R version 2.12.0 (2010-10-15)
Copyright (C) 2010 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(17848,19592,21092,20899,25890,24965,22225,20977,22897,22785,22769,19637,20203,20450,23083,21738,26766,25280,22574,22729,21378,22902,24989,21116,15169,15846,20927,18273,22538,15596,14034,11366,14861,15149,13577,13026,13190,13196,15826,14733,16307,15703,14589,12043,15057,14053,12698,10888,10045,11549,13767,12434,13116,14211,12266,12602,15714,13742,12745,10491,10057,10900,11771,11992,11933,14504,11727,11477,13578,11555,11846,11397,10066,10269,14279,13870,13695,14420,11424,9704,12464,14301,13464,9893,11572,12380,16692,16052,16459,14761,13654,13480,18068,16560,14530,10650,11651,13735,13360,17818,20613,16231,13862,12004,17734,15034,12609,12320,10833,11350,13648,14890,16325,18045,15616,11926,16855,15083,12520,12355)
> 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
      -0.6358
s.e.   0.1292

sigma^2 estimated as 3773218:  log likelihood = -857.22,  aic = 1718.44
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 12625.33 13823.48 15808.49 17022.06 18496.52 16669.88 14546.69 13383.76
 [9] 17546.41 16169.42 14603.01 12681.47

$se
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 1942.890 2747.488 3364.900 3885.411 4343.994 4758.587 5139.846 5494.714
 [9] 5828.015 6143.258 6443.096 6729.588

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 8817.2625 8438.4006 9213.2814 9406.6520 9982.2933 7343.0518 4472.5872
 [8] 2614.1169 6123.4970 4128.6294 1974.5396 -508.5257
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 16433.39 19208.55 22403.69 24637.46 27010.75 25996.71 24620.79 24153.40
 [9] 28969.31 28210.20 27231.48 25871.46
> 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$pred))
  [1] 17848.00 19592.00 21092.00 20899.00 25890.00 24965.00 22225.00 20977.00
  [9] 22897.00 22785.00 22769.00 19637.00 20203.00 20450.00 23083.00 21738.00
 [17] 26766.00 25280.00 22574.00 22729.00 21378.00 22902.00 24989.00 21116.00
 [25] 15169.00 15846.00 20927.00 18273.00 22538.00 15596.00 14034.00 11366.00
 [33] 14861.00 15149.00 13577.00 13026.00 13190.00 13196.00 15826.00 14733.00
 [41] 16307.00 15703.00 14589.00 12043.00 15057.00 14053.00 12698.00 10888.00
 [49] 10045.00 11549.00 13767.00 12434.00 13116.00 14211.00 12266.00 12602.00
 [57] 15714.00 13742.00 12745.00 10491.00 10057.00 10900.00 11771.00 11992.00
 [65] 11933.00 14504.00 11727.00 11477.00 13578.00 11555.00 11846.00 11397.00
 [73] 10066.00 10269.00 14279.00 13870.00 13695.00 14420.00 11424.00  9704.00
 [81] 12464.00 14301.00 13464.00  9893.00 11572.00 12380.00 16692.00 16052.00
 [89] 16459.00 14761.00 13654.00 13480.00 18068.00 16560.00 14530.00 10650.00
 [97] 11651.00 13735.00 13360.00 17818.00 20613.00 16231.00 13862.00 12004.00
[105] 17734.00 15034.00 12609.00 12320.00 12625.33 13823.48 15808.49 17022.06
[113] 18496.52 16669.88 14546.69 13383.76 17546.41 16169.42 14603.01 12681.47
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 0.1538883 0.1987552 0.2128541 0.2282574 0.2348547 0.2854602 0.3533345
 [8] 0.4105510 0.3321486 0.3799308 0.4412171 0.5306632
> postscript(file="/var/www/rcomp/tmp/1fto71292071839.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/rcomp/tmp/2t3mg1292071839.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/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/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/rcomp/tmp/3tv0c1292071839.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/rcomp/tmp/4weh01292071839.tab") 
> 
> try(system("convert tmp/1fto71292071839.ps tmp/1fto71292071839.png",intern=TRUE))
character(0)
> try(system("convert tmp/2t3mg1292071839.ps tmp/2t3mg1292071839.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.770   0.380   1.163