KFAS (version 0.6.1)

efsmoother: Kalman Smoother for exponential family models

Description

Performs Kalman smoothing for exponential family models via simulation.

Usage

efsmoother(out,nsim)

Arguments

out

Output from function 'expflik'.

nsim

Number of simulations used for smoothing.

Value

• A list with the output elements from expflik and following new elements:
• nsim
  Number of simulations used for smoothing.
• ahat
  m*n array of E(alphat | y_1, y_2, ... , y_n).
• that
  m*n array of Zt*ahat.
• ahatvar
  m*m*n array of Var(ahat|y_1, y_2, ... , y_n).
• thatvar
  1*1*n array of Zt*Var(ahat|y_1, y_2, ... , y_n)*Zt'.

Details

Function efsmoother performs Kalman smoothing of univariate exponential family state space model using the simulation algorithms by Koopman and Durbin (2001, 2002).

References

Koopman, S.J. and Durbin J. (2001). Time Series Analysis by State Space Methods. Oxford: Oxford University Press. Durbin J. and Koopman, S.J. (2002). A simple and efficient simulation smoother for state space time series analysis, Biometrika, Volume 89, Issue 3.

Examples

library(KFAS)


kk <- c(396, 399, 403, 434, 340, 519, 558, 566, 591, 566, 574, 646, 644,
646, 665, 693, 773, 834, 910,1035, 1002, 1161, 1056, 1097, 1094, 1042,
1194, 1316, 1246, 1503, 1428, 1477, 1490, 1465, 1560, 1860, 2008, 2020,
2167) 

vlk <- c(4623785, 4606307, 4612124, 4639657, 4666081, 4690574, 4711440,
4725664, 4738902, 4752528, 4764690, 4779535, 4799964, 4826933, 4855787,
4881803, 4902206, 4918154, 4932123, 4946481, 4964371, 4986431, 5013740,
5041992, 5066447, 5088333, 5107790, 5124573, 5139835, 5153498, 5165474,
5176209, 5188008, 5200598, 5213014, 5228172, 5246096, 5266268, 5288720)

#Model

n <- 39
m <- 2
r <- 2

yt <- array(kk,dim=c(1,n))

offset <- array(vlk,dim=c(1,n))

Zt <- array(c(1,0),dim=c(1,m))

Tt <- array(c(1,0,1,1),dim=c(m,m))

Rt <- array(c(1,0,0,1),dim=c(m,r))

psi_hat <- c(-5.356458, -16.348376)

Qt <- array(c(exp(psi_hat[1]), 0, 0, exp(psi_hat[2])), dim=c(r, r))

a1 <- matrix(0,nrow=m,ncol=1)

P1 <- matrix(0,nrow=m,ncol=m)

P1inf<-diag(1,2)

dist <- "Poisson"

eflikout <- eflik0(yt, Zt, Tt, Rt, Qt, a1, P1, P1inf, dist, offset)

nsim <- 1000

smef <- efsmoother(eflikout, nsim)