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Testing for linear autoregressive dynamics under heteroskedasticity

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  • Hafner, Christian M.
  • Herwartz, Helmut

Abstract

One puzzling behavior of asset returns for various frequencies is the often observed positive autocorrelation at lag 1. To some extent this can be explained by standard asset pricing models when assuming time varying risk premia. However, one often finds better results when directly fitting an autoregressive model, for which there is little economic foundation. One may ask whether the underlying process does in fact contain an autoregressive component. It is therefore of interest to have a statistical test at hand that performs well under the stylized facts of financial returns. In this paper, we investigate empirical properties of competing devices to test for autoregressive dynamics in case of heteroskedastic errors. For the volatility process we assume GARCH, TGARCH and stochastic volatility. The results indicate that standard QML inference for the autoregressive parameter is negatively affected by misspecification of the volatility process. We show that bootstrapped versions of a likelihood ratio and White's t-statistic have better size properties and comparable power properties. Applied to German stock data, the alternative tests in many cases yield very different p-values.

Suggested Citation

  • Hafner, Christian M. & Herwartz, Helmut, 1998. "Testing for linear autoregressive dynamics under heteroskedasticity," SFB 373 Discussion Papers 1999,7, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  • Handle: RePEc:zbw:sfb373:19997
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    Citations

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    Cited by:

    1. Jianqing Fan & Mingjin Wang & Qiwei Yao, 2008. "Modelling multivariate volatilities via conditionally uncorrelated components," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 679-702.
    2. repec:eee:intfor:v:33:y:2017:i:3:p:569-580 is not listed on IDEAS
    3. HAFNER, Christian & HERWARTZ, Helmut, 1998. "Volatility impulse response functions for multivariate GARCH models," CORE Discussion Papers 1998047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Hafner, Christian M., 2000. "Fourth moments of multivariate GARCH processes," SFB 373 Discussion Papers 2000,80, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    5. 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.
    6. Christian Hafner & Helmut Herwartz, 2008. "Analytical quasi maximum likelihood inference in multivariate volatility models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(2), pages 219-239, March.
    7. Ruiz, Esther & Veiga, Helena, 2008. "Modelling long-memory volatilities with leverage effect: A-LMSV versus FIEGARCH," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2846-2862, February.
    8. Hafner, Christian M. & Herwartz, Helmut, 2006. "Volatility impulse responses for multivariate GARCH models: An exchange rate illustration," Journal of International Money and Finance, Elsevier, vol. 25(5), pages 719-740, August.
    9. M. Angeles Carnero, 2004. "Persistence and Kurtosis in GARCH and Stochastic Volatility Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(2), pages 319-342.
    10. Hafner, Christian M. & Herwartz, Helmut, 2001. "Option pricing under linear autoregressive dynamics, heteroskedasticity, and conditional leptokurtosis," Journal of Empirical Finance, Elsevier, vol. 8(1), pages 1-34, March.
    11. Hafner, Christian M. & Herwartz, Helmut, 2002. "Testing for vector autoregressive dynamics under heteroskedasticity," SFB 373 Discussion Papers 2003,4, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    12. PREMINGER, Arie & HAFNER, Christian, 2006. "Deciding between GARCH and stochastic volatility via strong decision rules," CORE Discussion Papers 2006042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Herwartz, Helmut, 2015. "Are GARCH innovations independent - a long term assessment for the S&P 500," Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113109, Verein für Socialpolitik / German Economic Association.
    14. repec:spr:stpapr:v:58:y:2017:i:4:d:10.1007_s00362-016-0744-0 is not listed on IDEAS
    15. Hafner, C.M. & Franses, Ph.H.B.F., 2003. "A generalized dynamic conditional correlation model for many asset returns," Econometric Institute Research Papers EI 2003-18, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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