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(180144,173666,165688,161570,156145,153730,182698,200765,176512,166618,158644,159585,163095,159044,155511,153745,150569,150605,179612,194690,189917,184128,175335,179566,181140,177876,175041,169292,166070,166972,206348,215706,202108,195411,193111,195198,198770,194163,190420,189733,186029,191531,232571,243477,227247,217859,208679,213188,216234,213586,209465,204045,200237,203666,241476,260307,243324,244460,233575,237217,235243,230354,227184,221678,217142,219452,256446,265845,248624,241114,229245,231805,219277,219313,212610,214771,211142,211457,240048,240636,230580,208795,197922,194596)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '1'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> par1 = '36'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> 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
      0.0295
s.e.  0.1677

sigma^2 estimated as 24901166:  log likelihood = -347.7,  aic = 699.39
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 49 
End = 84 
Frequency = 1 
 [1] 216831.5 212226.6 208483.7 207796.7 204092.7 209594.7 250634.7 261540.7
 [9] 245310.7 235922.7 226742.7 231251.7 234895.2 230290.4 226547.4 225860.4
[17] 222156.4 227658.4 268698.4 279604.4 263374.4 253986.4 244806.4 249315.4
[25] 252958.9 248354.1 244611.1 243924.1 240220.1 245722.1 286762.1 297668.1
[33] 281438.1 272050.1 262870.1 267379.1

$se
Time Series:
Start = 49 
End = 84 
Frequency = 1 
 [1]  4990.107  7162.047  8816.656 10206.529 11428.609 12532.078 13545.953
 [8] 14489.054 15374.412 16211.490 17007.418 17767.727 20453.634 22891.447
[15] 25095.320 27120.738 29005.067 30774.232 32447.077 34037.806 35557.442
[22] 37014.742 38416.801 39769.461 42601.720 45307.030 47861.066 50285.587
[29] 52598.470 54813.847 56943.099 58995.553 60978.964 62899.864 64763.814
[36] 66575.599

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 49 
End = 84 
Frequency = 1 
 [1] 207050.9 198189.0 191203.1 187791.9 181692.6 185031.8 224084.6 233142.2
 [9] 215176.9 204148.2 193408.2 196427.0 194806.1 185423.1 177360.6 172703.8
[17] 165306.5 167340.9 205102.1 212890.3 193681.8 181437.5 169509.5 171367.3
[25] 169459.6 159552.3 150803.4 145364.4 137127.1 138287.0 175153.7 182036.8
[33] 161919.4 148766.4 135933.1 136891.0
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 49 
End = 84 
Frequency = 1 
 [1] 226612.1 226264.3 225764.4 227801.5 226492.8 234157.6 277184.8 289939.3
 [9] 275444.6 267697.2 260077.2 266076.5 274984.4 275157.6 275734.2 279017.1
[17] 279006.3 287975.9 332294.7 346318.5 333067.0 326535.3 320103.3 327263.6
[25] 336458.3 337155.8 338418.8 342483.9 343313.1 353157.3 398370.6 413299.4
[33] 400956.9 395333.9 389807.2 397867.3
> 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$pred))
 [1] 180144.0 173666.0 165688.0 161570.0 156145.0 153730.0 182698.0 200765.0
 [9] 176512.0 166618.0 158644.0 159585.0 163095.0 159044.0 155511.0 153745.0
[17] 150569.0 150605.0 179612.0 194690.0 189917.0 184128.0 175335.0 179566.0
[25] 181140.0 177876.0 175041.0 169292.0 166070.0 166972.0 206348.0 215706.0
[33] 202108.0 195411.0 193111.0 195198.0 198770.0 194163.0 190420.0 189733.0
[41] 186029.0 191531.0 232571.0 243477.0 227247.0 217859.0 208679.0 213188.0
[49] 216831.5 212226.6 208483.7 207796.7 204092.7 209594.7 250634.7 261540.7
[57] 245310.7 235922.7 226742.7 231251.7 234895.2 230290.4 226547.4 225860.4
[65] 222156.4 227658.4 268698.4 279604.4 263374.4 253986.4 244806.4 249315.4
[73] 252958.9 248354.1 244611.1 243924.1 240220.1 245722.1 286762.1 297668.1
[81] 281438.1 272050.1 262870.1 267379.1
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 49 
End = 84 
Frequency = 1 
 [1] 0.02301375 0.03374716 0.04228942 0.04911786 0.05599715 0.05979196
 [7] 0.05404659 0.05539885 0.06267322 0.06871526 0.07500756 0.07683285
[13] 0.08707556 0.09940254 0.11077292 0.12007743 0.13056146 0.13517722
[19] 0.12075649 0.12173558 0.13500720 0.14573512 0.15692726 0.15951465
[25] 0.16841357 0.18242919 0.19566185 0.20615258 0.21895946 0.22307249
[31] 0.19857259 0.19819238 0.21666917 0.23120689 0.24637191 0.24899325
> postscript(file="/var/www/html/rcomp/tmp/1ew9z1229277731.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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.se <- array(0, dim=fx)
> perf.mse <- 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$pred[i]
+ perf.mape[i] = perf.mape[i] + abs(perf.pe[i])
+ perf.se[i] = (x[nx+i] - forecast$pred[i])^2
+ perf.mse[i] = perf.mse[i] + perf.se[i]
+ 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 = perf.mape / fx
> perf.mse = perf.mse / fx
> perf.rmse = sqrt(perf.mse)
> postscript(file="/var/www/html/rcomp/tmp/240xg1229277731.ps",horizontal=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[1:12] <- x[(nx+1):lx]
Warning message:
In NextMethod("[<-") :
  number of items to replace is not a multiple of replacement length
> 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/328uu1229277731.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.mape[i],4))
+ a<-table.element(a,round(perf.se[i],4))
+ a<-table.element(a,round(perf.mse[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/4svq61229277731.tab") 
> 
> system("convert tmp/1ew9z1229277731.ps tmp/1ew9z1229277731.png")
> system("convert tmp/240xg1229277731.ps tmp/240xg1229277731.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.695   0.354   0.850