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

#

# W_Malthus (0-2000)

#

require(dse)

require(matlab)

# Measurement Matrix   (Growth) (Q-N)

#       Q      N

#[1,] 0.707  0.707

#[2,] 0.707 -0.707

#

# Fraction of Variance 

#[1] 0.96 1.00

#

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]}

f <- matrix( c(  1.023336956, 0.008819228, 0.0069498915,

                        0.006613558, 1.012095445, 0.0009444344,

                      0.0000000, 0.0000000,  1.0000000

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

#

# Create a Random Walk (uncomment next line)

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

# Stabilize (uncomment next line)

# f[1,1] <- f[2,2] <- .99

# Classical Malthus Model

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

#

h <- eye(2,3)

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

Malthus <- SS(F=f,H=h,K=k,z0=c( 0.0069498915, 0.0009444344,  1.0000000),

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

stability(Malthus)

#shockDecomposition(toSSChol(Malthus))

#tfplot(simulate(Malthus,sampleT=2000,noise=matrix(0,2000,2),start=1))

Malthus.data <- simulate(Malthus,sampleT=2000,start=1)

m <- l(Malthus,Malthus.data)

#tfplot(m)

Malthus.f <- forecast(m,horizon=500)

tfplot(Malthus.f)

AIC(m)

MalthusX<- SS(F=f,H=h,Q=eye(3,2),R=eye(2,2),z0=c( 0.0069498915, 0.0009444344,  1.0000000),

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

shockDecomposition(MalthusX)

#

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

# [1,]  1.0197290 1.0233370 1.028431    0.34    0.66 0.0033912 0.00101    0.2979

# [2,]  0.0054137 0.0066136 0.008318    0.33    0.67 0.0010994 1.01704  925.0700

# [3,] -0.0037078 0.0088192 0.025156    0.32    0.68 0.0106613 1.01916   95.5944

# [4,]  1.0079072 1.0120954 1.016778    0.33    0.67 0.0032656 0.01255    3.8423

# [5,]  0.0062602 0.0069499 0.007678    0.42    0.58 0.0006533 1.01647 1555.8314

# [6,]  0.0007261 0.0009444 0.001218    0.34    0.66 0.0001961 1.02243 5214.0136

#