AEGY Model

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

require(dse)

require(matlab)

#

# AEGY Model (Ancient Egypt 31000BCE - 1AD)

# Measurement Matrix 

#

#          N    Q

#[1,]  0.707 0.707

#[2,] -0.707 0.707

#

# Fraction of Variance 

#[1] 0.996 1.000

#

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

f <- matrix( c( 0.952957168, 0.9157134,  1.816266e-01,

                     -0.006214844, 0.8089116, -5.893046e-05,

                      0.0000000, 0.0000000,  1.0000000

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

#

# To Stabilize, Uncomment Next Line

#

# f[1,1] <- 0.943427596 

#

# To create a Random Walk, Uncomment Next Line

# f[1,1] <- f[2,2] <- 1

#

h <- eye(2,3)

k <- f[1:3,1:2,drop=FALSE]

AEGY <- SS(F=f,H=h,K=k,z0=c( 0.354655070, -0.001235381,  1.0000000),

              output.names=c("Growth","Q-N"))

#

stability(SS(F=f[1:2,1:2,drop=FALSE],R=eye(2),Q=eye(2),H=eye(2))

shockDecomposition(toSSChol(AEGY))

#tfplot(simulate(AEGY,sampleT=50,noise=matrix(0,50,2),start=1))

AEGY.data <- simulate(AEGY,sampleT=50,start=1)

m <- l(AEGY,AEGY.data)

#tfplot(m)

AEGY.f <- forecast(m,horizon=50)

tfplot(AEGY.f)

AIC(m)