DEL19C Model

# (Cut-and-Paste Code into Window Above and Run (Cmd-Enter)

#

# DEL19 Model (1872-1907)

#

# Measurement Matrix 

#           Q       L        I      K       W        N

#[1,]  0.4293  0.4218  0.38667  0.425  0.4298  0.35000

#[2,] -0.0535 -0.0636 -0.48407 -0.122 -0.0301  0.86200

#[3,]  0.0101 -0.4686  0.73404 -0.342 -0.1366  0.32515

#[4,]  0.7117 -0.5167 -0.27761 -0.146  0.3204 -0.15934

#[5,] -0.5500 -0.3884  0.00128  0.234  0.7013 -0.00447

#[6,]  0.0603 -0.4251 -0.01677  0.782 -0.4486  0.05763

#

# Fraction of Variance 

#[1] 0.895 0.967 0.996 0.999 1.000 1.000

#

#

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

require(dse)

require(matlab)

f <- matrix( c( 1.028709948, -0.15157849, -0.0969659,  0.216248062,

                     -0.037176740,  0.66612338,  0.4171702,  0.058414986,

                       0.005725789, -0.02203582,  0.7522939, -0.006697577,

                      0.00000000,  0.00000000,  0.0000000,  1.000000000

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

#

# To Stabilize Model, uncomment next line

# f[1,1] <- 0.95

#

h <- eye(3,4)

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

DEL19C <- SS(F=f,H=h,K=k,z0=c(  0.216248062,  0.058414986, -0.006697577,  1.000000000),

              output.names=c("DE1","DE2","DE3"))

print(DEL19C)

is.SS(DEL19C)

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

n <- 50

DEL19C.data <- simulate(DEL19C,sampleT=n,noise=matrix(0,n,3),start=1872)

DEL19C.data2 <- simulate(DEL19C,sampleT=n,start=1)

tfplot(DEL19C.data)

AIC(l(DEL19C,DEL19C.data))

tfplot(DEL19C.data2)

shockDecomposition(toSSChol(DEL19C))

#

# DEL19 Controlled Model W Input Held Constant

#

f <- matrix( c( 0.2568621, 0.06170521, 0.3612876, -0.002867862,

                     -0.2835427, 0.60782446, 0.7004361,  0.008146236,

                     -0.5108574, 0.14733003, 0.9090658, -0.159315011,

                      0.00000000,  0.00000000,  0.0000000,  1.000000000

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

DEL19CW <- SS(F=f,H=h,K=k,z0=c( -1.668745, -0.614395, -1.068699,  1.000000000),

              output.names=c("DE1","DE2","DE3"))

print(DEL19CW)

is.SS(DEL19CW)

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

n <- 150

DEL19CW.data <- simulate(DEL19CW,sampleT=n,noise=matrix(0,n,3),start=1872)

DEL19CW.data2 <- simulate(DEL19CW,sampleT=n,start=1872)

tfplot(DEL19CW.data)

AIC(l(DEL19CW,DEL19CW.data))

tfplot(DEL19CW.data2)

shockDecomposition(toSSChol(DEL19CW))