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Bootstrapping Autoregression under Non-stationary Volatility

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  • Ke-Li Xu

Abstract

This paper studies robust inference in autoregression around a polynomial trend with stable autoregressive roots under non-stationary volatility. The formulation of the volatility process is quite general including many existing deterministic and stochastic non-stationary volatility specifications. The aim of the paper is two-fold. First, it develops a limit theory for least squares estimators and shows how non-stationary volatility affects the consistency, convergence rates and asymptotic distributions of the slope and trend coefficients estimators in different ways. This complements the results recently obtained by Chung and Park (2007, Journal of Econometrics 137, 230--59. Second, it studies the recursive wild bootstrap procedure of Gonçalves and Kilian (2004, Journal of Econometrics 123, 89--120) in the presence of non-stationary volatility, and shows its validity when the estimates are asymptotically mixed Gaussian. Simulations are performed to compare favourably the recursive wild bootstrap with other inference procedures under non-stationary volatility. Copyright Royal Economic Society 2008

Suggested Citation

  • Ke-Li Xu, 2008. "Bootstrapping Autoregression under Non-stationary Volatility," Econometrics Journal, Royal Economic Society, vol. 11(1), pages 1-26, March.
  • Handle: RePEc:ect:emjrnl:v:11:y:2008:i:1:p:1-26
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    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1368-423X.2008.00235.x
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    Cited by:

    1. Hanck, Christoph & Demetrescu, Matei & Kruse, Robinson, 2015. "Fixed-b Asymptotics for t-Statistics in the Presence of Time-Varying Volatility," Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112916, Verein für Socialpolitik / German Economic Association.
    2. Cavaliere, Giuseppe & Nielsen, Morten Ørregaard & Taylor, A.M. Robert, 2015. "Bootstrap score tests for fractional integration in heteroskedastic ARFIMA models, with an application to price dynamics in commodity spot and futures markets," Journal of Econometrics, Elsevier, vol. 187(2), pages 557-579.
    3. Xu, Ke-Li, 2012. "Robustifying multivariate trend tests to nonstationary volatility," Journal of Econometrics, Elsevier, vol. 169(2), pages 147-154.
    4. Demetrescu, Matei & Kruse, Robinson, 2015. "Testing heteroskedastic time series for normality," Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113221, Verein für Socialpolitik / German Economic Association.
    5. Nikolaos Kourogenis, 2015. "Polynomial Trends, Nonstationary Volatility and the Eicker-White Asymptotic Variance Estimator," Economics Bulletin, AccessEcon, vol. 35(3), pages 1675-1680.
    6. Christian M. Hafner & Helmut Herwartz, 2009. "Testing for linear vector autoregressive dynamics under multivariate generalized autoregressive heteroskedasticity," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 63(3), pages 294-323.
    7. Cavaliere, Giuseppe & Rahbek, Anders & Taylor, A.M. Robert, 2010. "Testing for co-integration in vector autoregressions with non-stationary volatility," Journal of Econometrics, Elsevier, vol. 158(1), pages 7-24, September.
    8. repec:eee:ecmode:v:68:y:2018:i:c:p:388-408 is not listed on IDEAS
    9. Jarrow, Robert & Teo, Melvyn & Tse, Yiu Kuen & Warachka, Mitch, 2012. "An improved test for statistical arbitrage," Journal of Financial Markets, Elsevier, vol. 15(1), pages 47-80.
    10. Jinzhao Chen, 2012. "Crisis, Capital Controls and Covered Interest Parity: Evidence from China in Transformation," Working Papers halshs-00660654, HAL.
    11. Matei Demetrescu & Christoph Hanck & Robinson Kruse, 2016. "Fixed-b Inference in the Presence of Time-Varying Volatility," CREATES Research Papers 2016-01, Department of Economics and Business Economics, Aarhus University.
    12. Steenkamp, Daan, 2018. "Explosiveness in G11 currencies," Economic Modelling, Elsevier, vol. 68(C), pages 388-408.
    13. Grote, Claudia & Bertram, Philip, 2015. "A comparative Study of Volatility Breaks," Hannover Economic Papers (HEP) dp-558, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    14. repec:spr:stpapr:v:58:y:2017:i:4:d:10.1007_s00362-016-0744-0 is not listed on IDEAS

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