IDEAS home Printed from https://ideas.repec.org/p/bdr/borrec/420.html
   My bibliography  Save this paper

Modelling autoregressive processes with a shifting mean

Author

Listed:
  • 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 420, Banco de la Republica de Colombia.
    • Handle: RePEc:bdr:borrec:420
    DOI: 10.32468/be.420
    as

    Download full text from publisher

    File URL: https://doi.org/10.32468/be.420
    Download Restriction: no
    File URL: https://libkey.io/10.32468/be.420?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    2. James C. Morley & Charles R. Nelson & Eric Zivot, 2003. "Why Are the Beveridge-Nelson and Unobserved-Components Decompositions of GDP So Different?," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 235-243, May.
    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, vol. 81(4), pages 575-593, November.
    4. Christian Kleiber & Achim Zeileis, 2005. "Validating multiple structural change models-a case study," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(5), 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. 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, vol. 81(1), pages 29-64, November.
    8. Eitrheim, Oyvind & Terasvirta, Timo, 1996. "Testing the adequacy of smooth transition autoregressive models," Journal of Econometrics, Elsevier, vol. 74(1), pages 59-75, September.
    9. Garcia, Rene & Perron, Pierre, 1996. "An Analysis of the Real Interest Rate under Regime Shifts," The Review of Economics and Statistics, MIT Press, vol. 78(1), pages 111-125, February.
    10. Massmann, Michael & Mitchell, James & Weale, Martin, 2003. "Business Cycles and Turning Points: A Survey of Statistical Techniques," National Institute Economic Review, National Institute of Economic and Social Research, vol. 183, pages 90-106, January.
    11. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    12. Graham Elliott & Allan Timmermann, 2016. "Economic Forecasting," Economics Books, Princeton University Press, edition 1, number 10740.
    13. Lin, Chien-Fu Jeff & Terasvirta, Timo, 1994. "Testing the constancy of regression parameters against continuous structural change," Journal of Econometrics, Elsevier, vol. 62(2), pages 211-228, June.
    14. Racine, Jeff, 2000. "Consistent cross-validatory model-selection for dependent data: hv-block cross-validation," Journal of Econometrics, Elsevier, vol. 99(1), pages 39-61, November.
    15. 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, vol. 56(3), pages 269-290, April.
    16. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-1458, November.
    17. Goffe, William L. & Ferrier, Gary D. & Rogers, John, 1994. "Global optimization of statistical functions with simulated annealing," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 65-99.
    18. 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.
    19. 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.
    20. 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.
    21. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(3), pages 295-325, June.
    22. 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.
    23. Teräsvirta, Timo, 1996. "Smooth Transition Models," SSE/EFI Working Paper Series in Economics and Finance 132, Stockholm School of Economics.
    24. 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.
    25. White, Halbert, 2006. "Approximate Nonlinear Forecasting Methods," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 9, pages 459-512, Elsevier.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Friedrich, Marina & Lin, Yicong, 2024. "Sieve bootstrap inference for linear time-varying coefficient models," Journal of Econometrics, Elsevier, vol. 239(1).
    5. 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.
    6. 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.
    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. 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.
    9. Hungnes Håvard, 2015. "Testing for co-nonlinearity," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(3), pages 339-353, June.
    10. 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.
    11. Kulaksizoglu, Tamer, 2015. "Measuring the Core Inflation in Turkey with the SM-AR Model," MPRA Paper 62653, University Library of Munich, Germany.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Terasvirta, Timo, 2006. "Forecasting economic variables with nonlinear models," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 8, pages 413-457, Elsevier.
    2. Christopher J. Neely & David E. Rapach, 2008. "Real interest rate persistence: evidence and implications," Review, Federal Reserve Bank of St. Louis, vol. 90(Nov), pages 609-642.
    3. 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.
    4. Kanas, Angelos, 2008. "On real interest rate dynamics and regime switching," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2089-2098, October.
    5. Jesús Clemente & María Dolores Gadea & Antonio Montañés & Marcelo Reyes, 2017. "Structural Breaks, Inflation and Interest Rates: Evidence from the G7 Countries," Econometrics, MDPI, vol. 5(1), pages 1-17, February.
    6. Sandberg, Rickard, 2016. "Trends, unit roots, structural changes, and time-varying asymmetries in U.S. macroeconomic data: the Stock and Watson data re-examined," Economic Modelling, Elsevier, vol. 52(PB), pages 699-713.
    7. T. Berger, 2008. "Estimating Europe’s Natural Rates from a forward-looking Phillips curve," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 08/498, Ghent University, Faculty of Economics and Business Administration.
    8. Rapach, David E. & Weber, Christian E., 2004. "Are real interest rates really nonstationary? New evidence from tests with good size and power," Journal of Macroeconomics, Elsevier, vol. 26(3), pages 409-430, September.
    9. Mishra, Ankita & Moosa, Imad A. & Tawadros, George B. & Mishra, Vinod, 2023. "The effect of political and bureaucratic regime changes on Australia's real interest rate," International Review of Economics & Finance, Elsevier, vol. 85(C), pages 124-136.
    10. Alfred A. Haug, 2014. "On real interest rate persistence: the role of breaks," Applied Economics, Taylor & Francis Journals, vol. 46(10), pages 1058-1066, April.
    11. 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.
    12. Gil-Alana, Luis A. & Cunado, Juncal & Gupta, Rangan, 2017. "Evidence of persistence in U.S. short and long-term interest rates," Journal of Policy Modeling, Elsevier, vol. 39(5), pages 775-789.
    13. Jinho Bae & Chang-Jin Kim & Dong Kim, 2012. "The evolution of the monetary policy regimes in the U.S," Empirical Economics, Springer, vol. 43(2), pages 617-649, October.
    14. Milas Costas & Legrenzi Gabriella, 2006. "Non-linear Real Exchange Rate Effects in the UK Labour Market," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(1), pages 1-34, March.
    15. Kim, Dukpa & Oka, Tatsushi & Estrada, Francisco & Perron, Pierre, 2020. "Inference related to common breaks in a multivariate system with joined segmented trends with applications to global and hemispheric temperatures," Journal of Econometrics, Elsevier, vol. 214(1), pages 130-152.
    16. Günes Kamber & James Morley & Benjamin Wong, 2018. "Intuitive and Reliable Estimates of the Output Gap from a Beveridge-Nelson Filter," The Review of Economics and Statistics, MIT Press, vol. 100(3), pages 550-566, July.
    17. Rossi, Barbara, 2013. "Advances in Forecasting under Instability," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1203-1324, Elsevier.
    18. Christopher Martin & Costas Milas, 2004. "Uncertainty and UK Monetary Policy," Money Macro and Finance (MMF) Research Group Conference 2004 65, Money Macro and Finance Research Group.
    19. Perron, Pierre, 2020. "L'estimation de modèles avec changements structurels multiples," L'Actualité Economique, Société Canadienne de Science Economique, vol. 96(4), pages 789-837, Décembre.
    20. Costantini, Mauro & Lupi, Claudio, 2007. "An analysis of inflation and interest rates. New panel unit root results in the presence of structural breaks," Economics Letters, Elsevier, vol. 95(3), pages 408-414, June.

    More about this item

    Keywords

    deterministic shift; nonlinear autoregression; nonstationarity; nonlinear trend; 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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bdr:borrec:420. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Clorith Angélica Bahos Olivera (email available below). General contact details of provider: https://edirc.repec.org/data/brcgvco.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.