WE_M Model

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

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# WE_M Model (1900-2000)

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# Measurement Matrix 

#          Q      N      U  HOURS  XREAL     X       L

#[1,]  0.392  0.391  0.386 -0.357 0.3751 0.348  0.3941

#[2,]  0.150 -0.243 -0.313  0.526 0.4252 0.599 -0.0591

#[3,] -0.402 -0.235  0.122 -0.564 0.0747 0.464 -0.4785

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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(1.019119987, -0.008500298, -0.005688169, 0.088538918,

                      0.021974985,  1.019100181, -0.039619111, 0.009647611,

                      0.008570585,  0.028375621,  1.026266523, 0.006815983,

0.00000000,  0.0000000,  0.0000000,  1.0000000000

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

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# To stabilize growth, uncomment the following line

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

#

h <- eye(3,4)

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

WE_M <- SS(F=f,H=h,K=k,z0=c(   0.088538918, 0.009647611, 0.006815983,  1.0000000000),

              output.names=c("WE1","WE2","WE3"))

print(WE_M)

is.SS(WE_M)

stability(WE_M)

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

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

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

tfplot(WE_M.f)

AIC(m)

WE_Mx <- SS(F=f,H=h,Q=eye(4,3),R=eye(3),z0=c(   0.088538918, 0.009647611, 0.006815983,  1.0000000000),

              output.names=c("WE1","WE2","WE3"))

shockDecomposition(WE_Mx)

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

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

# To construct probable Counterfactuals, set coefficients between LCI and UCI

#

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

# [1,]  1.013789  1.019120  1.02495    0.43    0.57  0.004927

# [2,]  0.018544  0.021975  0.02583    0.44    0.56  0.003172

# [3,]  0.005900  0.008571  0.01164    0.42    0.58  0.002324

# [4,] -0.030152 -0.008500  0.01056    0.37    0.63  0.016115

# [5,]  1.008405  1.019100  1.03121    0.29    0.71  0.009321

# [6,]  0.021536  0.028376  0.03638    0.36    0.64  0.005925

# [7,] -0.067363 -0.005688  0.05383    0.40    0.60  0.042526

# [8,] -0.068165 -0.039619 -0.01279    0.32    0.68  0.023003

# [9,]  1.010786  1.026267  1.04255    0.19    0.81  0.012924

#[10,]  0.082253  0.088539  0.09488    0.65    0.35  0.005197

#[11,]  0.002130  0.009648  0.01723    0.56    0.44  0.006005

#[12,]  0.002551  0.006816  0.01114    0.52    0.48  0.003643

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