I am currently working on a research project about stock returns, but I really dont know how to proceed. I have generated a correlogram of the residuals on STATA to get an idea of the autocorrelation structure, which is shown in the image. But I really do not know how to apply newey-west errors in this context since it requires that I specify a specific truncation lag for the regression, and the autocorrelation structure is all over the place. I am really uncertain if the newey-west rule of thumb $q=4(T/100)^{2/9}$ is appropriate or should be used here, or if another lag lengths should be specified. If someone could help me with this, it would be highly appreciated.
1 Answer
Using the rule of thumb will probably result in the least amount of questions by coauthors, reviewers and such. But if you care more about squeezing the most out of your data than getting an easy and "uncontroversial" answer, there may be more efficient ways of handling autocorrelated errors; see Bailie et al. "On Robust Inference in Time Series Regression" (2024); I have also pasted their abstract below. But then again, stock returns are not likely to be autocorrelated, so perhaps an adjustment for heteroskedasticity alone would be enough.
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.
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$\begingroup$ Thank you for the response. Since there is some subjectivity in evaluating the optimal lag length here, I think it might make more sense to rely on the rule of thumb instead. Previous research within this topic that I am investigating used a lag length of 2, while the rule of thumb here would suggest a lag of 4, which is somewhat consistent. While a lag length of 4 leads to results that are mostly insignificant at a p-value of 0.05, using a truncation lag of say 40 (the lag in the which the coefficients become significant in my regression) could yield imprecise estimates. $\endgroup$ Commented Oct 9 at 10:36
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$\begingroup$ @Vanlorden, I would avoid choosing the lag length based on what results it gives (significant vs. nonsignificant). And 40 seems like a really looong lag... $\endgroup$ Commented Oct 9 at 13:19