WL203 Model

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# WL203 Model (Cut-and-Paste code into window above and Run (Cmd-Enter)

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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)

#Measurement Matrix 

#           N    OIL      QA     GWP P.Wheat. P.Oil.   TEMP     CO2

#[1,]  0.2845  0.271  0.2821  0.2824    0.236  0.243  0.251  0.2837

#[2,] -0.0161  0.241  0.0985 -0.1413    0.411  0.066 -0.235 -0.0983

#[3,] -0.1112 -0.241 -0.0883  0.0213    0.461  0.712  0.190 -0.0201

#      Carbon TotalFootprint Earths WorldGlobal LivingPlanet   URBAN

#[1,]  0.2833          0.275  0.279      0.2819      -0.1839  0.2840

#[2,]  0.0925          0.182  0.148     -0.0926       0.7705 -0.0868

#[3,] -0.0955         -0.293 -0.231     -0.0943      -0.0576 -0.0707

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# Fraction of Variance 

# [1] 0.874 0.941 0.973 0.986 0.995 0.998 0.999 0.999 1.000 1.000 1.000

#[12] 1.000 1.000 1.000

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f <- matrix( c(1.01169571, -0.02519461, -0.09358484,  0.210941578,

                    -0.01360718,  0.96330129, -0.05250691, -0.003862528,

                      0.02303607, -0.03631204,  0.93554760, 0.018115378,

0.00000000,  0.0000000,  0.0000000,  1.0000000000

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

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# Experiments (Uncomment each line separately and run

# f[2,1] <- 0

# f[2,3] <- 0

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

# f[1,1] <- 1

h <- eye(3,4)

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

WL203 <- SS(F=f,H=h,K=k,z0=c( 0.210941578, -0.003862528,  0.018115378,  1.0000000000),

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

print(WL203)

is.SS(WL203)

stability(WL203)

# tfplot(simulate(WL203,sampleT=100,start=1950))

WL203.data <- simulate(WL203,sampleT=150,noise=matrix(0,150,3),start=1950)

WL203.f <- forecast(m <- l(WL203,WL203.data),horizon=150)

# tfplot(WL203.f)

AIC(m)

WL20.fx <- merge.forecast(WL203.f)

tfplot(WL20.fx)

WL203x <- SS(F=f,H=h,Q=eye(4,3),R=eye(3),z0=c( 0.210941578, -0.003862528,  0.018115378,  1.0000000000),

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

shockDecomposition(WL203x)

#

# Bootstrap Confidence Intervals

#

#            LCI Parameter       UCI P>=T[1] P< T[1] Std. Dev.    Bias

# [1,]  0.996281  1.011696  1.027796    0.41    0.59  0.011032 0.00253

# [2,] -0.023932 -0.013607 -0.007148    0.29    0.71  0.006500 1.02938

# [3,]  0.014406  0.023036  0.030886    0.28    0.72  0.007194 0.99241

# [4,] -0.070961 -0.025195  0.016253    0.51    0.49  0.036336 1.03464

# [5,]  0.940930  0.963301  0.989088    0.42    0.58  0.019651 0.05109

# [6,] -0.070752 -0.036312 -0.008523    0.53    0.47  0.025045 1.05212

# [7,] -0.173415 -0.093585 -0.027504    0.32    0.68  0.055408 1.13162

# [8,] -0.106033 -0.052507 -0.008567    0.19    0.81  0.039006 1.09648

# [9,]  0.885856  0.935548  0.976298    0.04    0.96  0.039195 0.13638

#[10,]  0.192503  0.210942  0.232887    0.55    0.45  0.019344 0.79731

#[11,] -0.024368 -0.003863  0.013228    0.32    0.68  0.015423 1.02289

#[12,] -0.008279  0.018115  0.041528    0.34    0.66  0.020164 1.00146

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