World-System (0-500) Roman Empire

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

#

# WRE World Model Roman Empire  (RE 0-500)

#

# Measurement Matrix (Q+N-T) (Growth) (Q-N)

#         Q      N      T

#[1,] 0.577  0.578 -0.577

#[2,] 0.528  0.274  0.804

#[3,] 0.622 -0.769 -0.147

#

# Fraction of Variance 

#[1] 0.998 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]}

require(dse)

require(matlab)

f <- matrix( c(9.990858e-01, 6.700905e-03,  3.284895e+09,  1.173565e-02,

                    -6.563034e-04, 1.004810e+00,  2.358134e+09, -1.717386e-04,

                     8.324437e-19, 2.223337e-17, -7.995155e-02 , 1.087672e-15,

0.00000000,  0.0000000,  0.0000000,  1.0000000000

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

# To stabilize uncomment the following lines

#f[2,2] <- .9

# To clean up the system uncomment the following line

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

# To disable the Malthusian Controller,

# uncomment the following line

#f[1,3] <- f[2,3] <-  0;

h <- eye(3,4)

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

WRE <- SS(F=f,H=h,K=k,z0=c(1.173565e-02, -1.717386e-04 , 1.087672e-15,  1.0000000000),

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

print(WRE)

is.SS(WRE)

stability(WRE)

tfplot(WRE.data <- simulate(WRE,sampleT=150,start=1))

#WRE.data <- simulate(WRE,sampleT=20,noise=matrix(0,20,3))

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

tfplot(WRE.f)

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

AIC(m)

WREx <- SS(F=f,H=h,Q=eye(4,3),R=eye(3,3),z0=c(1.173565e-02, -1.717386e-04 , 1.087672e-15,  1.0000000000),

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

shockDecomposition(WREx)

# To run realistic counterfactuals set coefficients to values between LCI and UCI

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

# [1,]  9.987e-01  9.991e-01  9.995e-01    0.49    0.51 2.992e-04  2.435e-05  8.137e-02

# [2,] -6.937e-04 -6.563e-04 -6.257e-04    0.54    0.46 2.672e-05  9.997e-01  3.741e+04

# [3,] -1.609e-17  8.324e-19  1.935e-17    0.57    0.43 1.279e-17  9.991e-01  7.811e+16

# [4,] -2.495e-03  6.701e-03  1.452e-02    0.56    0.44 6.727e-03  9.917e-01  1.474e+02

# [5,]  1.004e+00  1.005e+00  1.006e+00    0.49    0.51 8.756e-04 -5.613e-03 -6.410e+00

# [6,] -4.397e-16  2.223e-17  4.464e-16    0.50    0.50 3.416e-16  9.991e-01  2.924e+15

# [7,] -9.021e+11  3.285e+09  7.415e+11    0.48    0.52 5.955e+11  5.679e+10  9.535e-02

# [8,] -9.033e+10  2.358e+09  1.094e+11    0.53    0.47 7.567e+10 -1.268e+10 -1.675e-01

# [9,] -1.294e-01 -7.995e-02 -1.534e-02    1.00    0.00 5.902e-02  6.913e-01  1.171e+01

#[10,]  1.098e-02  1.174e-02  1.270e-02    0.53    0.47 6.230e-04  9.873e-01  1.585e+03

#[11,] -2.988e-04 -1.717e-04 -5.609e-05    0.48    0.52 9.730e-05  9.993e-01  1.027e+04

#[12,]  1.022e-15  1.088e-15  1.146e-15    0.01    0.99 6.343e-17  9.991e-01  1.575e+16

#