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Testing for linear autoregressive dynamics under heteroskedasticity

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Author Info

  • CHRISTIAN M. HAFNER
  • HELMUT HERWARTZ

Abstract

A puzzling characteristic of asset returns for various frequencies is the often observed positive autocorrelation at lag one. 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 quasi-maximum-likelihood inference for the autoregressive parameter is negatively affected by misspecification of the volatility process. We show that bootstrapped versions of least-squares-based statistics have better empirical size and comparable power properties. Applied to German stock return data, the alternative tests yield very different p-values for a considerable number of stock return processes.

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Bibliographic Info

Article provided by Royal Economic Society in its journal The Econometrics Journal.

Volume (Year): 3 (2000)
Issue (Month): 2 ()
Pages: 177-197

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Handle: RePEc:ect:emjrnl:v:3:y:2000:i:2:p:177-197

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Related research

Keywords: Autoregression; Heteroskedasticity; Bootstrap; GARCH; Stochastic volatility.;

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Cited by:
  1. 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.
  2. Jianqing Fan & Mingjin Wang & Qiwei Yao, 2008. "Modelling multivariate volatilities via conditionally uncorrelated components," LSE Research Online Documents on Economics 22875, London School of Economics and Political Science, LSE Library.
  3. 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.
  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. Hafner, C.M. & Herwartz, H., 2003. "Analytical quasi maximum likelihood inference in multivariate volatility models," Econometric Institute Research Papers EI 2003-21, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  6. PREMINGER, Arie & HAFNER, Christian M., 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).
  7. 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.
  8. HAFNER, Christian & HERWARTZ, Helmut, 2001. "Volatility impulse response functions for multivariate GARCH models," CORE Discussion Papers 2001039, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Hafner, Christian M. & Herwartz, Helmut, 1999. "Option pricing under linear autoregressive dynamics, heteroskedasticity, and conditional leptokurtosis," SFB 373 Discussion Papers 1999,58, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  10. 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.

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