Time varying Shapley Decomposition

Question

I have read a lot on Shapley decompositions for relative contributions of regressors in linear regression. I was wondering if there is a way to do time-varying relative contributions. For example: If I have monthly data on stock prices and a set of regressors such as market volatility, market uncertainty index, other demand and supply variables, etc. Is there a way to find relative contributions (Shapley decompositions) for each of these regressors for each time period. For example: Hypothetically it is possible that before the 2008 recession, demand and supply variables were major contributors. After the recession, the relative contribution of market uncertainty might have increased. Therefore, is there a way to find continuous Shapley decompositions for time series data?

Answer 1

On your question "if there is a way to do time-varying relative contributions", I would surmise an answer of yes. Exhaustively, try performing the Shapley decompositions for relative contributions of regressors in the selected linear regression at each point in time, assuming that was the end of the data horizon.

As a side comment, a lot of computations for what is solely a simple regression analysis based partial R-square for a variable ${x_j}$ of interest (see, discussion here).

As I have voiced previously on this forum, regression analysis is reportedly not without its issues or necessarily, in the particular application, the most appropriate and/or advanced path forward (as in contrast, for example, the possible employment of also computationally intensive factor regression or time series analysis).