One of the hottest topics in today econometrics is financial networks models where researches use vector autoregressive (VAR) models applied to time series of daily volatility measurements of different firms to represent their connectedness as a graph. Different measures of connectedness were used, e.g. forecast error variance decomposition as in Diebold and Yilmaz (2015) or Granger causality and partial correlation in Barigozzi and Brownless (2016).
I wonder whether it is meaningful to use feature importance from e.g. Random Forest model to build a network. That is, suppose we have $n$ series in the panel. Then, we run the model for each series and obtain feature importance measures. And finally use them as inputs to construct a graph. What are possible pitfalls of this approach? From my perspective it might be appealing since VAR model sticks to a linear case, while Random Forest regression allows for non-linear relation. However, I am worrying that feature importance might be meaningless compared to traditional measures.