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?