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Abstract:
The Newey and West (1987) estimator has become the standard way to estimate a heteroskedasticity and autocorrelation consistent (HAC) covariance matrix, but it does not immediately apply to time series with missing observations. We demonstrate that the intuitive approach to estimate the true spectrum of the underlying process using only the observed data leads to incorrect inference. Instead, we propose two simple consistent HAC estimators for time series with missing data. First, we develop the Amplitude Modulated estimator by applying the Newey-West estimator and treating the missing observations as non-serially correlated. Secondly, we develop the Equal Spacing estimator by applying the Newey-West estimator to the series formed by treating the data as equally spaced. We show asymptotic consistency of both estimators for inference purposes and discuss finite sample variance and bias tradeoff. In Monte Carlo simulations, we demonstrate that the Equal Spacing estimator is preferred in most cases due to its lower bias, while the Amplitude Modulated estimator is preferred for small sample size and low autocorrelation due to its lower variance.
Full paper (660 KB PDF)
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Keywords
Heteroskedasticity, serial correlation, robust inference, missing data
Related Material
Programs (79 KB ZIP)
Matlab code and Stata instructions to make it easier for researchers to apply the estimators discussed in the paper.
PDF files: Adobe Acrobat Reader ZIP files: PKWARE
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