Return Heteroskedasticity Across Sampling Time Frames

Summary

The document asks whether the variance behavior of asset returns changes with the sampling interval, using five-minute returns as an example. It reports that returns for heavily traded individual assets are often approximately scalable across time frames by the square root of elapsed time. This suggests that shorter intervals do not necessarily remove heteroskedasticity, though the cited response does not quantify how the variance behavior itself changes.

For cross-asset covariance, the same simple scaling does not hold in practice. The response identifies this departure from theoretical linear scaling as the Epps Effect. A separate answer points to research describing heteroskedasticity in both daily and intraday returns. These are brief claims relayed through a question-and-answer discussion rather than a detailed empirical analysis; the document provides no dataset, estimation procedure, or conditions beyond the liquidity distinction for individual assets.

Key ideas

• Returns of heavily traded individual assets may scale approximately with the square root of the time interval.
• Cross-asset covariance may not scale linearly across sampling intervals in observed data.
• The time-dependent scaling behavior of cross-asset covariance is associated with the Epps Effect.
• Heteroskedasticity is reported in both daily and intraday returns.

Tags

# Does heteroskedasticity of returns depend on the time frame?


# Does heteroskedasticity of returns depend on the time frame?












Similarly to my last question, for which I obtained very interesting and useful answers, I would like to know if there has been any study regarding heteroskedasticity and time-frames of the returns.

As an example could it be that the lower the time frame (take the 5 minute returns) the less heteroskedastic are returns?

## Answer by Jianxun Li (score 2)

https://quant.stackexchange.com/a/18432

In practice, for heavily traded assets (above 60% quantile of average daily dollar volume), individual asset return is pretty scalable across different time frame by a factor of $\sqrt{T}$.

However, for covariance among different assets, moving between different time frame is not linearly scalable (although it should be in math). This is known as "Epps Effect".

## Answer by emcor (score 1)

https://quant.stackexchange.com/a/18416

This paper states that heteroskedasticity is a stylized fact in daily as well as intra-day returns: https://statistik.econ.kit.edu/download/doc_secure1/HandbookITandFinan.pdf

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