WBC Model

# WBC BAU Model (BCE -20,000BC - 0 BC)

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

#

require(dse)

require(matlab)

#

# Measurement Matrix 

#      Growth, (Growth-T) (Q-N)

#

#          N     Q         T

#[1,]  0.605 0.605  5.17e-01

#[2,]  0.366 0.366 -8.56e-01

#[3,] -0.707 0.707  3.20e-06

#

# Fraction of Variance 

#[1] 0.858 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]}

#

f <- matrix( c(1.041460e+00, 6.816948e-02, -3156.594970, 8.219978e-02,

                       3.598635e-02 ,1.045861e+00, -6739.885907, 1.857457e-02,

                        3.057330e-07, 8.048318e-07,     1.111575 ,1.517281e-07,

                        0.000000e+00, 0.000000e+00,     0.000000, 1.000000e+00

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

#

# To Stabilize, Uncomment Next Line

# f[1,1] <- f[2,2] <- f[3,3] <- 0.9

#

# To Eliminate Malthusian Controller, Uncomment Next line

# f[1,3] <- f[2,3] <- 0

#

h <- eye(3,4)

k <- f[1:4,1:3,drop=FALSE]

WBC <- SS(F=f,H=h,K=k,z0=c(8.219978e-02, 1.857457e-02, 1.517281e-07,  1.0000000),

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

stability(WBC)

shockDecomposition(toSSChol(WBC))

#tfplot(simulate(WBC,sampleT=50,noise=matrix(0,50,2),start=1))

WBC.data <- simulate(WBC,sampleT=50,start=1)

m <- l(WBC,WBC.data)

#tfplot(m)

WBC.f <- forecast(m,horizon=50)

tfplot(WBC.f)

AIC(m)