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HETEROSKEDASTICITY AUTOCORRELATION ROBUST INFERENCE IN TIME SERIES REGRESSIONS WITH MISSING DATA

Published online by Cambridge University Press:  25 May 2018

Seung-Hwa Rho and
Timothy J. Vogelsang
Seung-Hwa Rho*
Affiliation:
Amazon
Timothy J. Vogelsang*
Affiliation:
Michigan State University
*
†Seung-Hwa Rho, Amazon, Berlin, Germany; e-mail: seughr@amazon.com.
*Address correspondence to Timothy J. Vogelsang, Department of Economics, Michigan State University, East Lansing, MI, USA; e-mail: tvj@msu.edu
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Abstract

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In this article, we investigate the properties of heteroskedasticity and autocorrelation robust (HAR) test statistics in time series regression settings when observations are missing. We primarily focus on the nonrandom missing process case where we treat the missing locations to be fixed as T → ∞ by mapping the missing and observed cutoff dates into points on [0,1] based on the proportion of time periods in the sample that occur up to those cutoff dates. We consider two models, the amplitude modulated series (Parzen, 1963) regression model, which amounts to plugging in zeros for missing observations, and the equal space regression model, which simply ignores the missing observations. When the amplitude modulated series regression model is used, the fixed-b limits of the HAR test statistics depend on the locations of missing observations but are otherwise pivotal. When the equal space regression model is used, the fixed-b limits of the HAR test statistics have the standard fixed-b limits as in Kiefer and Vogelsang (2005). We discuss methods for obtaining fixed-b critical values with a focus on bootstrap methods and find the naive i.i.d. bootstrap with missing dates fixed to be an effective and practical way to obtain the fixed-b critical values.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 35 , Issue 3 , June 2019, pp. 601 - 629
Copyright
Copyright © Cambridge University Press 2018 

Footnotes

We are grateful for helpful suggestions and comments from the editor, a co-editor, anonymous referees, and seminar participants at Columbia University, the Joint Montreal Econometrics Seminar and participants at the 2017 NSF/NBER Time Series Conference.

References

REFERENCES

Andrews, D.W. (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59, 817–858.CrossRefGoogle Scholar
Bester, C.A., Conley, T.G., Hansen, C.B., & Vogelsang, T.J. (2016) Fixed-b asymptotics for spatially dependent robust nonparametric covariance matrix estimators. Econometric Theory 32, 154–186.CrossRefGoogle Scholar
Bloomfield, P. (1970) Spectral analysis with randomly missing observations. Journal of the Royal Statistical Society 32, 369–380.Google Scholar
Datta, D.D. & Du, W. (2012) Nonparametric HAC Estimation for Time Series Data With Missing Observations. Working paper.CrossRefGoogle Scholar
Dunsmuir, W. & Robinson, P. (1981) Asymptotic theory for time series containing missing and amplitude modulated observations. The Indian Journal of Statistics 43, 260–281.Google Scholar
Gonçalves, S. & Vogelsang, T.J. (2011) Block bootstrap HAC robust tests: The sophistication of the naive bootstrap. Econometric Theory 27, 745–791.CrossRefGoogle Scholar
Jansson, M. (2002) Consistent covariance matrix estimation for linear processes. Econometric Theory 18, 1449–1459.CrossRefGoogle Scholar
Kiefer, N.M. & Vogelsang, T.J. (2005) A new asymptotic theory for heteroskedasticity-autocorrelation robust tests. Econometric Theory 21, 1130–1164.CrossRefGoogle Scholar
Neave, H.R. (1970) Spectral analysis of a stationary time series using initially scarce data. Biometrika 57, 111–122.CrossRefGoogle Scholar
Newey, W.K. & West, K.D. (1987) A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55, 703–708.CrossRefGoogle Scholar
Parzen, E. (1963) On spectral analysis with missing observations and amplitude modulation. The Indian Journal of Statistics 25(4), 383–392.Google Scholar
Perron, P. (1991) A continuous time approximation to the unstable first-order autoregressive process: The case without an intercept. Econometrica 59(1), 211–236.CrossRefGoogle Scholar
Phillips, P.C. (1987) Towards a unified asymptotic theory for autoregression. Biometrika 74(3), 535–547.CrossRefGoogle Scholar
Scheinok, P.A. (1965) Spectral analysis with randomly missed observations: The binomial case. The Annals of Mathematical Statistics 36(3), 971–977.CrossRefGoogle Scholar
Sun, Y. (2014a) Fixed-smoothing asymptotics in a two-step generalized method of moments framework. Econometrica 82(6), 2327–2370.CrossRefGoogle Scholar
Sun, Y. (2014b) Lets fix it: Fixed-b asymptotics versus small-b asymptotics in heteroskedasticity and autocorrelation robust inference. Journal of Econometrics 178, 659–677.CrossRefGoogle Scholar
Sun, Y., Phillips, P.C.B., & Jin, S. (2008) Optimal bandwidth selection in heteroskedasticity-autocorrelation robust testing. Econometrica 76, 175–194.CrossRefGoogle Scholar
Vogelsang, T.J. (2012) Heteroskedasticity, autocorrelation, and spatial correlation robust inference in linear panel models with fixed-effects. Journal of Econometrics 166, 303–319.CrossRefGoogle Scholar