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(36700,35600,80900,174000,169422,153452,173570,193036,174652,105367,95963,82896,121747,120196,103983,81103,70944,57248,47830,60095,60931,82955,99559,77911,70753,69287,88426,91756,96933,174484,232595,266197,290435,304296,322310,415555,490042,545109,545720,505944,477930,466106,424476,383018,364696,391116,435721,511435,553997,555252,544897,540562,505282,507626,474427,469740,491480,538974,576612)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '0'
> par6 = '1'
> par5 = '1'
> par4 = '0'
> par3 = '2'
> par2 = '1'
> par1 = '24'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: Wessa P., (2009), ARIMA Forecasting (v1.0.5) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_arimaforecasting.wasp/
> #Source of accompanying publication: 
> #Technical description: 
> 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     sma1
      0.4189  -1.0000
s.e.  0.1631   0.1986

sigma^2 estimated as 796375846:  log likelihood = -386.34,  aic = 778.68
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 36 
End = 59 
Frequency = 1 
 [1] 334738.5 344827.5 353936.5 362634.9 371161.5 379616.0 388040.4 396452.1
 [9] 404858.5 413262.7 421666.0 430068.9 438471.6 446874.2 455276.9 463679.5
[17] 472082.1 480484.7 488887.3 497289.9 505692.5 514095.1 522497.7 530900.3

$se
Time Series:
Start = 36 
End = 59 
Frequency = 1 
 [1]  28615.23  50309.66  69178.98  85814.88 100798.69 114570.94 127442.66
 [8] 139630.57 151287.08 162521.40 173413.50 184023.32 194396.74 204569.59
[15] 214570.34 224421.98 234143.31 243749.93 253254.89 262669.22 272002.34
[22] 281262.33 290456.17 299589.98

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 36 
End = 59 
Frequency = 1 
 [1] 278652.701 246220.568 218345.662 194437.776 173596.049 155056.955
 [7] 138252.738 122776.150 108335.808  94720.758  81775.514  69383.150
[13]  57453.964  45917.832  34718.987  23812.395  13161.189   2734.821
[19]  -7492.291 -17541.777 -27432.079 -37179.045 -46796.383 -56296.028
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 36 
End = 59 
Frequency = 1 
 [1]  390824.4  443434.4  489527.3  530832.1  568726.9  604175.1  637828.0
 [8]  670128.0  701381.2  731804.6  761556.4  790754.6  819489.2  847830.6
[15]  875834.7  903546.6  931003.0  958234.6  985266.9 1012121.6 1038817.1
[22] 1065369.3 1091791.8 1118096.7
> 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$pred))
 [1]  36700.0  35600.0  80900.0 174000.0 169422.0 153452.0 173570.0 193036.0
 [9] 174652.0 105367.0  95963.0  82896.0 121747.0 120196.0 103983.0  81103.0
[17]  70944.0  57248.0  47830.0  60095.0  60931.0  82955.0  99559.0  77911.0
[25]  70753.0  69287.0  88426.0  91756.0  96933.0 174484.0 232595.0 266197.0
[33] 290435.0 304296.0 322310.0 334738.5 344827.5 353936.5 362634.9 371161.5
[41] 379616.0 388040.4 396452.1 404858.5 413262.7 421666.0 430068.9 438471.6
[49] 446874.2 455276.9 463679.5 472082.1 480484.7 488887.3 497289.9 505692.5
[57] 514095.1 522497.7 530900.3
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 36 
End = 59 
Frequency = 1 
 [1] 0.0854853 0.1458980 0.1954559 0.2366426 0.2715764 0.3018075 0.3284263
 [8] 0.3522004 0.3736789 0.3932641 0.4112580 0.4278927 0.4433508 0.4577789
[15] 0.4712964 0.4840024 0.4959801 0.5073001 0.5180231 0.5282014 0.5378809
[22] 0.5471017 0.5558994 0.5643055
> postscript(file="/var/www/html/rcomp/tmp/1zbjd1292772650.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/26uy71292772650.ps",horizontal=F,onefile=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/3vvdj1292772650.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/4gwc71292772650.tab") 
> 
> try(system("convert tmp/1zbjd1292772650.ps tmp/1zbjd1292772650.png",intern=TRUE))
character(0)
> try(system("convert tmp/26uy71292772650.ps tmp/26uy71292772650.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.633   0.333   1.323