I want to perform hypothesis testing on two "target" time series, a treatment and a control. I want to fit a GAM (Facebook's Prophet) and make a lower-variance estimate ("now-cast") of the time series (i.e. only trend + seasonality + regressors, no stochastic error term). Then using these lower-variance time series I want to do hypothesis testing.

I also have access to related metrics, which are lower variance than the targets.

My current method is to train Prophet on historical data and make a now-cast of the data I want to test on, using the related metrics as regressors. However, I am not using the useful information contained in the targets to make these now-casts.

My questions are:

- Can I add the target to Prophet as a regressor and use this to make the now-cast? Can I prevent it from assigning too much weight to it using priors?

- What other methods exist to reduce the variance in a given time series?

The motivations for this is to:

• reduce the sample size required for hypothesis testing

and when using related metrics as regressors:

• reduce the negative effect of a relationship change between related metric and target due to the intervention

For reference, the time series are nonstationary and have weak autocorrelation of 1-2 lags.