USGD Model

# Cut-and-Paste code below into window above and Run

#

# US_E20 Model

#

#Measurement Matrix   (Growth-P.CPAPER-OB-IMM) 

#.      ( P.CPAPER + P.FED.FUNS + P.S.P.EPR + P.WPI + OB + P.FUELS  -LU)

# (LU-GPG.G + P.US.TBILL +PFED.FUNDS + V.NYSE + K.US - M1  - P.W.AG - IMM.US)

#(Growth Controller), (Unemployment Controller) (Immigration Controller)

#

#       L.US.E.     L.U.   GNP.US.   GNP.C.   GNP.I.   GNP.X.   GNP.G. P.US.TBILL.

#[1,]  0.219255  0.03427  0.218049  0.22007  0.17070  0.19552  0.14036      0.1952

#[2,] -0.017407 -0.27196  0.005253  0.06497  0.21297  0.15989 -0.09423     -0.1388

#[3,] -0.009199  0.42160 -0.145851 -0.05149 -0.02629 -0.06495 -0.25493      0.2428

#    P.CPAPER. P.FED.FUNDS.  P.CPI.  P.GDP. P.SP500. V.NYSE. P.S.P.DPR. P.S.P.EPR.

#[1,]  -0.13383      0.02642 0.20701 0.21001  0.14791  0.1021     0.1938    0.07653

#[2,]   0.37032      0.29912 0.16164 0.14392  0.01707  0.1071    -0.1949    0.32595

#[3,]   0.03334      0.38465 0.06851 0.01672  0.09099  0.3312     0.1444    0.03397

#     Q.H.Starts.    K.US.       M1       M2   P.WPI.     Q.A.     Q.I.     O.B. P.FUELS.

#[1,]      0.1406  0.20647  0.20742  0.21574  0.17330  0.21310  0.20412 -0.07726  0.15609

#[2,]      0.1977 -0.06538 -0.03534 -0.02157  0.24171 -0.06952 -0.07594  0.39797  0.26114

#[3,]     -0.1238  0.21738 -0.21807 -0.14920 -0.06862 -0.05705 -0.15773  0.16908  0.06664

#     P.W.AG. P.W.MFG.   Q.OIL.    N.US. IMM.US.    U.US.

#[1,]  0.2040  0.22165  0.21454  0.21224 -0.1506  0.21075

#[2,]  0.0225  0.02006 -0.12565 -0.08458  0.1433 -0.08879

#[3,] -0.2419 -0.07337  0.02101  0.14950 -0.2477  0.17053

#

# Fraction of Variance 

# [1] 0.6369 0.7736 0.8551 0.9038 0.9373 0.9579 0.9697 0.9778 0.9842 0.9896 0.9932 0.9956

#[13] 0.9970 0.9978 0.9985 0.9989 0.9992 0.9995 0.9996 0.9998 0.9999 0.9999 0.9999 1.0000

#[25] 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

#

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)

}

#

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

require(dse)

require(matlab)

f <- matrix( c( 1.0276420120, -0.04037731, -0.09367185, 0.324320408,

                     -0.0008705484,  0.95523103, -0.18831136, 0.059323285,

                     -0.0038330655,  0.10040247,  0.95814360, 0.009650457,

                       0.0000000000,  0.00000000,  0.00000000, 1.000000000,

        0.00000000,  0.0000000,  0.0000000,  1.0000000000

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

#

# To Stabilize

# Uncomment next line

# f[1,1] <-  0.944211373; f[2,2] <- 1.00456195; f[3,3] <- 0.2597032

# To add Feedback Control to the Banking Component

# Uncomment next line

# f[1,2] <- -0.50

#

h <- eye(3,4)

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

US_E20 <- SS(F=f,H=h,K=k,z0=c(0.324320408, 0.059323285, 0.009650457,  1.0000000000),

              output.names=c("US1","US2","US3"))

print(US_E20)

is.SS(US_E20)

stability(US_E20)

US_E20.data <-simulate(US_E20,sampleT=50,start=1900)

#US_E20.data <- simulate(US_E20,sampleT=50,noise=matrix(0,50,3),start=1900)

US_E20.f <- forecast(m <- l(US_E20,US_E20.data),horizon=150)

tfplot(US_E20.f)

AIC(m)

US_E20x <- SS(F=f,H=h,Q=eye(4,3),R=eye(3,3),z0=c(0.324320408, 0.059323285, 0.009650457,  1.0000000000),

              output.names=c("US1","US2","US3"))

shockDecomposition(US_E20x,horizon=10,shock=rep(-1,10))