Table 1. Notations for State-Space Model

Definition Explanation
Ψ the information set
βt|t−1 = E[(βtt−1] expectation (estimate) of βt, conditional on information up to t−1
Pt|t−1 = E[(βt − βt|t−1)(βt − βt|t−1)′] covariance matrix of βt, conditional on information up to t−1
βt|t = E[(βtt] expectation (estimate) of βt, conditional on information up to t
Pt|t = E[(βt − βt|t)(βt − βt|t)′] covariance matrix of βt, conditional on information up to t
yt|t−1 = E[(ytt−1] forecast of yt, given information up to time t−1
ηt|t−1 = yt − yt|t−1 prediction error
ft|t-1=E[ ηt|t-12 ] conditional variance of the prediction error
Source: Kim and Nelson (1999, p.22)