# What is Kalman filter?

I am not an economics grad. I am an engineer. I was working on beta value in market model regression.This is how I proceed.

Firstly, I calculated daily returns from adjusted closing price of all stock. Then, I calculated daily market returns. This calculation was from period 2000 to 2018.

Based on this calculation, I computed beta value by performing regression analysis for two variables. Simple OLS method.

It is well known fact that beta is not constant. Thus I performed rolling regression for estimating beta. So, I did regression analysis for one year. I got beta value for each company for year 2000,2001,2002,2003.

This exercise proved well known fact that beta is not constant. Beta is time-varying. Thus, I researched and came to know about time varying parameter model.

$$y_t = \alpha_t + \beta_t X_t + \epsilon_t$$

And there are three different equation for beta

$$\beta_t=\beta_t-1 + \epsilon_t$$ <- Random walk model

$$\beta_t=β̄ + ξt$$ <- Mean reverting model

I thought this are part of Kalman filter. I read about Kalman filter. There are those matrices and all. How does Kalman filter help in beta value? Please explain me what Kalman filter does in estimating beta ?

• You might also ask this on the CrossValidated statistics stack exchange. – Trurl May 9 at 17:22