Malthus

#

# Malthus Theoretical Model

#

require(dse)

require(matlab)

# Measurement Matrix 

#          K      L      Q    QA

#[1,]  0.505  0.504  0.500 0.491

#[2,] -0.105 -0.213 -0.499 0.834

#

 #Fraction of Variance 

#[1] 0.98 1.00 1.00 1.00

#

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

f <- matrix( c(  1.04107567, -0.02550578,  0.177750815,

                    -0.02440285,  1.02300087, -0.005601134,

                      0.0000000, 0.0000000,  1.0000000

),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( 0.177750815, -0.005601134,  1.0000000),

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

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)