Nonparametric HAC Estimation for Time Series Data with Missing Observations

55 Pages Posted: 5 Dec 2012

See all articles by Deepa Datta

Deepa Datta

Board of Governors of the Federal Reserve System

Wenxin Du

University of Chicago Booth School of Business

Date Written: November 9, 2012

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.

Keywords: Heteroskedasticity, serial correlation, robust inference, missing data

JEL Classification: C22, C12, C14

Suggested Citation

Datta, Deepa and Du, Wenxin, Nonparametric HAC Estimation for Time Series Data with Missing Observations (November 9, 2012). FRB International Finance Discussion Paper No. 1060, Available at SSRN: https://ssrn.com/abstract=2180964 or http://dx.doi.org/10.2139/ssrn.2180964

Deepa Datta (Contact Author)

Board of Governors of the Federal Reserve System ( email )

20th Street and Constitution Avenue NW
Washington, DC 20551
United States

Wenxin Du

University of Chicago Booth School of Business ( email )

5807 South Woodlawn Avenue
Chicago, IL 60637
United States

HOME PAGE: http://https://sites.google.com/site/wenxindu/

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