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Higher-Order Accurate, Positive Semidefinite Estimation Of Large-Sample Covariance And Spectral Density Matrices


  • Politis, Dimitris N.


A new class of large-sample covariance and spectral density matrix estimators is proposed based on the notion of flat-top kernels. The new estimators are shown to be higher-order accurate when higher-order accuracy is possible. A discussion on kernel choice is presented as well as a supporting finite-sample simulation. The problem of spectral estimation under a potential lack of finite fourth moments is also addressed. The higher-order accuracy of flat-top kernel estimators typically comes at the sacrifice of the positive semidefinite property. Nevertheless, we show how a flat-top estimator can be modified to become positive semidefinite (even strictly positive definite) while maintaining its higher-order accuracy. In addition, an easy (and consistent) procedure for optimal bandwidth choice is given; this procedure estimates the optimal bandwidth associated with each individual element of the target matrix, automatically sensing (and adapting to) the underlying correlation structure.

Suggested Citation

  • Politis, Dimitris N., 2011. "Higher-Order Accurate, Positive Semidefinite Estimation Of Large-Sample Covariance And Spectral Density Matrices," Econometric Theory, Cambridge University Press, vol. 27(04), pages 703-744, August.
  • Handle: RePEc:cup:etheor:v:27:y:2011:i:04:p:703-744_00

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    Cited by:

    1. McCulloch, J. Huston, 2016. "Moment Ratio estimation of autoregressive/unit root parameters and autocorrelation-consistent standard errors," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 712-733.
    2. Kim, Min Seong & Sun, Yixiao, 2013. "Heteroskedasticity and spatiotemporal dependence robust inference for linear panel models with fixed effects," Journal of Econometrics, Elsevier, vol. 177(1), pages 85-108.
    3. Hassan Doosti & Peter Hall, 2016. "Making a non-parametric density estimator more attractive, and more accurate, by data perturbation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 445-462, March.
    4. Berkes, István & Horváth, Lajos & Rice, Gregory, 2016. "On the asymptotic normality of kernel estimators of the long run covariance of functional time series," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 150-175.
    5. repec:bla:jtsera:v:38:y:2017:i:4:p:591-609 is not listed on IDEAS
    6. Chang, Christopher & Politis, Dimitris, 2014. "Aggregation of spectral density estimators," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 204-213.
    7. Rasmus Tangsgaard Varneskov, 2011. "Generalized Flat-Top Realized Kernel Estimation of Ex-Post Variation of Asset Prices Contaminated by Noise," CREATES Research Papers 2011-31, Department of Economics and Business Economics, Aarhus University.
    8. Horváth, Lajos & Kokoszka, Piotr & Rice, Gregory, 2014. "Testing stationarity of functional time series," Journal of Econometrics, Elsevier, vol. 179(1), pages 66-82.
    9. Jungbin Hwang, 2017. "Simple and Trustworthy Cluster-Robust GMM Inference," Working papers 2017-19, University of Connecticut, Department of Economics.
    10. Preinerstorfer, David & Pötscher, Benedikt M., 2016. "On Size And Power Of Heteroskedasticity And Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 32(02), pages 261-358, April.
    11. Ikeda, Shin S., 2016. "A bias-corrected estimator of the covariation matrix of multiple security prices when both microstructure effects and sampling durations are persistent and endogenous," Journal of Econometrics, Elsevier, vol. 193(1), pages 203-214.
    12. Efromovich, Sam, 2014. "Nonparametric estimation of the spectral density of amplitude-modulated time series with missing observations," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 7-13.
    13. Bai, Shuyang & Taqqu, Murad S. & Zhang, Ting, 2016. "A unified approach to self-normalized block sampling," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2465-2493.
    14. Abadir, Karim M. & Distaso, Walter & Žikeš, Filip, 2014. "Design-free estimation of variance matrices," Journal of Econometrics, Elsevier, vol. 181(2), pages 165-180.
    15. Politis, Dimitris, 2014. "High-dimensional autocovariance matrices and optimal linear prediction," University of California at San Diego, Economics Working Paper Series qt3k58p0xr, Department of Economics, UC San Diego.
    16. repec:bla:scjsta:v:44:y:2017:i:4:p:866-898 is not listed on IDEAS
    17. repec:bla:jtsera:v:38:y:2017:i:3:p:479-504 is not listed on IDEAS
    18. repec:eca:wpaper:2013/131191 is not listed on IDEAS

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