US_M Model

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

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# US_M Model (1900-2000)

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# Measurement Matrix 

#          Q      N   HOURS XREAL      X      L

#[1,]  0.418  0.399  0.4181 0.409  0.391  0.414

#[2,] -0.102 -0.555 -0.0901 0.392  0.663 -0.284

#[3,]  0.484 -0.412  0.3458 0.339 -0.538 -0.268

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# Fraction of Variance 

#[1] 0.949 0.998 0.999 1.000 1.000 1.000

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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(1.032334642, -0.01313759, 0.14133680,  0.091785548,

                     0.022580531,  1.03242002, 0.07029664,  0.009258674,

                    -0.002991271, -0.01970478, 1.02700196, -0.004054557,

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.

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

#

h <- eye(3,4)

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

US_M <- SS(F=f,H=h,K=k,z0=c(  0.091785548,  0.009258674, -0.004054557,  1.0000000000),

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

print(US_M)

is.SS(US_M)

stability(US_M)

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

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

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

tfplot(US_M.f)

AIC(m)

US_Mx <- SS(F=f,H=h,Q=eye(4,3),R=eye(3),z0=c(  0.091785548,  0.009258674, -0.004054557,  1.0000000000),

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

shockDecomposition(US_Mx)

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

#shockDecomposition(US_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,]  1.022403  1.032335  1.044920    0.37    0.63  0.009635

# [2,]  0.016833  0.022581  0.030721    0.38    0.62  0.005279

# [3,] -0.005139 -0.002991 -0.001554    0.58    0.42  0.001403

# [4,] -0.051668 -0.013138  0.023995    0.33    0.67  0.032309

# [5,]  1.014150  1.032420  1.055952    0.30    0.70  0.017539

# [6,] -0.026039 -0.019705 -0.014005    0.63    0.37  0.004779

# [7,] -0.043130  0.141337  0.333174    0.60    0.40  0.170630

# [8,] -0.043284  0.070297  0.163875    0.75    0.25  0.082190

# [9,]  0.999037  1.027002  1.054223    0.33    0.67  0.021011

#[10,]  0.080128  0.091786  0.104725    0.53    0.47  0.011583

#[11,]  0.001436  0.009259  0.018868    0.43    0.57  0.007608

#[12,] -0.006214 -0.004055 -0.002518    0.56    0.44  0.001453

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