The Fundamental Properties of Time Varying AR Models with Non Stochastic Coefficients

31 Pages Posted: 21 Mar 2014

See all articles by Menelaos Karanasos

Menelaos Karanasos

Brunel University London - Economics and Finance

Alexandros Paraskevopoulos

The Center for Research and Applications of Nonlinear Systems (CRANS) Department of Mathematics, Division of Applied Analysis, University of Patras

Stavros Dafnos

Brunel University London - Department of Social Sciences, Media and Communications

Date Written: March 15, 2014

Abstract

The paper examines the problem of representing the dynamics of low order autoregressive (AR) models with time varying (TV) coefficients. The existing literature computes the forecasts of the series from a recursion relation. Instead, we provide the linearly independent solutions to TV-AR models. Our solution formulas enable us to derive the fundamental properties of these processes, and obtain explicit expressions for the optimal predictors. We illustrate our methodology and results with a few classic examples amenable to time varying treatment, e.g, periodic, cyclical, and AR models subject to multiple structural breaks.

Keywords: abrupt breaks, covariance structure, cyclical processes, homogeneous and particular solutions, optimal predictors, periodic AR models

JEL Classification: C22, C53, C58

Suggested Citation

Karanasos, Menelaos and Paraskevopoulos, Alexandros and Dafnos, Stavros, The Fundamental Properties of Time Varying AR Models with Non Stochastic Coefficients (March 15, 2014). Available at SSRN: https://ssrn.com/abstract=2409590 or http://dx.doi.org/10.2139/ssrn.2409590

Menelaos Karanasos (Contact Author)

Brunel University London - Economics and Finance ( email )

Uxbridge UB8 3PH
United Kingdom

Alexandros Paraskevopoulos

The Center for Research and Applications of Nonlinear Systems (CRANS) Department of Mathematics, Division of Applied Analysis, University of Patras ( email )

Patra
Greece

Stavros Dafnos

Brunel University London - Department of Social Sciences, Media and Communications ( email )

Kingston Lane
Uxbridge, Middlesex UB8 3PH
United Kingdom

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