . Estimating a gradual parameter change in an AR(1)-process. Metrika. HEIDELBERG: SPRINGER HEIDELBERG. ISSN 1435-926X

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DOI:10.1007/s00184-021-00844-z

Abstract

We discuss the estimation of a change-point t(0) at which the parameter of a (non-stationary) AR(1)-process possibly changes in a gradual way. Making use of the observations X-1,..., X-n, we shall study the least squares estimator (t(0)) over cap for t(0), which is obtained by minimizing the sum of squares of residuals with respect to the given parameters. As a first result it can be shown that, under certain regularity and moment assumptions, (t(0)) over cap /n is a consistent estimator for t(0), where t(0) = left perpendicularn tau(0)right perpendicular, with 0 < tau(0) < 1, i.e., (t(0)) over cap /n P ->(P) tau(0) (n ->infinity). Based on the rates obtained in the proof of the consistency result, a first, but rough, convergence rate statement can immediately be given. Under somewhat stronger assumptions, a precise rate can be derived via the asymptotic normality of our estimator. Some results from a small simulation study are included to give an idea of the finite sample behaviour of the proposed estimator.

Item Type:

Journal Article

Creators:

Creators	Email	ORCID	ORCID Put Code
Huskova, Marie	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Praskova, Zuzana	UNSPECIFIED	orcid.org/0000-0003-1089-5541	UNSPECIFIED
Steinebach, Josef G.	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED