R version 2.8.0 (2008-10-20)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(43880,43110,44496,44164,40399,36763,37903,35532,35533,32110,33374,35462,33508,36080,34560,38737,38144,37594,36424,36843,37246,38661,40454,44928,48441,48140,45998,47369,49554,47510,44873,45344,42413,36912,43452,42142,44382,43636,44167,44423,42868,43908,42013,38846,35087,33026,34646,37135,37985,43121,43722,43630,42234,39351,39327,35704,30466,28155,29257,29998,32529,34787,33855,34556,31348,30805,28353,24514,21106,21346,23335,24379,26290,30084,29429,30632,27349,27264,27474,24482,21453,18788,19282,19713,21917,23812,23785,24696,24562,23580,24939,23899,21454,19761,19815,20780,23462,25005,24725,26198,27543,26471,26558,25317,22896,22248,23406,25073,27691,30599,31948,32946,34012,32936,32974,30951,29812,29010,31068,32447,34844,35676,35387,36488,35652,33488,32914,29781,27951)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '0'
> par6 = '0'
> par5 = '12'
> par4 = '1'
> 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: 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:
         sma1
      -0.9484
s.e.   0.4796

sigma^2 estimated as 2884807:  log likelihood = -932.18,  aic = 1868.35
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 118 
End = 129 
Frequency = 1 
 [1] 27977.11 29729.72 31118.51 32981.83 34837.83 34683.01 35747.54 34844.59
 [9] 33672.75 33159.68 31214.22 28815.33

$se
Time Series:
Start = 118 
End = 129 
Frequency = 1 
 [1] 1751.202 2476.574 3033.171 3502.404 3912.232 4283.023 4624.177 4941.836
 [9] 5240.273 5522.607 5791.193 6047.862

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 118 
End = 129 
Frequency = 1 
 [1] 24544.75 24875.64 25173.49 26117.12 27169.86 26288.28 26684.15 25158.59
 [9] 23401.82 22335.37 19863.48 16961.52
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 118 
End = 129 
Frequency = 1 
 [1] 31409.47 34583.81 37063.52 39846.54 42505.81 43077.73 44810.92 44530.58
 [9] 43943.69 43983.99 42564.96 40669.14
> 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$pred))
  [1] 43880.00 43110.00 44496.00 44164.00 40399.00 36763.00 37903.00 35532.00
  [9] 35533.00 32110.00 33374.00 35462.00 33508.00 36080.00 34560.00 38737.00
 [17] 38144.00 37594.00 36424.00 36843.00 37246.00 38661.00 40454.00 44928.00
 [25] 48441.00 48140.00 45998.00 47369.00 49554.00 47510.00 44873.00 45344.00
 [33] 42413.00 36912.00 43452.00 42142.00 44382.00 43636.00 44167.00 44423.00
 [41] 42868.00 43908.00 42013.00 38846.00 35087.00 33026.00 34646.00 37135.00
 [49] 37985.00 43121.00 43722.00 43630.00 42234.00 39351.00 39327.00 35704.00
 [57] 30466.00 28155.00 29257.00 29998.00 32529.00 34787.00 33855.00 34556.00
 [65] 31348.00 30805.00 28353.00 24514.00 21106.00 21346.00 23335.00 24379.00
 [73] 26290.00 30084.00 29429.00 30632.00 27349.00 27264.00 27474.00 24482.00
 [81] 21453.00 18788.00 19282.00 19713.00 21917.00 23812.00 23785.00 24696.00
 [89] 24562.00 23580.00 24939.00 23899.00 21454.00 19761.00 19815.00 20780.00
 [97] 23462.00 25005.00 24725.00 26198.00 27543.00 26471.00 26558.00 25317.00
[105] 22896.00 22248.00 23406.00 25073.00 27691.00 30599.00 31948.00 32946.00
[113] 34012.00 32936.00 32974.00 30951.00 29812.00 27977.11 29729.72 31118.51
[121] 32981.83 34837.83 34683.01 35747.54 34844.59 33672.75 33159.68 31214.22
[129] 28815.33
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 118 
End = 129 
Frequency = 1 
 [1] 0.06259410 0.08330296 0.09747160 0.10619193 0.11229838 0.12349052
 [7] 0.12935652 0.14182506 0.15562356 0.16654584 0.18553058 0.20988352
> postscript(file="/var/www/html/freestat/rcomp/tmp/1ut721292923192.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/freestat/rcomp/tmp/2t4p81292923193.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/freestat/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/freestat/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/freestat/rcomp/tmp/30nm21292923193.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/freestat/rcomp/tmp/4lnkq1292923193.tab") 
> 
> try(system("convert tmp/1ut721292923192.ps tmp/1ut721292923192.png",intern=TRUE))
character(0)
> try(system("convert tmp/2t4p81292923193.ps tmp/2t4p81292923193.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.938   0.428   1.026