How to make predictions from the rolling regression module in statsmodel?
Yes, it is the right package. However, the regression coefficients will vary a lot, however you can smooth them by taking moving averages (of the coefficients), and then sampling from the moving averages.
I have two sequences (x_t, y_t) in time and would like to perform a perform rolling linear regression. The problem in my mind is that:

Given a window size w, compute y the time t based on the linear combination of x within time window (t-w,...,t,...t+w). That is, y_t = sum_{i=t-w}^{t+w} b_i x_{i} + b_0,

So I would like to fit the constants b_i using my data.

Is statsmodels.regression.rolling.RollingOLS the correct package to do that?
The problem is that it only gives me the predict values and parameters along the same time axis, i.e., y_hat_i and b_i for each t. Instead, I would like to have a small set of b that I can use it for x data at other time t.