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Inferences from parametric and non-parametric covariance matrix estimation procedures

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Abstract

We propose a parametric spectral estimation procedure for contructing heteroskedasticity and autocorrelation consistent (HAC) covariance matrices. We establish the consistency of this procedure under very general conditions similar to those considered in previous research. We also perform Monte Carlo simulations to evaluate the performance of this procedure in drawing reliable inferences from linear regression estimates. These simulations indicate that the parametric estimator matches, and in some cases greatly exceeds, the performance of the prewhitened kernel estimator proposed by Andrews and Monahan (1992). These simulations also illustrate the inherent limitations of non-parametric HAC covariance matrix estimation procedures, and highlight the advantages of explicitly modeling the temporal properties of the error terms.

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  • Wouter J. Den Haan & Andrew T. Levin, 1995. "Inferences from parametric and non-parametric covariance matrix estimation procedures," International Finance Discussion Papers 504, Board of Governors of the Federal Reserve System (U.S.).
    • Handle: RePEc:fip:fedgif:504
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    3. Chistiano, Lawrence J & den Haan, Wouter J, 1996. "Small-Sample Properties of GMM for Business-Cycle Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 309-327, July.
    4. Ionel Birgean & Lutz Kilian, 2002. "Data-Driven Nonparametric Spectral Density Estimators For Economic Time Series: A Monte Carlo Study," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 449-476.
    5. Carvalho, Carlos & Masini, Ricardo & Medeiros, Marcelo C., 2018. "ArCo: An artificial counterfactual approach for high-dimensional panel time-series data," Journal of Econometrics, Elsevier, vol. 207(2), pages 352-380.
    6. Shigeru Fujita, 2004. "Vacancy persistence," Working Papers 04-23, Federal Reserve Bank of Philadelphia.
    7. Giacomini, Raffaella & Komunjer, Ivana, 2005. "Evaluation and Combination of Conditional Quantile Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 416-431, October.
    8. Qunyong Wang & Na Wu, 2012. "Long-run covariance and its applications in cointegration regression," Stata Journal, StataCorp LP, vol. 12(3), pages 525-542, September.
    9. Bollen, Bernard & Inder, Brett, 2002. "Estimating daily volatility in financial markets utilizing intraday data," Journal of Empirical Finance, Elsevier, vol. 9(5), pages 551-562, December.
    10. Brüggemann, Ralf & Jentsch, Carsten & Trenkler, Carsten, 2016. "Inference in VARs with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 191(1), pages 69-85.
    11. den Haan, Wouter J. & Levin, Andrew T, 2000. "Robust Covariance Matrix Estimation with Data-Dependent VAR Prewhitening Order," University of California at San Diego, Economics Working Paper Series qt0127m2tp, Department of Economics, UC San Diego.
    12. 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.
    13. Nicolau, João & Rodrigues, Paulo M.M. & Stoykov, Marian Z., 2023. "Tail index estimation in the presence of covariates: Stock returns’ tail risk dynamics," Journal of Econometrics, Elsevier, vol. 235(2), pages 2266-2284.
    14. Wagenvoort, Rien & Waldmann, Robert, 2002. "On B-robust instrumental variable estimation of the linear model with panel data," Journal of Econometrics, Elsevier, vol. 106(2), pages 297-324, February.
    15. Zhihao Xu & Clifford M. Hurvich, 2021. "A Unified Frequency Domain Cross-Validatory Approach to HAC Standard Error Estimation," Papers 2108.06093, arXiv.org, revised Jun 2023.
    16. Petko Kalev & Brett Inder, 2006. "The information content of the term structure of interest rates," Applied Economics, Taylor & Francis Journals, vol. 38(1), pages 33-45.
    17. Hirukawa, Masayuki, 2023. "Robust Covariance Matrix Estimation in Time Series: A Review," Econometrics and Statistics, Elsevier, vol. 27(C), pages 36-61.
    18. Kuo, Biing-Shen, 1998. "Test for partial parameter instability in regressions with I(1) processes," Journal of Econometrics, Elsevier, vol. 86(2), pages 337-368, June.
    19. Shakila Aruman & Mardi Dungey, 2001. "A Perspective on Modelling the Real Trade Weighted Index Since the Float," CEPR Discussion Papers 435, Centre for Economic Policy Research, Research School of Economics, Australian National University.
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    23. Bansal, Ravi & Lundblad, Christian, 2002. "Market efficiency, asset returns, and the size of the risk premium in global equity markets," Journal of Econometrics, Elsevier, vol. 109(2), pages 195-237, August.

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    Keywords

    Econometrics;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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