Bayesian Time varying coefficient model

(This is more general econometric question) While I am writing a thesis on how the cyclicality of fiscal policy evolve over time in certain countries using Bayesian time varying regression. There are some questions that I would like to ask.

1. I know that Bayesian regression requires prior distribution (which is chosen by the model maker) and I have no idea what the prior distribution should be. Should I use non-informative prior?
2. How does Bayesian time varying regression really works? Is it similar to rolling window method in normal regression or is there a method where I can do time varying coefficient model in Bayesian regression?

Answer 1

[Rishi]

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:

https://stats.stackexchange.com/questions/20520/what-is-an-uninformative-prior-can-we-ever-have-one-with-truly-no-information

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!

[Yohan]

Hi Rishi,

Thank you for the answer! Does that mean that Bayesian linear regression itself is time varying already? For example, if we have data that start from year 2000 and ends with 2024. In year 2000, we have a coefficient that is assumed random walk, but more we add new data, the coefficient of 2001, 2002 is shown a posterior distribution with varying coefficient?

[Yohan]

I am very new to this topic so this confused me a lot :(

[Torsten]

@Yohan

You still seem to seek the answers to your question in MATLAB. You won't find them here - MATLAB is the second step after reading a book on Bayesian Statistics and having developped the idea on how to explore your data.

And if you have questions concerning this data analysis, you should address your professor or - if he/she also is not qualified to help in this difficult field - a statistics forum (e.g. Stackexchange Statistics:

https://math.stackexchange.com/questions/tagged/statistics