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(115.6,120.3,121.9,121.7,118.9,113.4,114,117.5,120.9,125.1,124.7,128.2,149.7,163.6,173.9,164.5,154.2,147.9,159.3,170.3,170,174.2,190.8,179.9,240.8,241.9,241.1,239.6,220.8,209.3,209.9,228.3,242.1,226.4,231.5,229.7,257.6,260,264.4,268.8,271.4,273.8,277.4,268.2,264.6,266.6,266,267.4,289.8,294,310.3,311.7,302.1,298.2,299.2,296.2,299,300,299.4,300.2,470.2,472.1,484.8,513.4,547.2,548.1,544.7,521.1,459,413.2)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '0'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '1'
> par1 = '50'
> #'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")


sigma^2 estimated as 71.77:  log likelihood = -67.56,  aic = 137.12
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 21 
End = 70 
Frequency = 1 
 [1] 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3
[13] 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3
[25] 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3
[37] 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3
[49] 170.3 170.3

$se
Time Series:
Start = 21 
End = 70 
Frequency = 1 
 [1]  8.47178 11.98091 14.67355 16.94356 18.94348 20.75154 22.41422 23.96181
 [9] 25.41534 26.79012 28.09771 29.34711 30.54544 31.69850 32.81106 33.88712
[17] 34.93004 35.94272 36.92763 37.88695 38.82257 39.73617 40.62923 41.50308
[25] 42.35890 43.19777 44.02066 44.82844 45.62193 46.40185 47.16887 47.92362
[33] 48.66667 49.39854 50.11973 50.83068 51.53182 52.22356 52.90625 53.58024
[41] 54.24586 54.90341 55.55318 56.19543 56.83043 57.45841 58.07960 58.69421
[49] 59.30246 59.90453

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 21 
End = 70 
Frequency = 1 
 [1] 153.69531 146.81742 141.53984 137.09062 133.17079 129.62699 126.36812
 [8] 123.33485 120.48593 117.79136 115.22848 112.77967 110.43094 108.17095
[15] 105.99032 103.88125 101.83712  99.85227  97.92184  96.04158  94.20776
[22]  92.41711  90.66671  88.95397  87.27656  85.63237  84.01951  82.43625
[29]  80.88102  79.35238  77.84901  76.36970  74.91333  73.47886  72.06534
[36]  70.67187  69.29762  67.94183  66.60375  65.28273  63.97812  62.68932
[43]  61.41578  60.15696  58.91236  57.68152  56.46399  55.25934  54.06718
[50]  52.88712
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 21 
End = 70 
Frequency = 1 
 [1] 186.9047 193.7826 199.0602 203.5094 207.4292 210.9730 214.2319 217.2652
 [9] 220.1141 222.8086 225.3715 227.8203 230.1691 232.4291 234.6097 236.7188
[17] 238.7629 240.7477 242.6782 244.5584 246.3922 248.1829 249.9333 251.6460
[25] 253.3234 254.9676 256.5805 258.1638 259.7190 261.2476 262.7510 264.2303
[33] 265.6867 267.1211 268.5347 269.9281 271.3024 272.6582 273.9962 275.3173
[41] 276.6219 277.9107 279.1842 280.4430 281.6876 282.9185 284.1360 285.3407
[49] 286.5328 287.7129
> 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$pred))
 [1] 115.6 120.3 121.9 121.7 118.9 113.4 114.0 117.5 120.9 125.1 124.7 128.2
[13] 149.7 163.6 173.9 164.5 154.2 147.9 159.3 170.3 170.3 170.3 170.3 170.3
[25] 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3
[37] 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3
[49] 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3
[61] 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 21 
End = 70 
Frequency = 1 
 [1] 0.04974621 0.07035177 0.08616297 0.09949242 0.11123591 0.12185283
 [7] 0.13161610 0.14070353 0.14923863 0.15731133 0.16498952 0.17232593
[13] 0.17936252 0.18613328 0.19266625 0.19898485 0.20510888 0.21105530
[19] 0.21683871 0.22247182 0.22796578 0.23333041 0.23857445 0.24370567
[25] 0.24873106 0.25365690 0.25848890 0.26323221 0.26789155 0.27247122
[31] 0.27697518 0.28140707 0.28577023 0.29006776 0.29430255 0.29847727
[37] 0.30259439 0.30665624 0.31066499 0.31462267 0.31853117 0.32239230
[43] 0.32620772 0.32997904 0.33370773 0.33739522 0.34104284 0.34465186
[49] 0.34822348 0.35175883
> postscript(file="/var/www/html/freestat/rcomp/tmp/1dgbg1229259095.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/freestat/rcomp/tmp/2nb1d1229259095.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/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/3ovl91229259095.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/freestat/rcomp/tmp/4w51h1229259095.tab") 
> 
> system("convert tmp/1dgbg1229259095.ps tmp/1dgbg1229259095.png")
> system("convert tmp/2nb1d1229259095.ps tmp/2nb1d1229259095.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.101   0.477   1.341