I have a time series that I've built a regression on, say Y = X + Y. For a data set of size 300, the coefficients of X and Y are statistically significant. But, the coefficients are not statistically significant for a (sequential) subset of the dataset of, say, 150 points. Now, since the computation for this second significance does not include the first, is there some way to adjust the second significance computation to account for the first? That is, I want to compute the statistical significance of the second computation conditioned on the fact that the first computation shows significance.