Inclusion probability

[Claire Austin]

We have a set of 60 multivariate time series and wish to investigate the impact of an intervention at one point in time on one of the variables (A). Considering only the covariates that are associated with A but that would be expected to have been not affected by the intervention, none of those covariates having an inclusion probability greater than 0.2, when used as the control variable, yield good results (i.e. the confidence intervals are extremely wide). However, one of the covariates (C), also associated with A but expected to have been not affected by the intervention, when used as the control variable, does yield a very nice causal impact analysis and the result is what we would expect in terms of impact and it results in very narrow confidence intervals. We have checked this with approximately 20 different such datasets and the causal impact results on variable A are similar for all datasets when covariate C is used as the control variable. Why might this be, given that the inclusion probability of C is always less than 0.05 for all 20 datasets? 

[Claire Austin]

I should have mentioned, also, that the time series are non-stationary with respect to mean and variance.