smoother: Kalman smoother for Gaussian state space model
In ClausDethlefsen/sspir: State Space Models in R

Description Usage Arguments Details Value Author(s) See Also Examples

Based on the output from kfilter, this function runs the Kalman smoother to produce the conditional means and variances of the state vectors given all observations.

1	smoother(ss)

`ss`	object of class `SS`, where the components `m` and `C` have been set by the `kfilter`.

The Kalman smoother yields the distribution

(θ_t|y[,1:n]) ~ N(m*_t, C*_t)

through the backward recursion for t=n..1,

R_{t+1}= G_{t+1} C_t G_{t+1}^T + W_{t+1}

B_t = C_t G_{t+1}^T R_{t+1}^{-1}

m*_t = m_t + B_t ( m*_{t+1} - G_{t+1} m_t)

C*_t = C_t + B_t ( C*_{t+1} - R_{t+1} ) B_t^T

where the matrices F, G, V, W are stored in the SS object as functions, eg. Fmat(tt,x,phi), see SS. The vectors m and matrices C are set by the kfilter and are overwritten by the Kalman smoother.

The smoother also calculates the signal, μ_t = F^T_t m*_t.

An object of class SS with the components m, C, and mu updated.

Claus Dethlefsen and Søren Lundbye-Christensen.

SS, kfilter

data(kurit)
m1 <- SS(kurit)
phi(m1) <- c(100,5)
m0(m1) <- matrix(130)
C0(m1) <- matrix(400)

m1.s <- smoother(kfilter(m1))
plot(m1$y)
lines(m1.s$m,lty=2)