ES_M Model

# Cut-and-Paste Code Below into Window Above and Run

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# ES_M Model (1900-2000)

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# Measurement Matrix 

#         Q      N       U  HOURS  XREAL      X      L

#[1,] 0.398  0.415  0.4145  0.348  0.344  0.335  0.383

#[2,] 0.192 -0.134 -0.1512 -0.503  0.512  0.529 -0.357

#[3,] 0.769  0.250 -0.0857 -0.102 -0.190 -0.399 -0.364

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# Fraction of Variance 

#[1] 0.807 0.985 1.000 1.000 1.000 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(1.013556897,  0.005104802, 0.01837777,  0.08768135,

                     0.037664684,  1.027637926, 0.06084375,  0.01656348,

                    -0.002244742, -0.024811661, 0.99699055, -0.01097830,

0.00000000,  0.0000000,  0.0000000,  1.0000000000

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

#
# To stabilize, uncomment the following code

# f[1,1] <- f[2,2] <- f[3,3] <- .97

#

h <- eye(3,4)

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

ES_M <- SS(F=f,H=h,K=k,z0=c(  0.08768135,  0.01656348, -0.01097830,  1.0000000000),

              output.names=c("ES1","ES2","ES3"))

print(ES_M)

is.SS(ES_M)

stability(ES_M)

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

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

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

tfplot(ES_M.f)

AIC(m)

ES_Mx <- SS(F=f,H=h,Q=eye(4,3),R=eye(3),z0=c(  0.08768135,  0.01656348, -0.01097830,  1.0000000000),

              output.names=c("ES1","ES2","ES3"))

shockDecomposition(ES_Mx)

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

#shockDecomposition(ES_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,]  1.006786  1.013557  1.020e+00    0.42    0.58  0.005617

# [2,]  0.029896  0.037665  4.570e-02    0.47    0.53  0.006560

# [3,] -0.005248 -0.002245  8.335e-05    0.58    0.42  0.002430

# [4,] -0.011115  0.005105  1.988e-02    0.42    0.58  0.012039

# [5,]  1.012311  1.027638  1.049e+00    0.30    0.70  0.014714

# [6,] -0.031370 -0.024812 -2.056e-02    0.65    0.35  0.004394

# [7,] -0.021849  0.018378  5.822e-02    0.63    0.37  0.031928

# [8,]  0.020385  0.060844  9.115e-02    0.67    0.33  0.028659

# [9,]  0.985099  0.996991  1.010e+00    0.23    0.77  0.010130

#[10,]  0.082851  0.087681  9.462e-02    0.67    0.33  0.005206

#[11,]  0.002617  0.016563  3.140e-02    0.51    0.49  0.011509

#[12,] -0.014866 -0.010978 -7.217e-03    0.44    0.56  0.003230

#