R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(206010,198112,194519,185705,180173,176142,203401,221902,197378,185001,176356,180449,180144,173666,165688,161570,156145,153730,182698,200765,176512,166618,158644,159585,163095,159044,155511,153745,150569,150605,179612,194690,189917,184128,175335,179566,181140,177876,175041,169292,166070,166972,206348,215706,202108,195411,193111,195198,198770,194163,190420,189733,186029,191531,232571,243477,227247,217859,208679,213188,216234,213586,209465,204045,200237,203666,241476,260307,243324,244460,233575,237217,235243,230354,227184,221678,217142,219452,256446,265845,248624,241114,229245,231805,219277,219313,212610,214771,211142,211457,240048,240636,230580,208795,197922,194596,194581,185686,178106,172608,167302,168053,202300,202388,182516,173476,166444,171297,169701,164182,161914,159612,151001,158114,186530,187069,174330,169362,166827,178037,186413,189226,191563,188906,186005,195309,223532,226899,214126,206903,204442)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '2'
> par7 = '1'
> par6 = '2'
> 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:
         ar1     ar2      ma1     sar1     sar2
      0.7183  0.2200  -0.8315  -0.4633  -0.3837
s.e.  0.1165  0.0985   0.0764   0.0958   0.1039

sigma^2 estimated as 20218426:  log likelihood = -1044.54,  aic = 2101.09
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 120 
End = 131 
Frequency = 1 
 [1] 170167.5 165981.5 163390.9 160089.3 160263.4 154798.4 159718.4 189541.8
 [9] 190895.6 179408.3 168414.6 163035.5

$se
Time Series:
Start = 120 
End = 131 
Frequency = 1 
 [1]  4496.490  6009.853  7575.004  9047.343 10498.423 11932.416 13357.425
 [8] 14776.066 16189.748 17598.851 19003.266 20402.606

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 120 
End = 131 
Frequency = 1 
 [1] 161354.4 154202.2 148543.9 142356.6 139686.5 131410.9 133537.9 160580.7
 [9] 159163.7 144914.6 131168.2 123046.4
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 120 
End = 131 
Frequency = 1 
 [1] 178980.7 177760.8 178238.0 177822.1 180840.3 178186.0 185899.0 218502.9
 [9] 222627.5 213902.1 205661.0 203024.6
> 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$pred))
  [1] 206010.0 198112.0 194519.0 185705.0 180173.0 176142.0 203401.0 221902.0
  [9] 197378.0 185001.0 176356.0 180449.0 180144.0 173666.0 165688.0 161570.0
 [17] 156145.0 153730.0 182698.0 200765.0 176512.0 166618.0 158644.0 159585.0
 [25] 163095.0 159044.0 155511.0 153745.0 150569.0 150605.0 179612.0 194690.0
 [33] 189917.0 184128.0 175335.0 179566.0 181140.0 177876.0 175041.0 169292.0
 [41] 166070.0 166972.0 206348.0 215706.0 202108.0 195411.0 193111.0 195198.0
 [49] 198770.0 194163.0 190420.0 189733.0 186029.0 191531.0 232571.0 243477.0
 [57] 227247.0 217859.0 208679.0 213188.0 216234.0 213586.0 209465.0 204045.0
 [65] 200237.0 203666.0 241476.0 260307.0 243324.0 244460.0 233575.0 237217.0
 [73] 235243.0 230354.0 227184.0 221678.0 217142.0 219452.0 256446.0 265845.0
 [81] 248624.0 241114.0 229245.0 231805.0 219277.0 219313.0 212610.0 214771.0
 [89] 211142.0 211457.0 240048.0 240636.0 230580.0 208795.0 197922.0 194596.0
 [97] 194581.0 185686.0 178106.0 172608.0 167302.0 168053.0 202300.0 202388.0
[105] 182516.0 173476.0 166444.0 171297.0 169701.0 164182.0 161914.0 159612.0
[113] 151001.0 158114.0 186530.0 187069.0 174330.0 169362.0 166827.0 170167.5
[121] 165981.5 163390.9 160089.3 160263.4 154798.4 159718.4 189541.8 190895.6
[129] 179408.3 168414.6 163035.5
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 120 
End = 131 
Frequency = 1 
 [1] 0.02642390 0.03620798 0.04636122 0.05651433 0.06550731 0.07708357
 [7] 0.08363108 0.07795679 0.08480944 0.09809384 0.11283624 0.12514208
> postscript(file="/var/www/html/rcomp/tmp/13w931293188151.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/rcomp/tmp/20noc1293188151.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/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/3hglr1293188151.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/rcomp/tmp/42yjw1293188151.tab") 
> 
> try(system("convert tmp/13w931293188151.ps tmp/13w931293188151.png",intern=TRUE))
character(0)
> try(system("convert tmp/20noc1293188151.ps tmp/20noc1293188151.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  2.583   0.374   5.465