On Robust Inference in Time Series Regression
arxiv(2022)
摘要
Least squares regression with heteroskedasticity consistent standard errors
("OLS-HC regression") has proved very useful in cross section environments.
However, several major difficulties, which are generally overlooked, must be
confronted when transferring the HC technology to time series environments via
heteroskedasticity and autocorrelation consistent standard errors ("OLS-HAC
regression"). First, in plausible time-series environments, OLS parameter
estimates can be inconsistent, so that OLS-HAC inference fails even
asymptotically. Second, most economic time series have autocorrelation, which
renders OLS parameter estimates inefficient. Third, autocorrelation similarly
renders conditional predictions based on OLS parameter estimates inefficient.
Finally, the structure of popular HAC covariance matrix estimators is
ill-suited for capturing the autoregressive autocorrelation typically present
in economic time series, which produces large size distortions and reduced
power in HAC-based hypothesis testing, in all but the largest samples. We show
that all four problems are largely avoided by the use of a simple and
easily-implemented dynamic regression procedure, which we call DURBIN. We
demonstrate the advantages of DURBIN with detailed simulations covering a range
of practical issues.
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