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(20503,22885,26217,26583,27751,28158,27373,28367,26851,26733,26849,26733,27951,29781,32914,33488,35652,36488,35387,35676,34844,32447,31068,29010,29812,30951,32974,32936,34012,32946,31948,30599,27691,25073,23406,22248,22896,25317,26558,26471,27543,26198,24725,25005,23462,20780,19815,19761,21454,23899,24939,23580,24562,24696,23785,23812,21917,19713,19282,18788,21453,24482,27474,27264,27349,30632,29429,30084,26290,24379,23335,21346,21106,24514,28353,30805,31348,34556,33855,34787,32529,29998,29257,28155,30466,35704,39327,39351,42234,43630,43722,43121,37985,37135,34646,33026,35087,38846,42013,43908,42868,44423,44167,43636,44382,42142,43452,36912,42413,45344,44873,47510,49554,47369,45998,48140,48441,44928,40454,38661,37246,36843,36424,37594,38144,38737,34560,36080,33508,35462,33374,32110,35533,35532,37903,36763,40399,44164,44496,43110,43880,43930,44327)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '0'
> par5 = '12'
> 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/
> #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:
          ma1     sma1
      -0.9238  -0.8760
s.e.   0.0438   0.1933

sigma^2 estimated as 2521930:  log likelihood = -1040.88,  aic = 2087.76
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 132 
End = 143 
Frequency = 1 
 [1] 31089.55 32272.44 34413.39 35954.13 36418.02 37033.08 37251.43 35552.16
 [9] 35670.12 33388.70 31394.61 29594.32

$se
Time Series:
Start = 132 
End = 143 
Frequency = 1 
 [1] 1602.541 2354.808 2993.428 3584.994 4153.251 4709.798 5261.174 5811.404
 [9] 6363.116 6918.098 7477.606 8042.539

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 132 
End = 143 
Frequency = 1 
 [1] 27948.57 27657.02 28546.27 28927.54 28277.65 27801.87 26939.53 24161.81
 [9] 23198.41 19829.22 16738.50 13830.95
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 132 
End = 143 
Frequency = 1 
 [1] 34230.53 36887.87 40280.51 42980.72 44558.39 46264.28 47563.33 46942.52
 [9] 48141.83 46948.17 46050.72 45357.70
> 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$pred))
  [1] 20503.00 22885.00 26217.00 26583.00 27751.00 28158.00 27373.00 28367.00
  [9] 26851.00 26733.00 26849.00 26733.00 27951.00 29781.00 32914.00 33488.00
 [17] 35652.00 36488.00 35387.00 35676.00 34844.00 32447.00 31068.00 29010.00
 [25] 29812.00 30951.00 32974.00 32936.00 34012.00 32946.00 31948.00 30599.00
 [33] 27691.00 25073.00 23406.00 22248.00 22896.00 25317.00 26558.00 26471.00
 [41] 27543.00 26198.00 24725.00 25005.00 23462.00 20780.00 19815.00 19761.00
 [49] 21454.00 23899.00 24939.00 23580.00 24562.00 24696.00 23785.00 23812.00
 [57] 21917.00 19713.00 19282.00 18788.00 21453.00 24482.00 27474.00 27264.00
 [65] 27349.00 30632.00 29429.00 30084.00 26290.00 24379.00 23335.00 21346.00
 [73] 21106.00 24514.00 28353.00 30805.00 31348.00 34556.00 33855.00 34787.00
 [81] 32529.00 29998.00 29257.00 28155.00 30466.00 35704.00 39327.00 39351.00
 [89] 42234.00 43630.00 43722.00 43121.00 37985.00 37135.00 34646.00 33026.00
 [97] 35087.00 38846.00 42013.00 43908.00 42868.00 44423.00 44167.00 43636.00
[105] 44382.00 42142.00 43452.00 36912.00 42413.00 45344.00 44873.00 47510.00
[113] 49554.00 47369.00 45998.00 48140.00 48441.00 44928.00 40454.00 38661.00
[121] 37246.00 36843.00 36424.00 37594.00 38144.00 38737.00 34560.00 36080.00
[129] 33508.00 35462.00 33374.00 31089.55 32272.44 34413.39 35954.13 36418.02
[137] 37033.08 37251.43 35552.16 35670.12 33388.70 31394.61 29594.32
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 132 
End = 143 
Frequency = 1 
 [1] 0.05154596 0.07296652 0.08698438 0.09971022 0.11404384 0.12717815
 [7] 0.14123416 0.16346134 0.17838784 0.20719882 0.23818121 0.27175952
> postscript(file="/var/www/wessaorg/rcomp/tmp/1vjnf1293653588.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2122r1293653588.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/3qlgl1293653588.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/4cmxr1293653588.tab") 
> 
> try(system("convert tmp/1vjnf1293653588.ps tmp/1vjnf1293653588.png",intern=TRUE))
character(0)
> try(system("convert tmp/2122r1293653588.ps tmp/2122r1293653588.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
   0.87    0.12    1.04