R version 2.7.0 (2008-04-22)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> x <- c(9005.73
+ ,9018.68
+ ,9349.44
+ ,9327.78
+ ,9753.63
+ ,10443.5
+ ,10853.87
+ ,10704.02
+ ,11052.23
+ ,10935.47
+ ,10714.03
+ ,10394.48
+ ,10817.9
+ ,11251.2
+ ,11281.26
+ ,10539.68
+ ,10483.39
+ ,10947.43
+ ,10580.27
+ ,10582.92
+ ,10654.41
+ ,11014.51
+ ,10967.87
+ ,10433.56
+ ,10665.78
+ ,10666.71
+ ,10682.74
+ ,10777.22
+ ,10052.6
+ ,10213.97
+ ,10546.82
+ ,10767.2
+ ,10444.5
+ ,10314.68
+ ,9042.56
+ ,9220.75
+ ,9721.84
+ ,9978.53
+ ,9923.81
+ ,9892.56
+ ,10500.98
+ ,10179.35
+ ,10080.48
+ ,9492.44
+ ,8616.49
+ ,8685.4
+ ,8160.67
+ ,8048.1
+ ,8641.21
+ ,8526.63
+ ,8474.21
+ ,7916.13
+ ,7977.64
+ ,8334.59
+ ,8623.36
+ ,9098.03
+ ,9154.34
+ ,9284.73
+ ,9492.49
+ ,9682.35
+ ,9762.12
+ ,10124.63
+ ,10540.05
+ ,10601.61
+ ,10323.73
+ ,10418.4
+ ,10092.96
+ ,10364.91
+ ,10152.09
+ ,10032.8
+ ,10204.59
+ ,10001.6
+ ,10411.75
+ ,10673.38
+ ,10539.51
+ ,10723.78
+ ,10682.06
+ ,10283.19
+ ,10377.18
+ ,10486.64
+ ,10545.38
+ ,10554.27
+ ,10532.54
+ ,10324.31
+ ,10695.25
+ ,10827.81
+ ,10872.48
+ ,10971.19
+ ,11145.65
+ ,11234.68
+ ,11333.88
+ ,10997.97
+ ,11036.89
+ ,11257.35
+ ,11533.59
+ ,11963.12
+ ,12185.15
+ ,12377.62
+ ,12512.89
+ ,12631.48
+ ,12268.53
+ ,12754.8
+ ,13407.75
+ ,13480.21
+ ,13673.28
+ ,13239.71
+ ,13557.69
+ ,13901.28
+ ,13200.58
+ ,13406.97
+ ,12538.12
+ ,12419.57
+ ,12193.88
+ ,12656.63
+ ,12812.48
+ ,12056.67
+ ,11322.38
+ ,11530.75
+ ,11114.08
+ ,9181.73
+ ,8614.55)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> par4 = '0'
> 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     ma1
      -0.8843  0.9885
s.e.   0.0839  0.0735

sigma^2 estimated as 111046:  log likelihood = -781.15,  aic = 1568.3
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 110 
End = 121 
Frequency = 1 
 [1] 13167.71 13196.78 13171.08 13193.80 13173.71 13191.48 13175.76 13189.66
 [9] 13177.37 13188.24 13178.63 13187.13

$se
Time Series:
Start = 110 
End = 121 
Frequency = 1 
 [1]  333.4636  496.4383  600.2602  702.1369  780.3603  860.0314  925.8937
 [8]  993.1888 1051.3585 1110.5386 1163.2938 1216.6581

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 110 
End = 121 
Frequency = 1 
 [1] 12514.13 12223.76 11994.57 11817.61 11644.20 11505.82 11361.01 11243.01
 [9] 11116.71 11011.58 10898.57 10802.48
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 110 
End = 121 
Frequency = 1 
 [1] 13821.30 14169.80 14347.59 14569.99 14703.21 14877.14 14990.52 15136.31
 [9] 15238.03 15364.89 15458.68 15571.78
> 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$pred))
  [1]  9005.73  9018.68  9349.44  9327.78  9753.63 10443.50 10853.87 10704.02
  [9] 11052.23 10935.47 10714.03 10394.48 10817.90 11251.20 11281.26 10539.68
 [17] 10483.39 10947.43 10580.27 10582.92 10654.41 11014.51 10967.87 10433.56
 [25] 10665.78 10666.71 10682.74 10777.22 10052.60 10213.97 10546.82 10767.20
 [33] 10444.50 10314.68  9042.56  9220.75  9721.84  9978.53  9923.81  9892.56
 [41] 10500.98 10179.35 10080.48  9492.44  8616.49  8685.40  8160.67  8048.10
 [49]  8641.21  8526.63  8474.21  7916.13  7977.64  8334.59  8623.36  9098.03
 [57]  9154.34  9284.73  9492.49  9682.35  9762.12 10124.63 10540.05 10601.61
 [65] 10323.73 10418.40 10092.96 10364.91 10152.09 10032.80 10204.59 10001.60
 [73] 10411.75 10673.38 10539.51 10723.78 10682.06 10283.19 10377.18 10486.64
 [81] 10545.38 10554.27 10532.54 10324.31 10695.25 10827.81 10872.48 10971.19
 [89] 11145.65 11234.68 11333.88 10997.97 11036.89 11257.35 11533.59 11963.12
 [97] 12185.15 12377.62 12512.89 12631.48 12268.53 12754.80 13407.75 13480.21
[105] 13673.28 13239.71 13557.69 13901.28 13200.58 13167.71 13196.78 13171.08
[113] 13193.80 13173.71 13191.48 13175.76 13189.66 13177.37 13188.24 13178.63
[121] 13187.13
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 110 
End = 121 
Frequency = 1 
 [1] 0.02532433 0.03761815 0.04557412 0.05321717 0.05923619 0.06519599
 [7] 0.07027249 0.07530056 0.07978514 0.08420675 0.08827123 0.09226105
> postscript(file="/var/www/html/rcomp/tmp/1oehk1229443637.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/230dp1229443637.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/3y69a1229443637.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/4zjan1229443637.tab") 
> 
> system("convert tmp/1oehk1229443637.ps tmp/1oehk1229443637.png")
> system("convert tmp/230dp1229443637.ps tmp/230dp1229443637.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.553   0.527   3.377