Roman Empire

#

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

#

# RE Roman Empire  (RE)

# ROMAN EMPIRE (500BC - 1500AD)

#

# Measurement Matrix 

# (Growth) (T-N) (AREA-N)

#          N      Q      T     AREA

#[1,]  0.560 0.5802  0.145   0.5736

#[2,] -0.203 0.0278  0.976  -0.0779

#[3,] -0.771 0.1798 -0.117   0.5999

#

# Fraction of Variance 

#[1] 0.730 0.976 0.994 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(0,    0,    0, -0.69066054,  0.075557550,  0.13445684,  0.000000000,

                      0,    0,    0, -0.07750604, -0.934172103,  0.05325588,  0.000000000,

                      0,    0,    0, -0.03679107, -0.004695734, -0.51970124,  0.000000000,

                      1,    0,    0,  1.66924556, -0.025423574, -0.09554433, -0.003370278,

                      0,    1,    0 , 0.07652123,  1.904990451, -0.04415323, -0.003394268,

                      0,    0,    1,  0.02847876,  0.003969387,  1.27392724,  0.002355218,

                      0,    0,    0,  0.00000000,  0.000000000,  0.00000000,  1.000000000

),byrow=TRUE,nrow=7,ncol=7)

#

# Eliminate Nonlinearities (Limits-to-Growth)

# Uncomment Next Line

#       A <- SystemMatrix(RE); A[1:3,4:6] <- 0; f <- A;

#

h <- eye(3,7)

k <- (f[,4:6,drop=FALSE])

RE <- SS(F=f,H=h,K=k,z0=c(0.000000000,  0.000000000,  0.000000000, -0.003370278,

    -0.003394268, 0.002355218,  1.000000000),

              output.names=c("RE1","RE2","RE3"))

print(RE)

is.SS(RE)

stability(SS(f[1:6,1:6,drop=FALSE],Q=eye(6,3),R=eye(3,3),H=eye(3,6)))

#

tfplot(RE.data <- simulate(RE,sampleT=200,start=1))

#RE.data <- simulate(RE,sampleT=200,noise=matrix(0,200,3))

RE.f <- forecast(m <- l(RE,RE.data),horizon=200)

tfplot(RE.f)

AIC(m)

shockDecomposition(m)