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Testing linearity against smooth transition autoregression using a parametric bootstrap

Author

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  • Skalin, Joakim

    () (Dept for Economic Affairs, Ministry of Finance)

Abstract

When testing the null hypothesis of linearity of a univariate time series against smooth transition autoregression (STAR), standard asymptotic distribution results do not apply since nuisance parameters in the model are unidentified under the null hypothesis. The prevailing test of Luukkonen, Saikkonen and Teräsvirta (1988) is based on a linearization, which may adversely affect its power. This paper discusses an alternative procedure, based on a parametric bootstrap of a likelihood ratio test statistic, and investigates its size and power properties by a small simulation study. The results, however, indicate that the power of the bootstrap test is inferior to that of the existing test.

Suggested Citation

  • Skalin, Joakim, 1998. "Testing linearity against smooth transition autoregression using a parametric bootstrap," SSE/EFI Working Paper Series in Economics and Finance 276, Stockholm School of Economics, revised 13 Dec 1998.
  • Handle: RePEc:hhs:hastef:0276
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    Citations

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    Cited by:

    1. Jonathan B. Hill, 2004. "Consistent Model Specification Tests Against Smooth Transition Alternatives," Econometrics 0402004, EconWPA, revised 05 Aug 2005.
    2. Jonathan B. Hill, 2004. "Consistent LM-Tests for Linearity Against Compound Smooth Transition Alternatives," Econometric Society 2004 North American Summer Meetings 42, Econometric Society.
    3. Till Strohsal & Enzo Weber, 2012. "The Signal of Volatility," SFB 649 Discussion Papers SFB649DP2012-043, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Taylor, Mark P & Peel, David A & Sarno, Lucio, 2001. "Nonlinear Mean-Reversion in Real Exchange Rates: Toward a Solution to the Purchasing Power Parity Puzzles," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(4), pages 1015-1042, November.
    5. Sarno, Lucio & Thornton, Daniel L., 2003. "The dynamic relationship between the federal funds rate and the Treasury bill rate: An empirical investigation," Journal of Banking & Finance, Elsevier, vol. 27(6), pages 1079-1110, June.
    6. repec:ebl:ecbull:v:6:y:2008:i:26:p:1-18 is not listed on IDEAS
    7. Matthew T. Holt & Joseph V. Balagtas, 2009. "Estimating Structural Change with Smooth Transition Regressions: An Application to Meat Demand," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 91(5), pages 1424-1431.
    8. Strohsal, Till & Weber, Enzo, 2015. "Time-varying international stock market interaction and the identification of volatility signals," Journal of Banking & Finance, Elsevier, vol. 56(C), pages 28-36.
    9. Jonathan B. Hill, 2004. "LM-Tests for Linearity Against Smooth Transition Alternatives: A Bootstrap Simulation Study," Econometrics 0401004, EconWPA, revised 05 Jul 2004.
    10. Sofiane Amri, 2008. "Analysing the forward premium anomaly using a Logistic Smooth Transition Regression model," Economics Bulletin, AccessEcon, vol. 6(26), pages 1-18.
    11. Weber, Enzo, 2009. "Financial Contagion, Vulnerability and Information Flow: Empirical Identification," University of Regensburg Working Papers in Business, Economics and Management Information Systems 431, University of Regensburg, Department of Economics.
    12. Coakley, Jerry & Fuertes, Ana-Maria, 2006. "Testing for sign and amplitude asymmetries using threshold autoregressions," Journal of Economic Dynamics and Control, Elsevier, vol. 30(4), pages 623-654, April.
    13. Lucio Sarno & Giorgio Valente & Hyginus Leon, 2006. "Nonlinearity in Deviations from Uncovered Interest Parity: An Explanation of the Forward Bias Puzzle," Review of Finance, European Finance Association, vol. 10(3), pages 443-482, September.
    14. Sarno, Lucio, 2001. "The behavior of US public debt: a nonlinear perspective," Economics Letters, Elsevier, vol. 74(1), pages 119-125, December.
    15. 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.
    16. 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.
    17. Strohsal, Till & Weber, Enzo, 2013. "Identifying Volatility Signals from Time-Varying Simultaneous Stock Market Interaction," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79903, Verein für Socialpolitik / German Economic Association.

    More about this item

    Keywords

    Linearity testing; smooth transition autoregression model; nuisance parameter; nonstandard testing problem; bootstrap test;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: 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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