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Asymptotic and bootstrap tests for linearity in a TAR-GARCH(1,1) model with a unit root

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  • Gospodinov, Nikolay

Abstract

This paper derives the limiting distribution of the Lagrange Multiplier (LM) test for threshold nonlinearity in a TAR model with GARCH errors when one of the regimes contains a unit root. It is shown that the asymptotic distribution is nonstandard and depends on nuisance parameters that capture the degree of conditional heteroskedasticity and non-Gaussian nature of the process. We propose a bootstrap procedure for approximating the exact finite-sample distribution of the test for linearity and establish its asymptotic validity.

Suggested Citation

  • Gospodinov, Nikolay, 2008. "Asymptotic and bootstrap tests for linearity in a TAR-GARCH(1,1) model with a unit root," Journal of Econometrics, Elsevier, vol. 146(1), pages 146-161, September.
    • Handle: RePEc:eee:econom:v:146:y:2008:i:1:p:146-161
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    2. Ghassan, Hassan Belkacem & AlHajhoj, Hassan Rafdan, 2016. "Long run dynamic volatilities between OPEC and non-OPEC crude oil prices," Applied Energy, Elsevier, vol. 169(C), pages 384-394.
    3. Nikolay Gospodinov & Ye Tao, 2011. "Bootstrap Unit Root Tests in Models with GARCH(1,1) Errors," Econometric Reviews, Taylor & Francis Journals, vol. 30(4), pages 379-405, August.
    4. Jesús Gonzalo & Jean-Yves Pitarakis, 2013. "Estimation and inference in threshold type regime switching models," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 8, pages 189-205, Edward Elgar Publishing.
    5. Hassan Ghassan & Prashanta Banerjee, 2015. "A threshold cointegration analysis of asymmetric adjustment of OPEC and non-OPEC monthly crude oil prices," Empirical Economics, Springer, vol. 49(1), pages 305-323, August.
    6. Bernard Njindan Iyke, 2019. "A Test Of The Efficiency Of The Foreign Exchange Market In Indonesia," Bulletin of Monetary Economics and Banking, Bank Indonesia, vol. 0(12th BMEB), pages 1-26, January.

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