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I've been fiddling around with different time frames when doing tests for cointegration between two timeseries, and I've realized that the dates that you use for your start/stop of the test will dramatically change the resulting p-value.

My question is from which time frame should I trust the results of my cointegration test? Do I want to look at the past year to determine coint? Do I want to look back as far as possible? Is there some magic number?

Given the wildly different results my cointegration tests are giving, I would assume that some of these p-values are more "right" than others. Any thoughts?

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If the data generating process was fixed over time, you would choose the longest available data sample for cointegration testing -- because a larger sample yields higher power for the test.

If the data generating process is changing over time, then you would identify the time period of interest and use only the corresponding subsample to test for cointegration -- because the test results would differ across periods/subsamples.

If the test results change depending on the period/subsample (your case), it is likely that the data generating process is changing over time (across subsamples). Then you have to choose the subsample of interest and test and make inference for that particular subsample, being aware that inference might not hold for other periods/subsamples.

Edit addressing the comment

I'm looking for cointegration because I want to be able to trade a pair of stocks that is both (1) cointegrated in my backtest and (2) will likely be cointegrated in the coming months.

This is a very challenging task, and you can never be guaranteed that the data generating process will remain the same over time, especially when it comes to financial time series. There is essentially no way to tell whether cointegration will or will not be present in the future. But you can try theoretical argumentation such as if shares of a company are traded on two exchanges, the prices in the two exchanges should not deviate far away from each other.

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  • $\begingroup$ Let me add a minor anecdote. A friend of mine discovered a profitable trading strategy for ETFs in different countries based on co-integration that would have made great profits in 2008-2009-2010. In 2011 he began trading it and did not make a penny. The big disruptions of the Finl Crisis were over, and his ETFs were no longer diverging and converging in price across time zones as before. As Richard would say it is likely that the data generating process had changed over time. $\endgroup$ – Alex C Oct 16 '16 at 13:14
  • $\begingroup$ thank you both! this is great information. Just to clarify, data generating process fixed over time = market conditions fixed? $\endgroup$ – Spencer Smolen Oct 16 '16 at 18:02
  • $\begingroup$ @SpencerSmolen, I am not sure about the equality there, but if the market conditions change, then you could expect cointegration to appear where it was absent or vanish where it was present. $\endgroup$ – Richard Hardy Oct 16 '16 at 18:11
  • $\begingroup$ oh i see, when you say data generating process do you mean stochastic process? does this mean that you create a model of the price history and run a test for cointegration on the data that fits the model? $\endgroup$ – Spencer Smolen Oct 16 '16 at 19:52
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    $\begingroup$ @SpencerSmolen, what happened? I see you un-accepted the answer. $\endgroup$ – Richard Hardy Nov 13 '16 at 16:47

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