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A new consistency proof for HAC variance estimators

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  • Davidson, James

Abstract

A consistency theorem for kernel HAC variance estimators was originally proposed by Hansen (1992) but corrected under stronger conditions on the order of existing moments by de Jong (2000). The present result restores and also generalizes the conditions of Hansen’s result by assuming the process to be adapted to a filtration. It allows for nonstationarity, and dependence is modelled by the assumption of near-epoch dependence on a mixing process.

Suggested Citation

  • Davidson, James, 2020. "A new consistency proof for HAC variance estimators," Economics Letters, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:ecolet:v:186:y:2020:i:c:s0165176519304112
    DOI: 10.1016/j.econlet.2019.108811
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    References listed on IDEAS

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    1. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    2. Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, vol. 60(4), pages 967-972, July.
    3. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    4. Robert M. De Jong & James Davidson, 2000. "Consistency of Kernel Estimators of Heteroscedastic and Autocorrelated Covariance Matrices," Econometrica, Econometric Society, vol. 68(2), pages 407-424, March.
    5. James Davidson & Robert M. De Jong, 2002. "Consistency of kernel variance estimators for sums of semiparametric linear processes," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 160-175, June.
    6. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    7. de Jong, Robert M., 1997. "Central Limit Theorems for Dependent Heterogeneous Random Variables," Econometric Theory, Cambridge University Press, vol. 13(3), pages 353-367, June.
    8. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1449-1459, December.
    9. de Jong, Robert M., 2000. "A Strong Consistency Proof For Heteroskedasticity And Autocorrelation Consistent Covariance Matrix Estimators," Econometric Theory, Cambridge University Press, vol. 16(2), pages 262-268, April.
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    2. Alessio Sancetta, 2023. "Intraday Trades Profile Estimation: An Intensity Approach," Journal of Financial Econometrics, Oxford University Press, vol. 21(3), pages 651-677.

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