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Modelling autoregressive processes with a shifting mean

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  • Timo Terasvirta

    ()

  • Andrés González

    ()

Abstract

This paper contains a nonlinear, nonstationary autoregressive model whose intercept changes deterministically over time. The intercept is a flexible function of time, and its construction bears some resemblance to neural network models. A modelling technique, modified from one for single hidden-layer neural network models, is developed for specification and estimation of the model. Its performance is investigated by simulation and further illustrated by two applications to macroeconomic time series.

Suggested Citation

  • Timo Terasvirta & Andrés González, 2006. "Modelling autoregressive processes with a shifting mean," BORRADORES DE ECONOMIA 003230, BANCO DE LA REPÚBLICA.
  • Handle: RePEc:col:000094:003230
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    References listed on IDEAS

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    1. Ng, S. & Pinkse, J., 1995. "Nonparametric-two-Step Estimation of Unknown Regression Functions when the Regressors and the Regression Error Are not Independent," Cahiers de recherche 9551, Universite de Montreal, Departement de sciences economiques.
    2. Charles Nelson & Eric Zivot, 2000. "Why are Beveridge-Nelson and Unobserved-Component Decompositions of GDP so Different?," Econometric Society World Congress 2000 Contributed Papers 0692, Econometric Society.
    3. Marianne Baxter & Robert G. King, 1999. "Measuring Business Cycles: Approximate Band-Pass Filters For Economic Time Series," The Review of Economics and Statistics, MIT Press, pages 575-593.
    4. Christian Kleiber & Achim Zeileis, 2005. "Validating multiple structural change models-a case study," Journal of Applied Econometrics, John Wiley & Sons, Ltd., pages 685-690.
    5. Morley, James C., 2002. "A state-space approach to calculating the Beveridge-Nelson decomposition," Economics Letters, Elsevier, vol. 75(1), pages 123-127, March.
    6. Jansen, Eilev S & Terasvirta, Timo, 1996. "Testing Parameter Constancy and Super Exogeneity in Econometric Equations," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(4), pages 735-763, November.
    7. Marianne Baxter & Robert G. King, 1999. "Measuring Business Cycles: Approximate Band-Pass Filters For Economic Time Series," The Review of Economics and Statistics, MIT Press, pages 575-593.
    8. Bierens, Herman J., 1997. "Testing the unit root with drift hypothesis against nonlinear trend stationarity, with an application to the US price level and interest rate," Journal of Econometrics, Elsevier, pages 29-64.
    9. Eitrheim, Oyvind & Terasvirta, Timo, 1996. "Testing the adequacy of smooth transition autoregressive models," Journal of Econometrics, Elsevier, pages 59-75.
    10. Garcia, Rene & Perron, Pierre, 1996. "An Analysis of the Real Interest Rate under Regime Shifts," The Review of Economics and Statistics, MIT Press, pages 111-125.
    11. Michael Massmann & James Mitchell & Martin Weale, 2003. "Business Cycles and Turning Points: A Survey of Statistical Techniques," National Institute Economic Review, National Institute of Economic and Social Research, vol. 183(1), pages 90-106, January.
    12. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, pages 817-858.
    13. Graham Elliott & Allan Timmermann, 2008. "Economic Forecasting," Journal of Economic Literature, American Economic Association, pages 3-56.
    14. Graham Elliott & Allan Timmermann, 2016. "Economic Forecasting," Economics Books, Princeton University Press, edition 1, number 10740, June.
    15. Lin, Chien-Fu Jeff & Terasvirta, Timo, 1994. "Testing the constancy of regression parameters against continuous structural change," Journal of Econometrics, Elsevier, pages 211-228.
    16. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, pages 47-78.
    17. Racine, Jeff, 2000. "Consistent cross-validatory model-selection for dependent data: hv-block cross-validation," Journal of Econometrics, Elsevier, pages 39-61.
    18. Lee, Tae-Hwy & White, Halbert & Granger, Clive W. J., 1993. "Testing for neglected nonlinearity in time series models : A comparison of neural network methods and alternative tests," Journal of Econometrics, Elsevier, pages 269-290.
    19. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-1458, November.
    20. Goffe, William L. & Ferrier, Gary D. & Rogers, John, 1994. "Global optimization of statistical functions with simulated annealing," Journal of Econometrics, Elsevier, pages 65-99.
    21. Caporale, Tony & Grier, Kevin B, 2000. "Political Regime Change and the Real Interest Rate," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 32(3), pages 320-334, August.
    22. Racine, Jeff, 1997. "Feasible Cross-Validatory Model Selection for General Stationary Processes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(2), pages 169-179, March-Apr.
    23. Bierens, Herman J, 2000. "Nonparametric Nonlinear Cotrending Analysis, with an Application to Interest and Inflation in the United States," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 323-337, July.
    24. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(03), pages 295-325, June.
    25. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
    26. Rapach, David E & Wohar, Mark E, 2005. "Regime Changes in International Real Interest Rates: Are They a Monetary Phenomenon?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(5), pages 887-906, October.
    27. White, Halbert, 2006. "Approximate Nonlinear Forecasting Methods," Handbook of Economic Forecasting, Elsevier.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Tamer Kulaksizoglu, 2016. "Measuring the Turkish core inflation with a shifting mean model," Empirical Economics, Springer, pages 57-70.
    9. 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.
    10. Rolf Aaberge & Eugenio Peluso, 2011. "A Counting Approach for Measuring Multidimensional Deprivation," Working Papers 07/2011, University of Verona, Department of Economics.
    11. Hungnes Håvard, 2015. "Testing for co-nonlinearity," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, pages 339-353.
    12. Kulaksizoglu, Tamer, 2015. "Measuring the Core Inflation in Turkey with the SM-AR Model," MPRA Paper 62653, University Library of Munich, Germany.

    More about this item

    Keywords

    deterministic shift; nonlinear autoregression; nonstationarity; nonlinear trend; structural change;

    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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