This won't make your life any easier, but the problem with regression or Manova is that they are essentionally cross sectional. They don't assume change over time. And they assume that data points are independent, which won't be true normally in time series data.
I have been looking for a year for the question you ask. If I find one I will let you know. Some form of ARIMA combined with covariates might apply, but I am not sure.