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Modelling autoregressive processes with a shifting mean

Author

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  • González, Andrés

    (Banco de la República, Colombia, Departamento de modelos macroeconómicos)

  • Teräsvirta, Timo

    (CREATES, School of Economics and Management, University of Aarhus, and Department of Economic Statistics, Stockholm School of Economics)

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).

Suggested Citation

  • González, Andrés & Teräsvirta, Timo, 2006. "Modelling autoregressive processes with a shifting mean," SSE/EFI Working Paper Series in Economics and Finance 637, Stockholm School of Economics, revised 22 May 2007.
    • Handle: RePEc:hhs:hastef:0637
    Note: This is the revised (May 2007) version of the paper.
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    Cited by:

    1. Enders, Walter & Holt, Matthew T., 2011. "Breaks, bubbles, booms, and busts: the evolution of primary commodity price fundamentals," MPRA Paper 31461, University Library of Munich, Germany.
    2. Baillie, Richard T. & Morana, Claudio, 2009. "Modelling long memory and structural breaks in conditional variances: An adaptive FIGARCH approach," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1577-1592, August.
    3. Strikholm, Birgit, 2006. "Determining the number of breaks in a piecewise linear regression model," SSE/EFI Working Paper Series in Economics and Finance 648, Stockholm School of Economics.
    4. Anders Bredahl Kock & Timo Teräsvirta, 2010. "Forecasting with nonlinear time series models," CREATES Research Papers 2010-01, Department of Economics and Business Economics, Aarhus University.
    5. Andrés González & Kirstin Hubrich & Timo Teräsvirta, 2009. "Forecasting inflation with gradual regime shifts and exogenous information," CREATES Research Papers 2009-03, Department of Economics and Business Economics, Aarhus University.
    6. Matthew T. Holt & Timo Teräsvirta, 2012. "Global Hemispheric Temperature Trends and Co–Shifting: A Shifting Mean Vector Autoregressive Analysis," CREATES Research Papers 2012-54, Department of Economics and Business Economics, Aarhus University.
    7. Mugera, Harriet & Gilbert, Christopher, 2015. "Structural Change in the Relationship Between Energy and Food Prices," 2015 Conference, August 9-14, 2015, Milan, Italy 212505, International Association of Agricultural Economists.
    8. Cushman, David O. & Michael, Nils, 2011. "Nonlinear trends in real exchange rates: A panel unit root test approach," Journal of International Money and Finance, Elsevier, vol. 30(8), pages 1619-1637.
    9. Friedrich, Marina & Lin, Yicong, 2024. "Sieve bootstrap inference for linear time-varying coefficient models," Journal of Econometrics, Elsevier, vol. 239(1).
    10. Hungnes Håvard, 2015. "Testing for co-nonlinearity," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(3), pages 339-353, June.
    11. Kulaksizoglu, Tamer, 2015. "Measuring the Core Inflation in Turkey with the SM-AR Model," MPRA Paper 62653, University Library of Munich, Germany.

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    More about this item

    Keywords

    deterministic shift; nonlinear autoregression; nonstationarity; nonlinear trend; smooth transition; structural change;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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