# Linear regression with overlapping observations

Suppose we’re doing univariate linear regression between X and Y. Let’s say X are daily observations, and Y reflects how some variable changes 1 year into the future. So Y observations will be overlapping and autocorrelated. The daily observations in X could be autocorrelated as well.

How do we measure $R^2$ and variance of $\beta$ in this situation? How do we know if the relationship between X and Y is statistically significant?

I have looked at a number of papers on this:

• “Dividend Yields and Expected Stock Returns: Alternative Procedures for Inference and Measurement”, Hodrick R., 1992
• “Tests of Financial Models in the Presence of Overlapping Observations”, Richardson M. and Smith T., 1991
• “Improved Inference and Estimation in Regression with Overlapping Observations”, Britten-Jones M. and Neuberger A., 2011

But it is still not clear to me what I should be doing in practice in these situations. Is there any tutorial that clearly summarizes how estimates should be corrected in the presence of overlapping observations, and what the assumptions behind each procedure are, stating which procedure tends to be the most conservative?