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(4716.99,4926.65,4920.10,5170.09,5246.24,5283.61,4979.05,4825.20,4695.12,4711.54,4727.22,4384.96,4378.75,4472.93,4564.07,4310.54,4171.38,4049.38,3591.37,3720.46,4107.23,4101.71,4162.34,4136.22,4125.88,4031.48,3761.36,3408.56,3228.47,3090.45,2741.14,2980.44,3104.33,3181.57,2863.86,2898.01,3112.33,3254.33,3513.47,3587.61,3727.45,3793.34,3817.58,3845.13,3931.86,4197.52,4307.13,4229.43,4362.28,4217.34,4361.28,4327.74,4417.65,4557.68,4650.35,4967.18,5123.42,5290.85,5535.66,5514.06,5493.88,5694.83,5850.41,6116.64,6175.00,6513.58,6383.78,6673.66,6936.61,7300.68,7392.93,7497.31,7584.71,7160.79,7196.19,7245.63,7347.51,7425.75,7778.51,7822.33,8181.22,8371.47,8347.71,8672.11,8802.79,9138.46,9123.29,9023.21,8850.41,8864.58,9163.74,8516.66,8553.44,7555.20,7851.22,7442.00,7992.53,8264.04,7517.39,7200.40,7193.69,6193.58,5104.21,4800.46,4461.61,4398.59,4243.63,4293.82)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '1'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '0.2'
> par1 = '12'
> #'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
      0.1705
s.e.  0.1020

sigma^2 estimated as 0.002258:  log likelihood = 154.61,  aic = -305.22
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 97 
End = 108 
Frequency = 1 
 [1] 5.936632 5.934771 5.934454 5.934400 5.934390 5.934389 5.934389 5.934389
 [9] 5.934389 5.934389 5.934389 5.934389

$se
Time Series:
Start = 97 
End = 108 
Frequency = 1 
 [1] 0.04752275 0.07316180 0.09274970 0.10899212 0.12312862 0.13580434
 [7] 0.14739441 0.15813737 0.16819557 0.17768531 0.18669331 0.19528623

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 97 
End = 108 
Frequency = 1 
 [1] 5.843488 5.791374 5.752664 5.720775 5.693058 5.668212 5.645496 5.624439
 [9] 5.604725 5.586125 5.568470 5.551628
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 97 
End = 108 
Frequency = 1 
 [1] 6.029777 6.078168 6.116243 6.148024 6.175723 6.200565 6.223282 6.244338
 [9] 6.264052 6.282652 6.300307 6.317150
> 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$pred))
  [1] 4716.990 4926.650 4920.100 5170.090 5246.240 5283.610 4979.050 4825.200
  [9] 4695.120 4711.540 4727.220 4384.960 4378.750 4472.930 4564.070 4310.540
 [17] 4171.380 4049.380 3591.370 3720.460 4107.230 4101.710 4162.340 4136.220
 [25] 4125.880 4031.480 3761.360 3408.560 3228.470 3090.450 2741.140 2980.440
 [33] 3104.330 3181.570 2863.860 2898.010 3112.330 3254.330 3513.470 3587.610
 [41] 3727.450 3793.340 3817.580 3845.130 3931.860 4197.520 4307.130 4229.430
 [49] 4362.280 4217.340 4361.280 4327.740 4417.650 4557.680 4650.350 4967.180
 [57] 5123.420 5290.850 5535.660 5514.060 5493.880 5694.830 5850.410 6116.640
 [65] 6175.000 6513.580 6383.780 6673.660 6936.610 7300.680 7392.930 7497.310
 [73] 7584.710 7160.790 7196.190 7245.630 7347.510 7425.750 7778.510 7822.330
 [81] 8181.220 8371.470 8347.710 8672.110 8802.790 9138.460 9123.290 9023.210
 [89] 8850.410 8864.580 9163.740 8516.660 8553.440 7555.200 7851.220 7442.000
 [97] 7373.960 7362.408 7360.440 7360.104 7360.047 7360.038 7360.036 7360.036
[105] 7360.036 7360.036 7360.036 7360.036
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 97 
End = 108 
Frequency = 1 
 [1] 0.04130084 0.06468974 0.08308164 0.09868449 0.11252941 0.12515665
 [7] 0.13688087 0.14790212 0.15835649 0.16834142 0.17792949 0.18717647
> postscript(file="/var/www/html/rcomp/tmp/1fafy1260475234.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/21tbs1260475235.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]
> 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/3wvoo1260475235.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/4xfv11260475235.tab") 
> 
> system("convert tmp/1fafy1260475234.ps tmp/1fafy1260475234.png")
> system("convert tmp/21tbs1260475235.ps tmp/21tbs1260475235.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.556   0.314   0.672