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(15
+ ,14.4
+ ,13.5
+ ,12.8
+ ,12.3
+ ,12.2
+ ,14.5
+ ,17.2
+ ,18
+ ,18.1
+ ,18
+ ,18.3
+ ,18.7
+ ,18.6
+ ,18.3
+ ,17.9
+ ,17.4
+ ,17.4
+ ,20.1
+ ,23.2
+ ,24.2
+ ,24.2
+ ,23.9
+ ,23.8
+ ,23.8
+ ,23.3
+ ,22.4
+ ,21.5
+ ,20.5
+ ,19.9
+ ,22
+ ,24.9
+ ,25.7
+ ,25.3
+ ,24.4
+ ,23.8
+ ,23.5
+ ,23
+ ,22.2
+ ,21.4
+ ,20.3
+ ,19.5
+ ,21.7
+ ,24.7
+ ,25.3
+ ,24.9
+ ,24.1
+ ,23.4
+ ,23.1
+ ,22.4
+ ,21.3
+ ,20.3
+ ,19.3
+ ,18.7
+ ,21
+ ,24
+ ,24.8
+ ,24.2
+ ,23.3
+ ,22.7
+ ,22.3
+ ,21.8
+ ,21.2
+ ,20.5
+ ,19.7
+ ,19.2
+ ,21.2
+ ,23.9
+ ,24.8
+ ,24.2
+ ,23
+ ,22.2
+ ,21.8
+ ,21.2
+ ,20.5
+ ,19.7
+ ,19
+ ,18.4
+ ,20.7
+ ,24.5
+ ,26
+ ,25.2
+ ,24.1
+ ,23.7
+ ,23.5
+ ,23.1
+ ,22.7
+ ,22.5
+ ,21.7
+ ,20.5
+ ,21.9
+ ,22.9
+ ,21.5
+ ,19
+ ,17
+ ,16.1
+ ,15.9
+ ,15.7
+ ,15.1
+ ,14.8
+ ,14.3
+ ,14.5
+ ,18.9
+ ,21.6
+ ,20.4
+ ,17.9
+ ,15.7
+ ,14.5
+ ,14
+ ,13.9
+ ,14.4
+ ,15.8
+ ,15.6
+ ,14.7
+ ,16.7
+ ,17.9
+ ,18.7
+ ,20.1
+ ,19.5
+ ,19.4
+ ,18.6
+ ,17.8
+ ,17.1
+ ,16.5
+ ,15.5
+ ,14.9
+ ,18.6
+ ,19.1
+ ,18.8
+ ,18.2
+ ,18
+ ,19
+ ,20.7
+ ,21.2
+ ,20.7
+ ,19.6
+ ,18.6
+ ,18.7
+ ,23.8
+ ,24.9
+ ,24.8
+ ,23.8
+ ,22.3
+ ,21.7
+ ,20.7
+ ,19.7
+ ,18.4
+ ,17.4
+ ,17
+ ,18
+ ,23.8
+ ,25.5
+ ,25.6
+ ,23.7
+ ,22
+ ,21.3
+ ,20.7
+ ,20.4
+ ,20.3
+ ,20.4
+ ,19.8
+ ,19.5
+ ,23.1
+ ,23.5
+ ,23.5
+ ,22.9
+ ,21.9
+ ,21.5
+ ,20.5
+ ,20.2
+ ,19.4
+ ,19.2
+ ,18.8
+ ,18.8
+ ,22.6
+ ,23.3
+ ,23
+ ,21.4
+ ,19.9
+ ,18.8
+ ,18.6
+ ,18.4
+ ,18.6
+ ,19.9
+ ,19.2
+ ,18.4
+ ,21.1
+ ,20.5
+ ,19.1
+ ,18.1
+ ,17
+ ,17.1
+ ,17.4
+ ,16.8
+ ,15.3
+ ,14.3
+ ,13.4
+ ,15.3
+ ,22.1
+ ,23.7
+ ,22.2
+ ,19.5
+ ,16.6
+ ,17.3
+ ,19.8
+ ,21.2
+ ,21.5
+ ,20.6
+ ,19.1
+ ,19.6
+ ,23.5
+ ,24
+ ,23.2
+ ,21.2)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '0'
> par6 = '3'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> par1 = '12'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> par1 <- as.numeric(par1) #cut off periods
> 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
> par7 <- as.numeric(par7) #q
> 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     sma1
      0.8278  -0.2916  -0.2078  -0.3928
s.e.  0.0740   0.0930   0.0722   0.0758

sigma^2 estimated as 0.3491:  log likelihood = -170.37,  aic = 350.74
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 203 
End = 214 
Frequency = 1 
 [1] 16.81525 15.90152 16.13593 16.35015 16.01630 15.96102 15.07874 15.75249
 [9] 20.86784 21.69134 20.45936 18.49953

$se
Time Series:
Start = 203 
End = 214 
Frequency = 1 
 [1] 0.5908204 1.2309315 1.7993212 2.1848975 2.4068857 2.5339438 2.6274313
 [8] 2.7256011 2.8473258 2.9912871 3.1412107 3.2805600

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 203 
End = 214 
Frequency = 1 
 [1] 15.65724 13.48889 12.60926 12.06775 11.29881 10.99449  9.92898 10.41031
 [9] 15.28708 15.82842 14.30259 12.06963
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 203 
End = 214 
Frequency = 1 
 [1] 17.97326 18.31414 19.66260 20.63255 20.73380 20.92755 20.22851 21.09467
 [9] 26.44860 27.55426 26.61613 24.92943
> 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] 15.00000 14.40000 13.50000 12.80000 12.30000 12.20000 14.50000 17.20000
  [9] 18.00000 18.10000 18.00000 18.30000 18.70000 18.60000 18.30000 17.90000
 [17] 17.40000 17.40000 20.10000 23.20000 24.20000 24.20000 23.90000 23.80000
 [25] 23.80000 23.30000 22.40000 21.50000 20.50000 19.90000 22.00000 24.90000
 [33] 25.70000 25.30000 24.40000 23.80000 23.50000 23.00000 22.20000 21.40000
 [41] 20.30000 19.50000 21.70000 24.70000 25.30000 24.90000 24.10000 23.40000
 [49] 23.10000 22.40000 21.30000 20.30000 19.30000 18.70000 21.00000 24.00000
 [57] 24.80000 24.20000 23.30000 22.70000 22.30000 21.80000 21.20000 20.50000
 [65] 19.70000 19.20000 21.20000 23.90000 24.80000 24.20000 23.00000 22.20000
 [73] 21.80000 21.20000 20.50000 19.70000 19.00000 18.40000 20.70000 24.50000
 [81] 26.00000 25.20000 24.10000 23.70000 23.50000 23.10000 22.70000 22.50000
 [89] 21.70000 20.50000 21.90000 22.90000 21.50000 19.00000 17.00000 16.10000
 [97] 15.90000 15.70000 15.10000 14.80000 14.30000 14.50000 18.90000 21.60000
[105] 20.40000 17.90000 15.70000 14.50000 14.00000 13.90000 14.40000 15.80000
[113] 15.60000 14.70000 16.70000 17.90000 18.70000 20.10000 19.50000 19.40000
[121] 18.60000 17.80000 17.10000 16.50000 15.50000 14.90000 18.60000 19.10000
[129] 18.80000 18.20000 18.00000 19.00000 20.70000 21.20000 20.70000 19.60000
[137] 18.60000 18.70000 23.80000 24.90000 24.80000 23.80000 22.30000 21.70000
[145] 20.70000 19.70000 18.40000 17.40000 17.00000 18.00000 23.80000 25.50000
[153] 25.60000 23.70000 22.00000 21.30000 20.70000 20.40000 20.30000 20.40000
[161] 19.80000 19.50000 23.10000 23.50000 23.50000 22.90000 21.90000 21.50000
[169] 20.50000 20.20000 19.40000 19.20000 18.80000 18.80000 22.60000 23.30000
[177] 23.00000 21.40000 19.90000 18.80000 18.60000 18.40000 18.60000 19.90000
[185] 19.20000 18.40000 21.10000 20.50000 19.10000 18.10000 17.00000 17.10000
[193] 17.40000 16.80000 15.30000 14.30000 13.40000 15.30000 22.10000 23.70000
[201] 22.20000 19.50000 16.81525 15.90152 16.13593 16.35015 16.01630 15.96102
[209] 15.07874 15.75249 20.86784 21.69134 20.45936 18.49953
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 203 
End = 214 
Frequency = 1 
 [1] 0.03513598 0.07740969 0.11151021 0.13363165 0.15027724 0.15875826
 [7] 0.17424735 0.17302671 0.13644563 0.13790237 0.15353417 0.17733210
> postscript(file="/var/www/html/rcomp/tmp/1hrei1262216805.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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.se <- array(0, dim=fx)
> perf.mse <- 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$pred[i]
+ perf.mape[i] = perf.mape[i] + abs(perf.pe[i])
+ perf.se[i] = (x[nx+i] - forecast$pred[i])^2
+ perf.mse[i] = perf.mse[i] + perf.se[i]
+ 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 = perf.mape / fx
> perf.mse = perf.mse / fx
> perf.rmse = sqrt(perf.mse)
> postscript(file="/var/www/html/rcomp/tmp/2y3b21262216805.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[1:12] <- 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/3du241262216805.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.mape[i],4))
+ a<-table.element(a,round(perf.se[i],4))
+ a<-table.element(a,round(perf.mse[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/4zbx01262216805.tab") 
> try(system("convert tmp/1hrei1262216805.ps tmp/1hrei1262216805.png",intern=TRUE))
character(0)
> try(system("convert tmp/2y3b21262216805.ps tmp/2y3b21262216805.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.040   0.348   1.604