R version 2.12.0 (2010-10-15)
Copyright (C) 2010 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: x86_64-redhat-linux-gnu (64-bit)

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> x <- c(621,587,655,517,646,657,382,345,625,654,606,510,614,647,580,614,636,388,356,639,753,611,639,630,586,695,552,619,681,421,307,754,690,644,643,608,651,691,627,634,731,475,337,803,722,590,724,627,696,825,677,656,785,412,352,839,729,696,641,695,638,762,635,721,854,418,367,824,687,601,676,740,691,683,594,729,731,386,331,706,715,657,653,642,643,718,654,632,731,392,344,792,852,649,629,685,617,715,715,629,916,531,357,917,828,708,858,775,785,1006,789,734,906,532,387,991,841,892,782,813,793,978,775,797,946,594,438,1022,868,795)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '2'
> par7 = '1'
> par6 = '3'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> par2 = '-0.5'
> 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      ar2     ar3      ma1     sar1     sar2    sma1
      0.8983  -0.3413  0.3585  -0.7954  -0.5604  -0.3788  0.2979
s.e.  0.1503   0.1297  0.1005   0.1316   0.4950   0.1433  0.5311

sigma^2 estimated as 6.219e-06:  log likelihood = 428.14,  aic = -840.28
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 107 
End = 130 
Frequency = 1 
 [1] 0.03792667 0.03704950 0.03845524 0.03661557 0.03757514 0.03825936
 [7] 0.03354579 0.04480598 0.05305924 0.03388865 0.03483568 0.03707974
[13] 0.03776504 0.03746538 0.03836467 0.03620907 0.03740433 0.03847824
[19] 0.03412691 0.04610794 0.05280135 0.03383245 0.03410798 0.03752850

$se
Time Series:
Start = 107 
End = 130 
Frequency = 1 
 [1] 0.002493846 0.002507023 0.002582702 0.002594661 0.002647717 0.002652938
 [7] 0.002653585 0.002660021 0.002667967 0.002671781 0.002674670 0.002678159
[13] 0.003325191 0.003339184 0.003357415 0.003369778 0.003404902 0.003411652
[19] 0.003414112 0.003421067 0.003428693 0.003433275 0.003436975 0.003440916

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 107 
End = 130 
Frequency = 1 
 [1] 0.03303873 0.03213574 0.03339314 0.03153003 0.03238561 0.03305960
 [7] 0.02834476 0.03959233 0.04783003 0.02865196 0.02959332 0.03183054
[13] 0.03124766 0.03092058 0.03178413 0.02960430 0.03073072 0.03179141
[19] 0.02743525 0.03940265 0.04608111 0.02710323 0.02737151 0.03078430
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 107 
End = 130 
Frequency = 1 
 [1] 0.04281460 0.04196327 0.04351733 0.04170110 0.04276467 0.04345912
 [7] 0.03874682 0.05001962 0.05828846 0.03912534 0.04007803 0.04232893
[13] 0.04428241 0.04401018 0.04494520 0.04281383 0.04407794 0.04516508
[19] 0.04081857 0.05281324 0.05952159 0.04056167 0.04084446 0.04427269
> 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$pred))
  [1] 621.0000 587.0000 655.0000 517.0000 646.0000 657.0000 382.0000 345.0000
  [9] 625.0000 654.0000 606.0000 510.0000 614.0000 647.0000 580.0000 614.0000
 [17] 636.0000 388.0000 356.0000 639.0000 753.0000 611.0000 639.0000 630.0000
 [25] 586.0000 695.0000 552.0000 619.0000 681.0000 421.0000 307.0000 754.0000
 [33] 690.0000 644.0000 643.0000 608.0000 651.0000 691.0000 627.0000 634.0000
 [41] 731.0000 475.0000 337.0000 803.0000 722.0000 590.0000 724.0000 627.0000
 [49] 696.0000 825.0000 677.0000 656.0000 785.0000 412.0000 352.0000 839.0000
 [57] 729.0000 696.0000 641.0000 695.0000 638.0000 762.0000 635.0000 721.0000
 [65] 854.0000 418.0000 367.0000 824.0000 687.0000 601.0000 676.0000 740.0000
 [73] 691.0000 683.0000 594.0000 729.0000 731.0000 386.0000 331.0000 706.0000
 [81] 715.0000 657.0000 653.0000 642.0000 643.0000 718.0000 654.0000 632.0000
 [89] 731.0000 392.0000 344.0000 792.0000 852.0000 649.0000 629.0000 685.0000
 [97] 617.0000 715.0000 715.0000 629.0000 916.0000 531.0000 357.0000 917.0000
[105] 828.0000 708.0000 695.2014 728.5095 676.2216 745.8792 708.2699 683.1635
[113] 888.6360 498.1133 355.2040 870.7459 824.0461 727.3220 701.1649 712.4260
[121] 679.4182 762.7203 714.7535 675.4131 858.6302 470.3796 358.6823 873.6412
[129] 859.5831 710.0315
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 107 
End = 130 
Frequency = 1 
 [1] 0.1621323 0.1679558 0.1664090 0.1778565 0.1766126 0.1731158 0.2044145
 [8] 0.1432177 0.1176587 0.2035421 0.1967723 0.1821513 0.2350231 0.2388428
[15] 0.2331335 0.2530497 0.2456573 0.2371991 0.2792375 0.1884216 0.1596621
[22] 0.2847988 0.2820390 0.2480376
> postscript(file="/var/www/wessaorg/rcomp/tmp/1jf011293651945.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/wessaorg/rcomp/tmp/2qgfv1293651945.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/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/wessaorg/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/wessaorg/rcomp/tmp/3xzu71293651945.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/wessaorg/rcomp/tmp/4ihtd1293651945.tab") 
> try(system("convert tmp/1jf011293651945.ps tmp/1jf011293651945.png",intern=TRUE))
character(0)
> try(system("convert tmp/2qgfv1293651945.ps tmp/2qgfv1293651945.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
   3.46    0.55    4.07