6.13 As an example of the way the state-space model handles the missing data problem, suppose the first-order autoregressive process xt = φxt−1 + wt has an observation missing at t = m, leading to the observations yt =

Atxt, where At = 1 for all t, except t = m wherein At = 0. Assume x0 = 0 with variance σ2w

/(1 − φ2), where the variance of wt is σ2w

. Show the Kalman smoother estimators in this case are

with mean square covariances determined by

Transcribed Image Text:

t = 0, 1+62 (Ym-1+Ym+1), t=m, Yt, t0,m,