Malthusian Population Model

#

# Malthus Basic Population Model Model

# Cut and paste this code into the window above and Run (Cmd-Enter)

#

merge.forecast <- 

function (fx,n=1) {

# Merges a forecast with the outputdata

x <- splice(fx$pred,fx$forecast[[n]])

colnames(x) <- seriesNames(fx$data$output)

return(x)

}

require(dse)

require(matlab)

#

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

f <- matrix( c(  1.040323e+00, 0.009051444, 0.06349123,

                        0.000000000, 1.000000000, 0.05000000,

                       0.000000e+00, 0.000000000, 1.00000000

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

h <- eye(2,3)

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

Malthus <- SS(F=f,H=h,K=k,z0=c( 0.06349123, 0.05000000,  1.0000000),

              output.names=c("N","QA"))

stability(Malthus)

shockDecomposition(toSSChol(Malthus))

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

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

m <- l(Malthus,Malthus.data)

#tfplot(m)

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

tfplot(Malthus.f)

AIC(m)