World-System Steady State or Collapse

# Cut-and-Paste code into Window Above and Run

#

#

# WL20 World  Model

#

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 (Growth-LP) (LP+OIL-TEMP)  (P.OIL. - OIL - EF)

#

#           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

#

# 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

#

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"))

print(WL20)

is.SS(WL20)

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

# tfplot(simulate(WL20,sampleT=150))

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)

tfplot(WL20.f)

AIC(l(WL20,WL20.data))