LAC1 Model

#

# LAC1 World  Model Input (requires WL20.fx)

#

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)

#

# WL20 World  Model

#

f <- matrix( c(1.000000000,  0.00000000,  0.00000000,  0.00000000,

                      0.210941578,  1.01169571, -0.02519461, -0.09358484,

                     -0.003862528, -0.01360718,  0.96330129, -0.05250691,

                       0.018115378,  0.02303607, -0.03631204,  0.93554760

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

#

# Growth-and-Collapse Model

# To create a high-level steady state, uncomment next line

# f[2,2] <- 0.90

#

h <- matrix(c(0,    1,    0,    0,

0,    0,    1,    0,

                     0,    0,    0,    1

),byrow=TRUE,nrow=3,ncol=4)

k <- (f[,2:4,drop=FALSE])

WL20 <- SS(F=f,H=h,K=k,z0=c(1.0000000, -5.3541066, -0.7239263,  0.7703831),

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

WL20.data <- simulate(WL20,sampleT=150,noise=matrix(0,150,3))

WL20.f <- forecast(l(WL20,WL20.data),horizon=50)

WL20.fx <- merge.forecast(WL20.f)

#

# LAC1 World  Model Input (requires WL20.fx)

#

#

# Measurement Matrix  # Growth, (LU-Q-E), (N+L-CO2-Q

#

#     EN.ATM.CO2E.KT EG.USE.COMM.KT.OE NY.GDP.MKTP.KD SL.TLF.TOTL.IN

#[1,]          0.412             0.412          0.411          0.413

#[2,]         -0.190            -0.239         -0.272         -0.144

#[3,]         -0.532            -0.169         -0.252          0.497

#     SP.POP.TOTL SL.UEM.TOTL.ZS

#[1,]     0.41317          0.388

#[2,]    -0.00377          0.901

#[3,]     0.59551         -0.152

#

# Fraction of Variance 

#[1] 0.972 0.997 0.999 1.000 1.000 1.000

#

f <- matrix( c(  0.7537367, -0.1158698,

                        0.0000000, 1.0000000

),byrow=TRUE,nrow=2,ncol=2)

h <- eye(1,2)

k <- f[1:2,1,drop=FALSE]

g <- matrix(c(0.1966073, 0.02923806, -0.06832,

                      0.0000000,  0.000000, 0.0000000

),byrow=TRUE,nrow=2,ncol=3)                      

LAC1 <- SS(F=f,H=h,K=k,G=g,z0=c( -0.2439615,  1.0000000),

              output.names=c("LAC1"),input.names=c("W1","W2","W3"))

tfplot(simulate(LAC1,sampleT=150,noise=matrix(0,150,1),start=1950,input=WL20.fx))

#