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Efficient Iv Estimation For Autoregressive Models With Conditional Heteroskedasticity

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  • Kuersteiner, Guido M.

Abstract

This paper analyzes autoregressive time series models where the errors are assumed to be martingale difference sequences that satisfy an additional symmetry condition on their fourth-order moments. Under these conditions quasi maximum likelihood estimators of the autoregressive parameters are no longer efficient in the generalized method of moments (GMM) sense. The main result of the paper is the construction of efficient semiparametric instrumental variables estimators for the autoregressive parameters. The optimal instruments are linear functions of the innovation sequence.It is shown that a frequency domain approximation of the optimal instruments leads to an estimator that only depends on the data periodogram and an unknown linear filter. Semiparametric methods to estimate the optimal filter are proposed.The procedure is equivalent to GMM estimators where lagged observations are used as instruments. As a result of the additional symmetry assumption on the fourth moments the number of instruments is allowed to grow at the same rate as the sample. No lag truncation parameters are needed to implement the estimator, which makes it particularly appealing from an applied point of view.

Suggested Citation

  • Kuersteiner, Guido M., 2002. "Efficient Iv Estimation For Autoregressive Models With Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 18(3), pages 547-583, June.
  • Handle: RePEc:cup:etheor:v:18:y:2002:i:03:p:547-583_18
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    Cited by:

    1. Oscar Jorda, 2007. "Inference for Impulse Responses," Working Papers 77, University of California, Davis, Department of Economics.
    2. Oscar Jorda, 2007. "Joint Inference and Counterfactual experimentation for Impulse Response Functions by Local Projections," Working Papers 107, University of California, Davis, Department of Economics.
    3. West, Kenneth D, 2001. "On Optimal Instrumental Variables Estimation of Stationary Time Series Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(4), pages 1043-1050, November.
    4. Douglas Hodgson, 2002. "Semiparametric Efficient Estimation of the Mean of a Time Series in the Presence of Conditional Heterogeneity of Unknown Form," Cahiers de recherche CREFE / CREFE Working Papers 146, CREFE, Université du Québec à Montréal.
    5. Stanislav Anatolyev, 2007. "Optimal Instruments In Time Series: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 21(1), pages 143-173, February.
    6. Jean Jacod & Michael Sørensen, 2018. "A review of asymptotic theory of estimating functions," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 415-434, July.
    7. Kenneth West & Ka-fu Wong & Stanislav Anatolyev, 2009. "Instrumental Variables Estimation of Heteroskedastic Linear Models Using All Lags of Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 28(5), pages 441-467.
    8. Kuersteiner, Guido M., 2001. "Optimal instrumental variables estimation for ARMA models," Journal of Econometrics, Elsevier, vol. 104(2), pages 359-405, September.
    9. Gospodinov, Nikolay & Otsu, Taisuke, 2012. "Local GMM estimation of time series models with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 170(2), pages 476-490.
    10. Ke Zhu, 2018. "Statistical inference for autoregressive models under heteroscedasticity of unknown form," Papers 1804.02348, arXiv.org, revised Aug 2018.
    11. Oscar Jorda, 2007. "Joint Inference and Counterfactual experimentation for Impulse Response Functions by Local Projections," Working Papers 624, University of California, Davis, Department of Economics.
    12. Prono Todd, 2018. "Closed-form estimators for finite-order ARCH models as simple and competitive alternatives to QMLE," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(5), pages 1-25, December.
    13. Xu, Ke-Li & Phillips, Peter C.B., 2008. "Adaptive estimation of autoregressive models with time-varying variances," Journal of Econometrics, Elsevier, vol. 142(1), pages 265-280, January.
    14. Kuersteiner, Guido M., 2012. "Kernel-weighted GMM estimators for linear time series models," Journal of Econometrics, Elsevier, vol. 170(2), pages 399-421.
    15. Oscar Jorda, 2007. "Inference for Impulse Responses," Working Papers 201, University of California, Davis, Department of Economics.
    16. Hansen, Bruce E., 2005. "Challenges For Econometric Model Selection," Econometric Theory, Cambridge University Press, vol. 21(1), pages 60-68, February.

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