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(595.130,526.883,562.254,545.427,522.084,483.414,528.797,532.749,511.380,472.941,516.118,502.940,476.118,432.418,475.525,453.638,431.417,390.934,436.414,418.451,399.528,367.749,423.433,420.450,415.906,392.949,453.203,455.926,451.879,434.996,498.811,505.940,517.395,508.456,585.132,587.971,584.027,557.196,613.433,600.049,588.993,559.271,622.580,616.645,603.243,557.949,608.882,582.930,570.492,542.907,598.067,568.717,551.773,514.465,569.055,528.897,515.229,481.141,535.612,498.547,478.587,445.911,503.412,469.797,458.365,436.761,502.205,481.627,473.698,457.200,521.671,513.354,515.369,505.652,575.676,555.865,559.504,540.994,605.635,600.315,588.224,569.861,625.950,601.554,587.760,573.307,621.764,570.214,547.034,511.873,553.870,517.058,505.702,479.060,526.638,508.060,532.394,532.115,587.896,565.710,572.708,544.417,597.160)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '1'
> par5 = '4'
> par4 = '1'
> par3 = '2'
> par2 = '1'
> par1 = '12'
> #'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#output/
> #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      ma1     sma1
      0.0190  -0.4503  -0.5182
s.e.  0.3049   0.2879   0.1041

sigma^2 estimated as 70.32:  log likelihood = -306.03,  aic = 620.06
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 92 
End = 103 
Frequency = 1 
 [1] 504.4447 472.9530 432.4026 465.8805 409.1033 370.2818 322.4021 348.5508
 [9] 284.4443 238.2935 183.0845 201.9038

$se
Time Series:
Start = 92 
End = 103 
Frequency = 1 
 [1]   8.385476  15.600114  23.710226  32.724321  45.278821  59.298702
 [7]  74.594168  91.054688 110.850315 132.443741 155.620460 180.241864

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 92 
End = 103 
Frequency = 1 
 [1]  488.00917  442.37675  385.93053  401.74083  320.35681  254.05638
 [7]  176.19756  170.08357   67.17764  -21.29623 -121.93161 -151.37023
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 92 
End = 103 
Frequency = 1 
 [1] 520.8802 503.5292 478.8746 530.0202 497.8498 486.5073 468.6067 527.0179
 [9] 501.7109 497.8832 488.1006 555.1779
> 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$pred))
  [1] 595.1300 526.8830 562.2540 545.4270 522.0840 483.4140 528.7970 532.7490
  [9] 511.3800 472.9410 516.1180 502.9400 476.1180 432.4180 475.5250 453.6380
 [17] 431.4170 390.9340 436.4140 418.4510 399.5280 367.7490 423.4330 420.4500
 [25] 415.9060 392.9490 453.2030 455.9260 451.8790 434.9960 498.8110 505.9400
 [33] 517.3950 508.4560 585.1320 587.9710 584.0270 557.1960 613.4330 600.0490
 [41] 588.9930 559.2710 622.5800 616.6450 603.2430 557.9490 608.8820 582.9300
 [49] 570.4920 542.9070 598.0670 568.7170 551.7730 514.4650 569.0550 528.8970
 [57] 515.2290 481.1410 535.6120 498.5470 478.5870 445.9110 503.4120 469.7970
 [65] 458.3650 436.7610 502.2050 481.6270 473.6980 457.2000 521.6710 513.3540
 [73] 515.3690 505.6520 575.6760 555.8650 559.5040 540.9940 605.6350 600.3150
 [81] 588.2240 569.8610 625.9500 601.5540 587.7600 573.3070 621.7640 570.2140
 [89] 547.0340 511.8730 553.8700 504.4447 472.9530 432.4026 465.8805 409.1033
 [97] 370.2818 322.4021 348.5508 284.4443 238.2935 183.0845 201.9038
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 92 
End = 103 
Frequency = 1 
 [1] 0.01662318 0.03298449 0.05483368 0.07024188 0.11067821 0.16014478
 [7] 0.23136996 0.26123796 0.38970840 0.55580090 0.84999260 0.89271150
> postscript(file="/var/www/html/rcomp/tmp/1ot7o1293559570.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2vu4i1293559570.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/3kd1u1293559570.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/4ne001293559570.tab") 
> 
> try(system("convert tmp/1ot7o1293559570.ps tmp/1ot7o1293559570.png",intern=TRUE))
character(0)
> try(system("convert tmp/2vu4i1293559570.ps tmp/2vu4i1293559570.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.631   0.340   2.112