WL20 World-System

# Cut-and-Paste Code Below into Window Above and Run

#

# WL20 World Model

#

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

require(dse)

require(matlab)

#

# Measurement Matrix (Growth-LP) (LP + P.Wheat + OIL) (P.OIL. + P.Wheat. - EF)

#

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

#[1,]  0.2845  0.271  0.2821  0.2824    0.236  0.243  0.251  0.2837  0.2833

#[2,] -0.0161  0.241  0.0985 -0.1413    0.411  0.066 -0.235 -0.0983  0.0925

#[3,] -0.1112 -0.241 -0.0883  0.0213    0.461  0.712  0.190 -0.0201 -0.0955

#     TotalFootprint Earths WorldGlobal LivingPlanet   URBAN

#[1,]          0.275  0.279      0.2819      -0.1839  0.2840

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

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

#

 #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 1.000

#[13] 1.000 1.000

#

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,  0.935547600

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

h <- matrix(c(0,    1,    0,    0,

              0,    0,    1,    0,

              0,    0,    0,    1

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

k <- (f[1:4,2:4,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"))

print(WL20)

is.SS(WL20)

stability(SS(F=f[2:4,2:4,drop=FALSE],R=eye(3),Q=eye(3),H=eye(3)))

# tfplot(simulate(WL20,sampleT=100))

WL20.data <- simulate(WL20,sampleT=50,noise=matrix(0,50,3),start=1950)

WL20.f <- forecast(l(WL20,WL20.data),horizon=150)

tfplot(WL20.f)

AIC(l(WL20,WL20.data))