Testing Serial Correlation in Overlapping Long-Horizon Regression Models

Summary

The document asks how to compare a quarterly regression of GDP changes on business investment changes with a regression using rolling five-year percentage changes. It observes that the rolling series produces a much higher adjusted fit, while raising concern that overlapping windows induce serial dependence and make ordinary residual tests fail. The proposed alternatives are to use quarterly data, accept the rolling model despite the diagnostic, or difference its residuals before testing.

No answer or empirical analysis is provided, so the document does not establish which model is preferable or whether differencing residuals is a valid correction. It frames a useful modeling issue: smoothing and overlap can inflate apparent fit and violate regression assumptions, while changing the residual series changes the diagnostic question. Model choice would require attention to the intended forecast horizon, dependence structure, and inference method; the reported fit values are illustrative rather than documented results.

Key ideas

• Overlapping rolling percentage changes can induce serial dependence in regression errors.
• A higher adjusted fit on smoothed data does not by itself establish a better forecasting model.
• The document raises quarterly and rolling-horizon specifications as alternatives but does not resolve the choice.
• Differencing residuals changes the series being tested and is not presented as a validated correction.

Tags

# Serial Correlation in Rolling Change Linear Regression Models


# Serial Correlation in Rolling Change Linear Regression Models












1.) Lets say I have two time series GDP, BUSINV from (1948, 2019); Frequency of Data is Quarterly.

2.) Say I want to predict GDP i.e. GDP ~ BUSINV

3.) Since GDP is not stationary (i.e. level) and its not conceptually sound to forecast level of a metric like GDP, I would take the difference (i.e. returns)

4.) Say I create two models

4.a) pchGDP(QoQ) ~ pchBUSINV (QoQ)

4.b) pchGDP(5Y) ~ pchBUSINV(5Y), note this is a rolling change series, implying we are introducing serial auto-correlation. pch is percent change.

5.) the Adj RSQ for QoQ model is say 60% due to quarterly noise. While the Adj RSQ 5Y model is 95% due to smoothing effect of rolling change. The second model despite the good fit fails the serial Auto - Correlation test.

What is the best way to deal with this problem?

1.) Use the QoQ Model

2.) Use the 5Y Model ignore the serial correlation in residuals (if QoQ model doesn't also exhibit serial correlation)

3.) Should I be performing Serial Auto Correlation test on residuals after converting them to quarterly residuals for the 5Y % change Model i.e. QuarterlyResiduals = residual - lag(residual,1), and then CheckSerialCorrelation (QuarterlyResiduals ).

4.) Any other options?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.