Why Cointegration Results Can Differ Between Daily and Intraday Data

Summary

The document asks whether two price series that appear cointegrated at a daily frequency should also be expected to show cointegration or mean reversion intraday. The questioner reports finding cointegration in daily prices but not in intraday price levels, while transformed intraday series produce different results. They ask whether these findings imply distinct relationships across time horizons or whether daily results can inform intraday expectations.

No analysis or resolution is provided, so the document offers no evidence that daily cointegration predicts intraday mean reversion. Its useful point is the distinction between observing a relationship at one sampling frequency and establishing it at another. Frequency, sampling choices, and transformations can affect statistical tests; the reported outcomes alone do not settle the relationship or justify an intraday trading strategy. Further analysis would need to define the series and test the relevant relationship at the intended trading horizon.

Key ideas

• Cointegration observed in daily price levels does not by itself establish cointegration intraday.
• The question reports different test outcomes across frequencies and after transforming intraday prices.
• Daily cointegration alone does not demonstrate that intraday prices will mean revert.
• The document poses the frequency comparison but supplies no answer or empirical evidence.

Tags

# Cointegration between daily time series and intraday time series


# Cointegration between daily time series and intraday time series












I am working with time series data of daily prices, and intraday prices. For simplicity sake I will refer to the daily time series as 'A' and 'B', and the intraday time series of the same instruments as 'a' and 'b'. When I check for cointegration between A and B my results tell me that the series are indeed cointegrated, but when checking their intraday series, a and b, my analysis shows no cointegration unless I apply some form of differencing to the series ( ie. taking returns of a and b , or log(a) and log(b) ).

Is the conclusion here as simple as declaring that intraday the series are not cointegrated, but over longer time frames they are? Or can I reach some generalized conclusion that I should be able to expect some degree of mean reversion intraday of a and b due to the daily cointegration between A and B.

I am mainly having a hard time connecting whether or not there are implications to be drawn from daily results -> intraday data, or vice versa in general.

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