AXIS_of_Evil Models

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

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# help(dse)

# help(SS)

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# AXIS BAU Growth

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merge.forecast <- function (fx,n=1) {

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# Merges a forecast with the outputdata

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)

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# Measurement Matrix 

#       RU1    IN1    CN1

#[1,] 0.514  0.601  0.612

#[2,] 0.855 -0.414 -0.311

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# Fraction of Variance 

#[1] 0.843 0.994 1.000

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f <- matrix( c(   1.01460086, -0.03779872, 0.115936692,

                       -0.01948855,  0.96412537, 0.009885037,

                         0.00000000,  0.00000000, 1.000000000

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

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# To stabilize, uncomment the next line

# f[1,1] <- 0.98; f[2,2] <- 0.94

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h <- eye(2,3)

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

AXIS <- SS(F=f,H=h,K=k,z0=c(  0.115936692, 0.009885037, 1.000000000),

output.names=c("AXIS1", "AXIS2"))

print(AXIS)

is.SS(AXIS)

stability(AXIS)

AXIS.data <- simulate(AXIS,sampleT=150,noise=matrix(0,150,2),start=1960)

#tfplot(AXIS.data)

AXIS.f <- forecast(l(AXIS,AXIS.data),horizon=150,start=1960)

tfplot(AXIS.f)

AXIS.fx <- merge.forecast(AXIS.f)

AIC(l(AXIS,AXIS.data))

shockDecomposition(toSSChol(AXIS))

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# AXIS_US_W Input Model

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f1 <- matrix( c(   0.4019768, -0.3374256, 1.737707,

                          -0.3795936,  0.5531931, 1.442896,

                         0.00000000,  0.00000000, 1.000000000

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

g1 <- matrix(c(2.793952, -1.493413,

                      2.248613, -1.174908,

                      0.000000,  0.000000

),nrow=3,ncol=2, byrow=TRUE)

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h1 <- eye(2,3)

k1 <- (f[,1:2,drop=FALSE])

AXIS_USW <- SS(F=f1,H=h1,K=k1,G=g1,z0=c(  2.363615, 1.947099, 1.000000000),

output.names=c("AXIS_US", "AXIS_W"))

print(AXIS_USW)

is.SS(AXIS_USW)

stability(AXIS_USW)

AXIS_USW.data <- simulate(AXIS_USW,sampleT=50,noise=matrix(0,50,2),start=1960,input=window(AXIS.fx,start=1960,end=2010))

#tfplot(AXIS_USW.data)

AXIS_USW.f <- forecast(l(AXIS_USW,AXIS_USW.data),conditioning.inputs=AXIS.fx)

tfplot(AXIS_USW.f )

shockDecomposition(SS(F=f1,H=h1,R=eye(2),Q=eye(3,2),z0=c(  2.363615, 1.947099, 1.000000000),output.names=c("AXIS_US", "AXIS_W")))

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# Take out the Axis Input"

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AXIS_USWx <- SS(F=f1,H=h1,K=k1,z0=c(  2.0, 1.947099, 1.000000000),

output.names=c("AXIS_US", "AXIS_W"))

print(AXIS_USWx)

is.SS(AXIS_USWx)

stability(AXIS_USWx)

AXIS_USWx.data <- simulate(AXIS_USWx,sampleT=50,noise=matrix(0,50,2),start=1960,horizon=150)

#tfplot(AXIS_USWx.data)

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

tfplot(AXIS_USWx.f )

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