helske
commented
7 years ago Currently KFS only returns smoothed estimates (alphahat) and one-step-ahead predictions (a). Originally I left out the output of filtered estimates, as I personally didn't need those, and after that there has been surprisingly little questions about these, so I haven't bothered to add those. But now I did this, the latest version of KFAS in github now returns also filtered estimates att and Ptt for Gaussian models (for simplicity the diffuse part of P is disregarded as that is generally not that interesting).
yuanyuan2319
Hello, I have two questions about KFAS. The first one is about filtered estimator(a_t|t) versus one-step ahead predictor(a_t).
In Time Series Analysis by State Space Methods by Durbin and Koopman, a_t is the one step ahead predictor of alpha_t, a_t|t is the filtered estimator of alpha_t. In other words, a_t is E(alpha_t | y_t-1, ..., y_1), a_t|t is E(alpha_t | y_t, ..., y_1). For local level model, a_t+1 = a_t|t. But for general linear Gaussian, a_t|t != a_t+1.
My question is: which one is the a_t|t in KFS results? I only find two state estimations, a and alphahat. And a is a_t, alphahat is smoothed one. It seems you take a also as filtered estimation. But I think they are different?
Secondly, I want to confirm the definition of univariate approach. I am using Kalman filter to perform Fama/French factor analysis on stock returns, so the model would be y_t = alpha + beta1_tfactor1_t + beta2_tfactor2_t + beta3_tfactor3_t + error_t (betas are state variables, y_t is a 11 vector at time t). This is a univariate model, right?
Thank you very much for your time! Look forward to your reply.