Non-stationary regression


Fortran must die
I am trying to analyze the effect of various X on Y when both x and y are not stationary over time (our data is never stationary for very long). So far every approach to do this involves very complex models where it is difficult to interpret the slopes (VAR/VECM) or requires lengthy work to identify the series (transfer functions). I am not confident I can identify the ARIMA pattern in our data (I know the ideal models, our data likely won't match one of them requiring more judgement than I have).

Anyone know a reasonable alternative? UCM models might be one, but I am far from clear how UCM models actually run their regression. A related question is that many variables probably need to be controlled for and controlling for many variables in a time series is probably unrealistic particularly if lags of X and Y are required. The model becomes too complex to analyze very quickly and most feel only a small number of variables should be included in any case.

I have been working on this now for six years and don't feel any closer than I was six years ago.... :(