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Asymptotic Inference For Unit Root Processes With Garch(1,1) Errors

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  • Ling, Shiqing
  • Li, W.K.

Abstract

This paper investigates the so-called one-step local quasi maximum likelihood estimator for the unit root process with GARCH(1,1) errors. When the scaled conditional errors (the ratio of the disturbance to the conditional standard deviation) follow a symmetric distribution, the asymptotic distribution of the estimated unit root is derived only under the second-order moment condition. It is shown that this distribution is a functional of a bivariate Brownian motion as in Ling and Li (1998, Annals of Statistics 26, 84 125) and can be used to construct the unit root test.The authors thank the co-editor, Bruce Hansen, and two referees for very helpful comments and suggestions. W.K. Li s research is partially supported by the Hong Kong Research Grants Council. Ling s research is supported by RGC Competitive Earmarked Research grant HKUST6113 02P.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 19 (2003)
Issue (Month): 04 (August)
Pages: 541-564

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Handle: RePEc:cup:etheor:v:19:y:2003:i:04:p:541-564_19

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Cited by:
  1. Li, Yushu & Shukur, Ghazi, 2009. "Testing for Unit Root against LSTAR model – wavelet improvements under GARCH distortion," Working Paper Series in Economics and Institutions of Innovation 184, Royal Institute of Technology, CESIS - Centre of Excellence for Science and Innovation Studies.
  2. Li, Yushu, 2012. "Wavelet Based Outlier Correction for Power Controlled Turning Point Detection in Surveillance Systems," Working Papers 2012:12, Lund University, Department of Economics.
  3. H. Peter Boswijk & Franc Klaassen, 2005. "Why Frequency Matters for Unit Root Testing," Tinbergen Institute Discussion Papers 04-119/4, Tinbergen Institute.
  4. Francq, Christian & Makarova, Svetlana & Zakoi[diaeresis]an, Jean-Michel, 2008. "A class of stochastic unit-root bilinear processes: Mixing properties and unit-root test," Journal of Econometrics, Elsevier, vol. 142(1), pages 312-326, January.
  5. Li, Yong & Chong, Terence Tai-Leung & Zhang, Jie, 2012. "Testing for a unit root in the presence of stochastic volatility and leverage effect," Economic Modelling, Elsevier, vol. 29(5), pages 2035-2038.
  6. 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.
  7. Jin-Yu Zhang & Yong Li & Zhu-Ming Chen, 2013. "Unit Root Hypothesis in the Presence of Stochastic Volatility, a Bayesian Analysis," Computational Economics, Society for Computational Economics, vol. 41(1), pages 89-100, January.
  8. Horváth, Lajos & Kokoszka, Piotr, 2003. "A bootstrap approximation to a unit root test statistic for heavy-tailed observations," Statistics & Probability Letters, Elsevier, vol. 62(2), pages 163-173, April.
  9. Wang, Gaowen, 2006. "A note on unit root tests with heavy-tailed GARCH errors," Statistics & Probability Letters, Elsevier, vol. 76(10), pages 1075-1079, May.
  10. Chor-yiu SIN, 2004. "Estimation and Testing for Partially Nonstationary Vector Autoregressive Models with GARCH: WLS versus QMLE," Econometric Society 2004 Australasian Meetings 92, Econometric Society.
  11. Paulo Rodrigues & Antonio Rubia, 2008. "A note on testing for nonstationarity in autoregressive processes with level dependent conditional heteroskedasticity," Statistical Papers, Springer, vol. 49(3), pages 581-593, July.
  12. Westerlund, Joakim, 2014. "On the choice of test for a unit root when the errors are conditionally heteroskedastic," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 40-53.
  13. Li, Yushu & Shukur, Ghazi, 2009. "Wavelet Improvement of the Over-rejection of Unit root test under GARCH errors," CAFO Working Papers 2009:7, Centre for Labour Market Policy Research (CAFO), School of Business and Economics, Linnaeus University.

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