A Univariate Time Varying Analysis of Periodic ARMA Processes

26 Pages Posted: 21 Mar 2014 Last revised: 22 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 18, 2014

Abstract

The standard approach for studying the periodic ARMA model with coefficients that vary over the seasons is to express it in a vector form. In this paper we introduce an alternative method which views the periodic formulation as a time varying univariate process and obviates the need for vector analysis. The specification, interpretation, and solution of a periodic ARMA process enable us to formulate a forecasting method which avoids recursion and allows us to obtain analytic expressions of the optimal predictors. Our results on periodic models are general, analogous to those for stationary specifications, and place the former on the same computational basis as the latter.

Keywords: covariance structure, homogeneous and particular solutions, optimal predictors, periodic ARMA models

JEL Classification: C22, C53, C58

Suggested Citation

Karanasos, Menelaos and Paraskevopoulos, Alexandros and Dafnos, Stavros, A Univariate Time Varying Analysis of Periodic ARMA Processes (March 18, 2014). Available at SSRN: https://ssrn.com/abstract=2411538 or http://dx.doi.org/10.2139/ssrn.2411538

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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