Smith Exponential Growth

#

# Smith Exponential Growth (Cut and paste code into window above and Run (Cmd-Enter)

#

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( 0.7812470, 0.3255224, -0.1022999, 0.028117500,

                      -0.2466271,0.9, -0.1827155, 0.023367413,

                      -0.5330617, 0.6412153,  0.8753853, 0.008156255,

0.00000000,  0.0000000, 0, 1.0000000000

),byrow=TRUE,nrow=4,ncol=4)

#

# To stabilize the model, uncomment following line

# f[1,1] <-  0.7281732; f[2,2] <- 1.3319361; f[3,3] <- 0.8159163

# To create unstable cyclical growth, uncomment following line

# f[2,2] <- 1.4290158

#

h <- eye(3,4)

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

Smith <- SS(F=f,H=h,K=k,z0=c(0.028117500, 0.023367413, 0.008156255,  1.0000000000),

              output.names=c("Smith1","Smith2","Smith3"))

print(Smith)

is.SS(Smith)

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

# tfplot(simulate(Smith,sampleT=100))

Smith.data <- simulate(Smith,sampleT=100,noise=matrix(0,100,3))

Smith.f <- forecast(l(Smith,Smith.data),horizon=150)

tfplot(Smith.f)

AIC(l(Smith,Smith.data))