# Parameters estimation using Kalman filter

I have a model like this: $$P_t=\alpha_t+gP_{t-1}+u_t$$

$$\alpha_t=\alpha_{t-1}+d+n_t$$ Where {$$u_t$$} and {$$n_t$$} are normal, iid with 0 mean but unknown variance.

I want to estimate the parameters $$g$$ and $$d$$, and all I have is a series of $$P_t$$. Can I solve this problem by using Kalman Filter? If yes, how to do this with pykalman (or some other python packages); if no, what else can I use?

This problem origins from an empirical study about market quality, you can find the paper here: https://www.sciencedirect.com/science/article/pii/S0378426608000393

• "Can I solve this problem by using Kalman Filter?" <- yes! (depending on what you mean by solve) – Taylor Mar 14 '19 at 3:40
• By saying "solve" I mean "get reliable estimations of the parameters" :) – jqf Mar 14 '19 at 3:49