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Testing for threshold effect in ARFIMA models: Application to US unemployment rate data

Author

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  • Amine LAHIANI

    (ESC-Rennes School of Business and EconomiX, University of Paris 10 Nanterre)

  • Olivier SCAILLET

    (Université de Genève HEC and Swiss Finance Institute)

Abstract

Macroeconomic time series often involve a threshold effect in their ARMA representation, and exhibit long memory features. In this paper we introduce a new class of threshold ARFIMA models to account for this. The threshold effect is introduced in the autoregressive and/or the fractional integration parameters, and can be tested for using LM tests. Monte Carlo experiments show the desirable finite sample size and power of the test with an exact maximum likelihood estimator of the long memory parameter. Simulations also show that a model selection strategy is available to discriminate between the competing threshold ARFIMA models. The methodology is applied to US unemployment rate data where we find a significant threshold effect in the ARFIMA representation and a better forecasting performance relative to TAR and symmetric ARFIMA models.

Suggested Citation

  • Amine LAHIANI & Olivier SCAILLET, 2008. "Testing for threshold effect in ARFIMA models: Application to US unemployment rate data," Swiss Finance Institute Research Paper Series 08-42, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp0842
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    1. Andersson, Michael K. & Eklund, Bruno & Lyhagen, Johan, 1999. "A simple linear time series model with misleading nonlinear properties," Economics Letters, Elsevier, vol. 65(3), pages 281-284, December.
    2. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
    3. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521770415, September.
    4. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    5. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    6. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    7. Hidalgo, Javier & Robinson, Peter M., 1996. "Testing for structural change in a long-memory environment," Journal of Econometrics, Elsevier, vol. 70(1), pages 159-174, January.
    8. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
    9. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    10. Philip Rothman, 1998. "Forecasting Asymmetric Unemployment Rates," The Review of Economics and Statistics, MIT Press, vol. 80(1), pages 164-168, February.
    11. Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 165-188.
    12. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    13. George Kapetanios, 2001. "Model Selection in Threshold Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(6), pages 733-754, November.
    14. Bhardwaj, Geetesh & Swanson, Norman R., 2006. "An empirical investigation of the usefulness of ARFIMA models for predicting macroeconomic and financial time series," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 539-578.
    15. Anas, Jacques & Ferrara, Laurent, 2002. "Un indicateur d'entrée et sortie de récession: application aux Etats-Unis [A start-end recession index: Application for United-States]," MPRA Paper 4043, University Library of Munich, Germany.
    16. Benoit Bellone & David Saint-Martin, 2004. "Detecting Turning Points with Many Predictors through Hidden Markov Models," Econometrics 0407001, University Library of Munich, Germany.
    17. van Dijk, Dick & Franses, Philip Hans & Paap, Richard, 2002. "A nonlinear long memory model, with an application to US unemployment," Journal of Econometrics, Elsevier, vol. 110(2), pages 135-165, October.
    18. Alain Guay & Olivier Scaillet, 1999. "Indirect Inference, Nuisance Parameter and Threshold Moving Average," Cahiers de recherche CREFE / CREFE Working Papers 95, CREFE, Université du Québec à Montréal.
    19. Offer Lieberman & Judith Rousseau & David M. Zucker, 2002. "Valid Asymptotic Expansions for the Maximum Likelihood Estimator of the Parameter of a Stationary, Gaussian, Strongly Dependent Process," Cowles Foundation Discussion Papers 1351, Cowles Foundation for Research in Economics, Yale University.
    20. Guay, Alain & Scaillet, Olivier, 2003. "Indirect Inference, Nuisance Parameter, and Threshold Moving Average Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 122-132, January.
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    Cited by:

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    2. Guglielmo Maria Caporale & Luis A. Gil-Alana & Pablo Vicente Trejo, 2021. "Unemployment Persistence in Europe: Evidence from the 27 EU Countries," CESifo Working Paper Series 9392, CESifo.
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    9. Donya Rahmani & Damien Fay, 2022. "A state‐dependent linear recurrent formula with application to time series with structural breaks," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(1), pages 43-63, January.

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    More about this item

    Keywords

    Threshold ARFIMA; LM test; Asymmetric time series;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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