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Modelling autoregressive processes with a shifting mean

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Author Info
Timo Terasvirta ()
Andrés González ()

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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.

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Paper provided by Banco de la Republica de Colombia in its series Borradores de Economia with number 420.

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Handle: RePEc:bdr:borrec:420

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Related research
Keywords: deterministic shift; nonlinear autoregression; nonstationarity; nonlinear trend; structural change Classification JEL: C22; C52.;

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This paper has been announced in the following NEP Reports: References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
  2. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May. [Downloadable!] (restricted)
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  3. 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. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
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  5. 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. [Downloadable!] (restricted)
  6. Eitrheim, Oyvind & Terasvirta, Timo, 1996. "Testing the adequacy of smooth transition autoregressive models," Journal of Econometrics, Elsevier, vol. 74(1), pages 59-75, September. [Downloadable!] (restricted)
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  7. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-58, November. [Downloadable!] (restricted)
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  8. Graham Elliott & Allan Timmermann, 2008. "Economic Forecasting," Journal of Economic Literature, American Economic Association, vol. 46(1), pages 3-56, March.
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  9. 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. [Downloadable!] (restricted)
  10. 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 320-34, August.
  11. 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 735-63, November.
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  12. Racine, Jeff, 1997. "Feasible Cross-Validatory Model Selection for General Stationary Processes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(2), pages 169-79, March-Apr. [Downloadable!]
  13. 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 323-37, July.
  14. 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.
  15. 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. [Downloadable!]
  16. 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. [Downloadable!] (restricted)
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  17. 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. [Downloadable!]
  18. 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. [Downloadable!]
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  19. White, Halbert, 2006. "Approximate Nonlinear Forecasting Methods," Handbook of Economic Forecasting, Elsevier. [Downloadable!] (restricted)
  20. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
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  21. 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 111-25, February. [Downloadable!] (restricted)
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  22. 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. [Downloadable!]
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Strikholm, Birgit, 2006. "Determining the number of breaks in a piecewise linear regression model," Working Paper Series in Economics and Finance 648, Stockholm School of Economics. [Downloadable!]
  2. Andrés González & Kirstin Hubrich & Timo Teräsvirta, 2009. "Forecasting inflation with gradual regime shifts and exogenous information," CREATES Research Papers 2009-03, School of Economics and Management, University of Aarhus. [Downloadable!]
  3. Richard T. Baillie & Claudio Morana, 2007. "Modeling Long Memory and Structural Breaks in Conditional Variances: an Adaptive FIGARCH Approach," ICER Working Papers - Applied Mathematics Series 11-2007, ICER - International Centre for Economic Research. [Downloadable!]
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