Setting Thresholds for Short Mean-Reverting Time Series
Summary
The document considers how to choose entry and exit thresholds for a cointegration-based mean-reversion strategy on transaction-level series that may contain only about 1,600 observations, or seconds. It explains why thresholds based on a rolling standard deviation can be unreliable early in a short sample, while fixed thresholds may not adapt to series with different scales. High-watermark rules are also raised as a possible approach, but not developed.
The responses suggest estimating a plausible scale or quantiles from prior knowledge of recurring series, rather than waiting for the current sample to become long enough. Another proposal is to use a Tukey chart and its upper and lower control limits as an alternative to standard-deviation bands. These are suggestions rather than tested results: the document supplies no performance comparison, threshold calibration procedure, or treatment of the initial trend-removal distortions. Any method would need validation on the intended data and trading horizon.
Key ideas
- Short samples can make rolling standard-deviation thresholds unreliable before a trading opportunity passes.
- Fixed thresholds may not transfer well across series with different magnitudes.
- Prior knowledge about recurring series can inform initial estimates of scale or quantiles.
- Tukey charts and their control limits are suggested as an alternative threshold framework.
- The suggestions are not backed by comparative tests in the document.
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# Entry and exit points for very short mean-reverting timeseries # Entry and exit points for very short mean-reverting timeseries I have a model specifying a cointegration relationship on a number of transaction-level timeseries. I would like to specify entry and exit points for trades where these points ideally would be just before the turning points of the time series (bottoms for exit and tops for entry). The issue I am having is that the timeseries itself are very short -- usually around 1600 observations/seconds. Thus the usual +- 1/2 standard deviation entry points do not work because I do not know the standard deviation reliably before the window of opportunity is over. I see a number of solutions but perhaps there's better ones in the literature? - Rolling standard deviation: very unreliable at the beginning, and losing out on trading opportunities before having reliable results - Fixed level entry/exit points: could be very wrong since the series vary in magnitude - High watermark entry/exit points Here are some example series. You might notice the distortions at the beginning of the series, this is because I'm removing a quadratic trend. ## Answer by Tal Fishman (score 2) https://quant.stackexchange.com/a/3353 This sounds like a case where you will need to apply some good old-fashioned judgment to determine what the standard deviation "should be" before you have enough data to measure it. Surely this process repeats with some frequency, and perhaps given some attributes and more details you could make an educated guess as to the standard deviation (or quantiles, or whatever you want to use for your entry/exit points) before you have enough data for the specific series at hand. ## Answer by babelproofreader (score 2) https://quant.stackexchange.com/a/3354 Following on from Tal Fishman's idea of using "some good old-fashioned judgment," you might find the idea of applying a Tukey chart and its related upper and lower control limits more useful than standard deviation.
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