Handling Overnight Gaps and Jumps in Intraday Beta Estimation

Summary

The document discusses estimating beta from 15-minute returns of XLF against SPY over several days, with a focus on apparent jumps at the next day's opening. The response assumes beta is calculated from returns rather than price levels and notes that overnight gaps should not enter a regression intended to use only intraday returns. A moving average of returns is offered as one way to smooth the observations.

Other suggestions include excluding observations whose returns exceed a chosen threshold, such as two standard deviations, and comparing beta estimates across sampling intervals. Longer intervals may smooth smaller jumps, so the interval with the most stable and statistically significant estimate can be selected. Another approach is to estimate a separate beta for each day and average those estimates. These are practical suggestions rather than a tested universal rule; the document does not specify a formal jump-detection method or compare the methods on empirical results.

Key ideas

• For a beta estimated from intraday returns, overnight opening gaps fall outside the intraday return series.
• Smoothing returns with a moving average is suggested as one way to reduce noise.
• Large return observations can be excluded using a threshold such as two standard deviations.
• Comparing sampling intervals can show which produces a more stable and significant beta.
• Daily beta estimates can be computed separately and then averaged.

Tags

# How to account for jumps in intraday data when calculating beta?


# How to account for jumps in intraday data when calculating beta?












I am calculating betas on intraday trade data at 15-minute intervals. For simplicity sake, let's assume I am modeling

\begin{equation} Y = \beta * X + c \end{equation}

where $Y$ is the return of XLF and $X$ is the return of SPY.

If I want to run this on five days of intraday data, should I remove the jump that happens due to opening gaps on the next day?

How do you guys usually handle this jump in returns ?

## Answer by chrisaycock (score 6, accepted)

https://quant.stackexchange.com/a/2714

I assume you're using returns to compute beta, not the prices. And yes, remove the "jumps", though this should happen automatically since you're looking only at intraday returns. One final piece of advice: you'll get more meaningful results if you smooth the returns via a moving average.

## Answer by Suminda Sirinath S. Dharmasena (score 3)

https://quant.stackexchange.com/a/2715

In addition to the above I can suggest:

- ignore data point if returns are more than a certain threshold (2 s.d.)

- calculate at different sampling intervals and choose most stable beta with the best significance (certain longer intervals "smooth out" small to mid size jumps)

## Answer by LazyCat (score 1)

https://quant.stackexchange.com/a/2718

You can run the regression separately for 5 days, and average the betas you get for different days.

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