PT_M Model

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

#

# PT_M Model (1900-2000)

#

# Measurement Matrix    (Growth), (X-N), (N-Q)

#          Q      N      U     X

#[1,]  0.520  0.488  0.524 0.465

#[2,]  0.267 -0.581 -0.338 0.691

#[3,] -0.655  0.476 -0.260 0.527

#

# Fraction of Variance 

#[1] 0.854 0.977 1.000 1.000

#

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(1.021933178, 0.02115352, -0.01791158, 0.072947411,

                      0.027151093, 1.00805861, -0.04841158, 0.003853785,

                      0.006984669, 0.03614813,  1.01325902, 0.009616332,

0.00000000,  0.0000000,  0.0000000,  1.0000000000

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

#

# To stabilize growth, uncomment the next line

# f[1,1] <- 1.0 ; f[2,2] <- f[3,3] <- 0.98

#

h <- eye(3,4)

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

PT_M <- SS(F=f,H=h,K=k,z0=c(  0.072947411, 0.003853785, 0.009616332,  1.0000000000),

              output.names=c("PT1","PT2","PT3"))

print(PT_M)

is.SS(PT_M)

stability(PT_M)

#tfplot(PT_M.data <-  simulate(PT_M,sampleT=150,start=1900))

PT_M.data <- simulate(PT_M,sampleT=150,noise=matrix(0,150,3),start=1900)

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

tfplot(PT_M.f)

AIC(m)

PT_Mx <- SS(F=f,H=h,Q=eye(4,3),R=eye(3),z0=c(   0.072947411, 0.003853785, 0.009616332,  1.0000000000),

              output.names=c("PT1","PT2","PT3"))

shockDecomposition(PT_Mx)

# To explore Negative Shocks, Uncomment the next line for a -1 sd shock

#shockDecomposition(PT_Mx,shock=rep(-1,10))

# To create probable counterfactuals, set coefficients between LCI and UCI

#

#            LCI Parameter      UCI P>=T[1] P< T[1] Std. Dev.

# [1,]  1.014782  1.021933  1.03007    0.41    0.59  0.007496

# [2,]  0.023317  0.027151  0.03141    0.41    0.59  0.003856

# [3,]  0.003701  0.006985  0.01054    0.44    0.56  0.003378

# [4,]  0.004368  0.021154  0.03851    0.39    0.61  0.015766

# [5,]  0.998894  1.008059  1.01831    0.29    0.71  0.008554

# [6,]  0.029628  0.036148  0.04283    0.44    0.56  0.006152

# [7,] -0.055728 -0.017912  0.01578    0.32    0.68  0.029014

# [8,] -0.073043 -0.048412 -0.02696    0.34    0.66  0.018967

# [9,]  1.000552  1.013259  1.02696    0.21    0.79  0.012042

#[10,]  0.067583  0.072947  0.07910    0.50    0.50  0.005397

#[11,] -0.003640  0.003854  0.01061    0.47    0.53  0.005755

#[12,]  0.005971  0.009616  0.01343    0.49    0.51  0.003347

#