US_LM Model

# Cut-and-paste code below into window above and Run

#

# United States (US) Model (1950-2000)

#

# Measurement Matrix  (Growth), (X+XREAL-N-L), (L+XREAL-X-N)

#

#           Q      N  HOURS XREAL      X      L

#[1,]  0.4124  0.403  0.413 0.410  0.399  0.412

#[2,] -0.1464 -0.580 -0.122 0.310  0.711 -0.160

#[3,] -0.0825 -0.546  0.137 0.358 -0.466  0.575

#

# Fraction of Variance 

#[1] 0.977 0.999 1.000 1.000 1.000 1.000

#

merge.forecast <- function (fx,n=1) {

x <- splice(fx$pred,fx$forecast[[n]])

colnames(x) <- seriesNames(fx$data$output)

return(x)

}

AIC <- function(model) {informationTestsCalculations(model)[3]}

require(dse)

require(matlab)

f <- matrix( c(1.026261160, -0.04873236, 0.04995449,  0.166789178,

                     0.023195483,  0.97301183, 0.06694359,  0.004293523,

                    -0.002685722, -0.04074830, 1.00342561, -0.006797188,

0.00000000,  0.0000000,  0.0000000,  1.0000000000

),byrow=TRUE,nrow=4,ncol=4)

#

# To stabilize model, uncomment next line

# f[1,1] <- 0.985822375; f[2,2] <- 1.01538263; f[3,3] <- 0.95659221

#

h <- eye(3,4)

k <- (f[,1:3,drop=FALSE])

US_LM <- SS(F=f,H=h,K=k,z0=c(0.166789178,  0.004293523, -0.006797188,  1.0000000000),

              output.names=c("US1","US2","US3"))

print(US_LM)

is.SS(US_LM)

stability(US_LM)

US_LM.data <- simulate(US_LM,sampleT=100,start=1950)

#US_LM.data <- simulate(US_LM,sampleT=20,noise=matrix(0,20,3),start=1950)

US_LM.f <- forecast(l(US_LM,US_LM.data),horizon=150)

US_LM.fx <- merge.forecast(US_LM.f)

tfplot(US_LM.f)

AIC(m <-  l(US_LM,US_LM.data))

US_LMx <- SS(F=f,H=h,Q=eye(4,3),R=eye(3,3),z0=c(0.166789178,  0.004293523, -0.006797188,  1.0000000000),

              output.names=c("US1","US2","US3"))

     shockDecomposition(US_LMx)