AF_LM Model

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

#

# Africa (AF) Model (1950-2000)

#

#

# Measurement Matrix (Overall), (XREAL-Q-N), (Q-N)  (Malthusian))

#

#          Q      N   XREAL

#[1,]  0.589  0.584  0.5587

#[2,] -0.343 -0.445  0.8271

#[3,]  0.732 -0.679 -0.0614

#

# Fraction of Variance 

#[1] 0.940 0.998 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( 1.025381733, -0.016310665, -0.6741595,  0.137157658,

                       0.007851544,  0.988233026, -1.2077588,  0.029628882,

                      -0.006312777,  0.009605595,  1.0707305, -0.002758338,

0.00000000,  0.0000000,  0.0000000,  1.0000000000

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

#

# To stabilize model, uncomment next three lines

# f[1,1] <-   0.984977601

# f[2,2] <-  0.949292702

# f[3,3] <- 1.0285394

#

h <- eye(3,4)

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

AF_LM <- SS(F=f,H=h,K=k,z0=c(0.137157658,  0.029628882, -0.002758338,  1.0000000000),

              output.names=c("AF1","AF2","AF3"))

print(AF_LM)

is.SS(AF_LM)

stability(AF_LM)

AF_LM.data <- simulate(AF_LM,sampleT=100,start=1950)

#AF_LM.data <- simulate(AF_LM,sampleT=100,noise=matrix(0,100,3),start=1950)

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

AF_LM.fx <- merge.forecast(AF_LM.f)

tfplot(AF_LM.f)

AIC(m <-  l(AF_LM,AF_LM.data))

AF_LMx <- SS(F=f,H=h,Q=eye(4,3),R=eye(3,3),z0=c(0.279172909,  0.063317428, -0.0062930188,  1.0000000000),

              output.names=c("AF1","AF2","AF3"))

     shockDecomposition(AF_LMx)

#

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

# [1,]  1.001581  1.025382  1.0541371    0.36    0.64  0.023142  0.002421   0.1046

# [2,] -0.007663  0.007852  0.0284854    0.36    0.64  0.016283  1.017494  62.4867

# [3,] -0.008642 -0.006313 -0.0046471    0.69    0.31  0.002031  1.031633 507.9199

# [4,] -0.095541 -0.016311  0.0365371    0.40    0.60  0.049099  1.060378  21.5965

# [5,]  0.957108  0.988233  1.0252309    0.21    0.79  0.028297  0.057326   2.0259

# [6,]  0.003593  0.009606  0.0141696    0.76    0.24  0.004463  1.013501 227.0968

# [7,] -1.280303 -0.674160 -0.0555197    0.70    0.30  0.608512  1.546150   2.5409

# [8,] -1.724356 -1.207759 -0.8630077    0.72    0.28  0.386870  2.212082   5.7179

# [9,]  1.015755  1.070731  1.1271480    0.26    0.74  0.054468 -0.029064  -0.5336

#[10,]  0.123930  0.137158  0.1528226    0.56    0.44  0.016417  0.883720  53.8291

#[11,]  0.012988  0.029629  0.0449267    0.47    0.53  0.015758  0.996019  63.2089

#[12,] -0.005969 -0.002758 -0.0004332    0.56    0.44  0.002209  1.028213 465.5432

#