Visualizing time series regression results in a causal framework

Question

Suppose I have a set of independent variables that I believe to, collectively, cause the observed level and changes in the value of the dependent variable, and I have the results of a regression of the latter on the former. Is there a good way of visualizing these time series multivariate regression results?

Specifically, I am looking for some form of visualization that can show how the independent variables differentially affect the dependent variable over the period of my sample, i.e. something showing changes in the relative importance of the various independent variables with the passage of time.

Answer 1

You can plot the time series of the point estimates of the time-varying regression coefficients (or perhaps standardized coefficients) just as you would plot the time series themselves.
You can add the corresponding time series of confidence intervals (at a desired level of confidence) as dashed lines in the same plot.
You would then have as many plots as there are independent variables.
Consider making the axis ranges equal across the plots for easier comparability.

If you skip the confidence intervals and only have a few independent variables, the time series of their coefficients could be fit into a single plot.