Scandinavian Working Papers in Economics

SSE/EFI Working Paper Series in Economics and Finance,
Stockholm School of Economics

No 637: Modelling autoregressive processes with a shifting mean

Andrés González () and Timo Teräsvirta ()
Additional contact information
Andrés González: Banco de la República, Colombia, Departamento de modelos macroeconómicos, Postal: Bogotá, Colombia
Timo Teräsvirta: CREATES, School of Economics and Management, University of Aarhus, and Department of Economic Statistics, Stockholm School of Economics, Postal: Universitetsparken, Building 1322, DK-8000 Aarhus C, Denmark

Abstract: In this paper we introduce an autoregressive model with a deterministically shifting intercept. This implies that the model has a shifting mean and is thus nonstationary but stationary around a nonlinear deterministic component. The shifting intercept is defined as a linear combination of logistic transition functions with time as the transition variables. The number of transition functions is determined by selecting the appropriate functions from a possibly large set of alternatives using a sequence of specification tests. This selection procedure is a modification of a similar technique developed for neural network modelling by White (2006). A Monte Carlo experiment is conducted to show how the proposed modelling procedure and some of its variants work in practice. The paper contains two applications in which the results are compared with what is obtained by assuming that the time series used as examples may contain structural breaks instead of smooth transitions and selecting the number of breaks following the technique of Bai and Perron (1998).

Keywords: deterministic shift; nonlinear autoregression; nonstationarity; nonlinear trend; smooth transition; structural change

JEL-codes: C22; C52

26 pages, First version: September 27, 2006. Revised: May 22, 2007.

Note: This is the revised (May 2007) version of the paper.

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