The applications of regressions and estimations on rolling windows such rolling causality and rolling VECM are very popular in the literature of economics and finance, especially in income-money relationship. Although some of its applications are straightforward, it has some drawbacks which seem to be overlooked in literature, using rolling windows to estimate the time varying relationship between variables has some serious implications. Since a rolling window is used, it is a given that the statistical characteristics will change throughout the windows and the sub-samples, the high values would be more common in one window than other windows, therefore the windows would probably move from stationary to non-stationary state, in addition the sub-samples especially if they are small will not be a good representatives for the population, which leads to sampling errors, even worse some of windows may have standard asymptotics, normal distributions, unbiased estimator...etc, but other windows may not. Therefore using an approach that treat all the windows and sub-samples as they are the same would be really a bad idea.

I've been trying to estimate rolling Granger causality, but I changed my mind after reading this thread on Estima forum

https://estima.com/forum/viewtopic.php?f=8&t=2914

RATS application of rolling causality seems to offer some good solutions to problem of instability and sampling errors, see the link below

https://estima.com/ratshelp/index.html?rollingcausalityrpf.html

But from their perspective, it still not advisable to implement a rolling window regression.

Except this thread, I haven't found any other paper that addresses the problem of rolling causality.

Please, share your thoughts about the usefulness of the rolling window regression. Despite its drawbacks, do you still think it's good approach to estimate the time varying relationship? If you recommend using it, would you suggest in which case it could be useful? Do you have ideas on how to fix its problems and apply it flawlessly?