R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(152.60,153.32,165.50,139.18,136.53,115.92,96.65,83.77,84.66,106.03,86.92,54.66,151.66,121.27,132.95,119.64,122.16,117.44,106.69,87.45,80.98,110.30,87.01,55.73,146.00,137.54,138.54,135.62,107.27,99.04,91.36,68.35,82.59,98.41,71.25,47.58,130.83,113.60,125.69,113.60,97.12,104.43,91.84,75.11,89.24,110.23,78.42,68.45,122.81,129.66,159.06,139.03,102.16,113.59,81.46,77.36,87.57,101.23,87.21,64.94,133.12,117.99,135.90,125.67,108.03,128.31,84.74,86.38,92.24,95.83,92.33,54.27)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '1'
> par7 = '1'
> par6 = '0'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> par1 = '24'
> par1 <- as.numeric(par1) #cut off periods
> par1 <- 28
> par2 <- as.numeric(par2) #lambda
> par3 <- as.numeric(par3) #degree of non-seasonal differencing
> par4 <- as.numeric(par4) #degree of seasonal differencing
> par5 <- as.numeric(par5) #seasonal period
> par6 <- as.numeric(par6) #p
> par6 <- 3
> par7 <- as.numeric(par7) #q
> par7 <- 3
> par8 <- as.numeric(par8) #P
> par9 <- as.numeric(par9) #Q
> if (par10 == 'TRUE') par10 <- TRUE
> if (par10 == 'FALSE') par10 <- FALSE
> if (par2 == 0) x <- log(x)
> if (par2 != 0) x <- x^par2
> lx <- length(x)
> first <- lx - 2*par1
> nx <- lx - par1
> nx1 <- nx + 1
> fx <- lx - nx
> if (fx < 1) {
+ fx <- par5
+ nx1 <- lx + fx - 1
+ first <- lx - 2*fx
+ }
> first <- 1
> if (fx < 3) fx <- round(lx/10,0)
> (arima.out <- arima(x[1:nx], order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5), include.mean=par10, method='ML'))

Call:
arima(x = x[1:nx], order = c(par6, par3, par7), seasonal = list(order = c(par8, 
    par4, par9), period = par5), include.mean = par10, method = "ML")

Coefficients:
          ar1      ar2     ar3      ma1     ma2      ma3     sar1    sma1
      -0.7148  -0.3580  0.4838  -0.0067  0.0067  -0.9999  -0.9601  0.5530
s.e.   0.1866   0.2335  0.1813   0.2018  0.2023   0.2628   0.1554  0.8029

sigma^2 estimated as 30.21:  log likelihood = -109.53,  aic = 237.06
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1]  78.08709  94.16604  74.65538  46.54149 123.83736 130.29489 128.51132
 [8] 120.33365  96.17362  85.07595  76.83501  61.46504  68.50329  85.05900
[15]  62.67807  32.10645 118.67516 104.41929 109.97935 103.31160  85.88184
[22]  88.14122  81.58806  61.95480  63.02109  84.49589  60.33845  32.43892

$se
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1]  5.862838  6.078762  6.609768  6.663239  6.643388  6.835386  6.828498
 [8]  6.811540  6.955393  6.961397  6.955595  7.048429  7.518885  7.676663
[15]  8.002288  7.975961  8.009368  8.110646  8.093660  8.160160  8.192485
[22]  8.169954  8.275601  8.271535  9.954141 10.393102 10.701206 10.735407

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1]  66.59593  82.25167  61.70023  33.48154 110.81632 116.89753 115.12746
 [8] 106.98304  82.54105  71.43161  63.20205  47.65012  53.76628  70.01274
[15]  46.99358  16.47357 102.97680  88.52243  94.11578  87.31769  69.82457
[22]  72.12810  65.36788  45.74259  43.51097  64.12541  39.36409  11.39753
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1]  89.57825 106.08042  87.61053  59.60143 136.85840 143.69225 141.89517
 [8] 133.68427 109.80619  98.72029  90.46798  75.27996  83.24031 100.10526
[15]  78.36255  47.73933 134.37352 120.31616 125.84293 119.30552 101.93911
[22] 104.15433  97.80824  78.16701  82.53120 104.86637  81.31282  53.48032
> if (par2 == 0) {
+ x <- exp(x)
+ forecast$pred <- exp(forecast$pred)
+ lb <- exp(lb)
+ ub <- exp(ub)
+ }
> if (par2 != 0) {
+ x <- x^(1/par2)
+ forecast$pred <- forecast$pred^(1/par2)
+ lb <- lb^(1/par2)
+ ub <- ub^(1/par2)
+ }
> if (par2 < 0) {
+ olb <- lb
+ lb <- ub
+ ub <- olb
+ }
> (actandfor <- c(x[1:nx], forecast$pred))
 [1] 152.60000 153.32000 165.50000 139.18000 136.53000 115.92000  96.65000
 [8]  83.77000  84.66000 106.03000  86.92000  54.66000 151.66000 121.27000
[15] 132.95000 119.64000 122.16000 117.44000 106.69000  87.45000  80.98000
[22] 110.30000  87.01000  55.73000 146.00000 137.54000 138.54000 135.62000
[29] 107.27000  99.04000  91.36000  68.35000  82.59000  98.41000  71.25000
[36]  47.58000 130.83000 113.60000 125.69000 113.60000  97.12000 104.43000
[43]  91.84000  75.11000  78.08709  94.16604  74.65538  46.54149 123.83736
[50] 130.29489 128.51132 120.33365  96.17362  85.07595  76.83501  61.46504
[57]  68.50329  85.05900  62.67807  32.10645 118.67516 104.41929 109.97935
[64] 103.31160  85.88184  88.14122  81.58806  61.95480  63.02109  84.49589
[71]  60.33845  32.43892
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1] 0.07508076 0.06455365 0.08853707 0.14316772 0.05364607 0.05246089
 [7] 0.05313538 0.05660545 0.07232121 0.08182568 0.09052637 0.11467379
[13] 0.10975947 0.09025104 0.12767286 0.24842239 0.06748985 0.07767383
[19] 0.07359254 0.07898590 0.09539252 0.09269165 0.10143153 0.13350919
[25] 0.15794937 0.12300127 0.17735302 0.33094215
> postscript(file="/var/www/html/rcomp/tmp/1mxjs1261336931.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$pred , lwd=2 , col ='white')
> box()
> par(opar)
> dev.off()
null device 
          1 
> prob.dec <- array(NA, dim=fx)
> prob.sdec <- array(NA, dim=fx)
> prob.ldec <- array(NA, dim=fx)
> prob.pval <- array(NA, dim=fx)
> perf.pe <- array(0, dim=fx)
> perf.mape <- array(0, dim=fx)
> perf.mape1 <- array(0, dim=fx)
> perf.se <- array(0, dim=fx)
> perf.mse <- array(0, dim=fx)
> perf.mse1 <- array(0, dim=fx)
> perf.rmse <- array(0, dim=fx)
> for (i in 1:fx) {
+ locSD <- (ub[i] - forecast$pred[i]) / 1.96
+ perf.pe[i] = (x[nx+i] - forecast$pred[i]) / forecast$pred[i]
+ perf.se[i] = (x[nx+i] - forecast$pred[i])^2
+ prob.dec[i] = pnorm((x[nx+i-1] - forecast$pred[i]) / locSD)
+ prob.sdec[i] = pnorm((x[nx+i-par5] - forecast$pred[i]) / locSD)
+ prob.ldec[i] = pnorm((x[nx] - forecast$pred[i]) / locSD)
+ prob.pval[i] = pnorm(abs(x[nx+i] - forecast$pred[i]) / locSD)
+ }
> perf.mape[1] = abs(perf.pe[1])
> perf.mse[1] = abs(perf.se[1])
> for (i in 2:fx) {
+ perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i])
+ perf.mape1[i] = perf.mape[i] / i
+ perf.mse[i] = perf.mse[i-1] + perf.se[i]
+ perf.mse1[i] = perf.mse[i] / i
+ }
> perf.rmse = sqrt(perf.mse1)
> postscript(file="/var/www/html/rcomp/tmp/2hezq1261336931.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> plot(forecast$pred, pch=19, type='b',main='ARIMA Extrapolation Forecast', ylab='Forecast and 95% CI', xlab='time',ylim=c(min(lb),max(ub)))
> dum <- forecast$pred
> dum[1:par1] <- x[(nx+1):lx]
> lines(dum, lty=1)
> lines(ub,lty=3)
> lines(lb,lty=3)
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Univariate ARIMA Extrapolation Forecast',9,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'time',1,header=TRUE)
> a<-table.element(a,'Y[t]',1,header=TRUE)
> a<-table.element(a,'F[t]',1,header=TRUE)
> a<-table.element(a,'95% LB',1,header=TRUE)
> a<-table.element(a,'95% UB',1,header=TRUE)
> a<-table.element(a,'p-value<br />(H0: Y[t] = F[t])',1,header=TRUE)
> a<-table.element(a,'P(F[t]>Y[t-1])',1,header=TRUE)
> a<-table.element(a,'P(F[t]>Y[t-s])',1,header=TRUE)
> mylab <- paste('P(F[t]>Y[',nx,sep='')
> mylab <- paste(mylab,'])',sep='')
> a<-table.element(a,mylab,1,header=TRUE)
> a<-table.row.end(a)
> for (i in (nx-par5):nx) {
+ a<-table.row.start(a)
+ a<-table.element(a,i,header=TRUE)
+ a<-table.element(a,x[i])
+ a<-table.element(a,'-')
+ a<-table.element(a,'-')
+ a<-table.element(a,'-')
+ a<-table.element(a,'-')
+ a<-table.element(a,'-')
+ a<-table.element(a,'-')
+ a<-table.element(a,'-')
+ a<-table.row.end(a)
+ }
> for (i in 1:fx) {
+ a<-table.row.start(a)
+ a<-table.element(a,nx+i,header=TRUE)
+ a<-table.element(a,round(x[nx+i],4))
+ a<-table.element(a,round(forecast$pred[i],4))
+ a<-table.element(a,round(lb[i],4))
+ a<-table.element(a,round(ub[i],4))
+ a<-table.element(a,round((1-prob.pval[i]),4))
+ a<-table.element(a,round((1-prob.dec[i]),4))
+ a<-table.element(a,round((1-prob.sdec[i]),4))
+ a<-table.element(a,round((1-prob.ldec[i]),4))
+ a<-table.row.end(a)
+ }
> a<-table.end(a)
> table.save(a,file="/var/www/html/rcomp/tmp/3akg91261336931.tab") 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Univariate ARIMA Extrapolation Forecast Performance',7,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'time',1,header=TRUE)
> a<-table.element(a,'% S.E.',1,header=TRUE)
> a<-table.element(a,'PE',1,header=TRUE)
> a<-table.element(a,'MAPE',1,header=TRUE)
> a<-table.element(a,'Sq.E',1,header=TRUE)
> a<-table.element(a,'MSE',1,header=TRUE)
> a<-table.element(a,'RMSE',1,header=TRUE)
> a<-table.row.end(a)
> for (i in 1:fx) {
+ a<-table.row.start(a)
+ a<-table.element(a,nx+i,header=TRUE)
+ a<-table.element(a,round(perc.se[i],4))
+ a<-table.element(a,round(perf.pe[i],4))
+ a<-table.element(a,round(perf.mape1[i],4))
+ a<-table.element(a,round(perf.se[i],4))
+ a<-table.element(a,round(perf.mse1[i],4))
+ a<-table.element(a,round(perf.rmse[i],4))
+ a<-table.row.end(a)
+ }
> a<-table.end(a)
> table.save(a,file="/var/www/html/rcomp/tmp/4xtsq1261336931.tab") 
> 
> try(system("convert tmp/1mxjs1261336931.ps tmp/1mxjs1261336931.png",intern=TRUE))
character(0)
> try(system("convert tmp/2hezq1261336931.ps tmp/2hezq1261336931.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.591   0.357   4.217