Hello Yohan,
I understand from your question that you would like some general information regarding Bayesian time-varying coefficient. I have answered both your questions to the best of my understanding below:
1. Non-informative priors are generally chosen when you have little to no prior information about the parameters. They are designed to have minimal impact on the posterior estimates. Since you have mentioned that you do not have an idea about what the prior distribution should be, it is better to use a non-informative prior. You can also go through the following discussion on stackexchange about what a non-informative prior is and its importance:
2. Bayesian time-varying regression is different than a rolling window method in normal regression. It allows the coefficients in the model to change over tie. The coefficients theselves are stochastic processes. Think that the coefficients follow a random walk, where the current value of the coefficient is a function of its past value and some error term. This allows the coefficient to evolve over time in a potentially smooth manner, depending on the specification of the process.
Hope this helps!
