Long-run covariance and its applications in cointegration regression

Long-run covariance plays a major role in much of time-series inference, such as heteroskedasticity- and autocorrelation-consistent standard errors, generalized method of moments estimation, and cointegration regression. We propose a Stata command, lrcov, to compute long-run covariance with a prewhitening strategy and various kernel functions. We illustrate how long-run covariance matrix estimation can be used to obtain heteroskedasticity- and autocorrelation-consistent standard errors via the new hacreg command; we also illustrate cointegration regression with the new cointreg command. hacreg has several improvements compared with the official newey command, such as more kernel functions, automatic determination of the lag order, and prewhitening of the data. cointreg enables the estimation of cointegration regression using fully modified ordinary least squares, dynamic ordinary least squares, and canonical cointegration regression methods. We use several classical examples to demonstrate the use of these commands.