Improved Inference in Regression with Overlapping Observations

Abstract

We present an improved method for inference in linear regressions with overlapping observations. By aggregating the matrix of explanatory variables in a simple way, our method transforms the original regression into an equivalent representation in which the dependent variables are non-overlapping. This transformation removes that part of the autocorrelation in the error terms which is induced by the overlapping scheme.Our method can easily be applied within standard software packages since conventional inference procedures (OLS-, White-, Newey-West-standard errors) are asymptotically valid when applied to the transformed regression. Through Monte Carlo analysis we show that they perform better in finite samples than the methods applied to the original regression that are in common usage. We illustrate the significance of our method with two empirical applications.JEL classification: C20, G12

Business cycle, storage, and energy prices

“…It is well known that the standard errors are biased downward in finite samples when overlapping observations are used (e.g., Nelson & Kim, 1993). Britten‐Jones, Neuberger, and Nolte (2011) show in Monte‐Carlo simulations that when the overlapping horizon is short in comparison to the length of the sample, the downward bias in the Newey–West standard errors is fairly modest. For example, when the sample length is 250 and the overlapping horizon is 3, the 95% confidence interval contains the true value of the coefficient about 90% of the time when the Newey–West HAC is used.…”

How news and its context drive risk and returns around the world

“…For example,Cochrane and Piazzesi (2005) claim on p. 139 that to see the underlying economic structure in their model for bond returns they can't use monthly observations, and must use overlapping annual ones. Also seeBritten-Jones, Neuberger, and Nolte (2011).26 SeeBarberis (2000) for a comparison of myopic versus dynamic portfolio rules in the presence of return predictability.…”

Improving portfolio diversification: Identifying the right baskets for putting your eggs

“…Note that the presence of overlapping observations in the dependent variable (portfolio performance) can induce considerable positive autocorrelation in the slopes, particularly when the predictor variable (portfolio diversification) is persistent. Because the FM standard error does not adjust for possible autocorrelation in the slopes, it tends to overstate the significance of the average slope (Britten‐Jones, Neuberger, & Nolte, ; Petersen, ). The heteroscedasticity and autocorrelation consistent Newey–West (NW) standard errors (Newey & West, ) are used to draw the inferences for this analysis.…”