Handling Autocorrelation in Regressions on Rolling Returns
Summary
The discussion considers why a multivariate regression of monthly returns on fundamental factors such as valuation, book value, and cash flow may have strongly autocorrelated residuals. Suggested responses include fitting an ARMA model to the returns first and then regressing on the resulting residuals, or specifying ARMA errors in the regression. These approaches aim to account for serial dependence, but the thread does not compare them empirically or establish which is best.
A separate explanation is that monthly returns may not align with fundamentals reported quarterly or less often. Matching the return horizon to the frequency of the predictor data may make the analysis more coherent. The answers also caution that overlapping rolling returns can be persistent, and that standard remedies may not settle the modeling question. The evidence is diagnostic guidance based on the reported Durbin–Watson result and commenters’ reasoning; no dataset, performance results, or definitive econometric recommendation is provided.
Key ideas
- Autocorrelated residuals may indicate that the regression needs an explicit time-series error model.
- One proposal is to model returns with ARMA and use the resulting residuals in a factor regression.
- Another proposal is to use ARMA errors directly in the regression.
- Return horizons should be considered in relation to how often fundamental predictors are updated.
- Overlapping rolling returns can be persistent, and the discussion offers no conclusive remedy.
Tags
Full text
# Using rolling returns in a multivariate linear regression? # Using rolling returns in a multivariate linear regression? I am trying to use fundamental factors such as PE, BV, & CFO in a multivariate linear regression with the response variable being the rolling 1 month returns. But this approach seems flawed as the autocorrelation of the residuals is to high and the Durbin Watson test points also to such flaws. What is the best what to use long time horizon rolling returns in a linear regression? ## Answer by psandersen (score 2) https://quant.stackexchange.com/a/3781 Why not fit an ARMA model to the rolling returns first, and then model the residuals in your regression equation? That way you should be removing most of the effects of auto-correlation. ## Answer by Matt Wolf (score 1) https://quant.stackexchange.com/a/3762 It simply points to the fact that your model as stands does not have much explanatory power of monthly returns. One reason could be of a observation period mismatch. I am not a fundamental type of guy, but I imagine that the monthly returns are measured over too short a period (1 month) while most fundamental factors are updated on a quarterly basis (sometimes semi-annually or annually depending on local market regulations). Thus, changes or absolute levels in cash flows on a quarterly basis may not be able to explain changes in monthly returns. Can you run the same model again but use quarterly returns (or match the periodicity of the independent variables periodicity) and report back? ## Answer by Vishal Belsare (score 1) https://quant.stackexchange.com/a/3958 Try fitting a model with ARMA errors? However, if by "rolling returns" you imply a moving average of returns or some QoQ or YoY return series, which has much persistence, I am not so sure what the right way to proceed really is (with the exception that you can apply some corrections suggested in econometrics literature).
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