The Long Sixteenth Century

#

# W_L16 Model (1450-1640) (Cut-and-Paste Code into window above and Run (Cmd-Enter))

#

#

# Measurement Matrix    (Growth-T), (Q+T), (Q-N)

 #        Q       N      T

#[1,] 0.576  0.5831 -0.573

#[2,] 0.651  0.0971  0.753

#[3,] 0.495 -0.8066 -0.324

#

# Fraction of Variance 

#[1] 0.98 1.00 1.00

#

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(0.9943698154,  0.030771900, 0.3589261,  0.0274095487,

                    -0.0043335350,  1.022279770, 0.2692689, -0.0030295812,

                    -0.0001074497, -0.002679999, 0.9905856,  0.0003015236,

0.00000000,  0.0000000,  0.0000000,  1.0000000000

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

#

# To stabilize, uncomment next command

#

# f[2,2]=.90

#

h <- eye(3,4)

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

W16 <- SS(F=f,H=h,K=k,z0=c( 0.0274095487, -0.0030295812,  0.0003015236,  1.0000000000),

              output.names=c("W1","W2","W3"))

print(W16)

is.SS(W16)

stability(W16)

# tfplot(simulate(W16,sampleT=100))

W16.data <- simulate(W16,sampleT=200,start=1450)

#W16.data <- simulate(W16,sampleT=200,noise=matrix(0,200,3),start=1450)

W16.f <- forecast(l(W16,W16.data),horizon=200)

tfplot(W16.f)

W16.fx <- merge.forecast(W16.f)

tfplot(W16.fx)

AIC(m <- l(W16,W16.data))

shockDecomposition(toSSChol(m))