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)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> x <- c(100.00,100.42,100.50,101.14,101.98,102.31,103.27,103.80,103.46,105.06,106.08,106.74,107.35,108.96,109.85,109.81,109.99,111.60,112.74,112.78,113.66,115.37,116.26,116.24,116.73,118.76,119.78,120.23,121.48,124.07,125.82,126.92,128.48,131.44,133.51,134.58,136.68,140.10,142.45,143.91,146.19,149.84,152.31,153.62,155.79,159.89,163.21,165.32,167.68,171.79,175.38,177.81,181.09,186.48,191.07,194.23,197.82,204.41,209.26,212.24,214.88,218.87,219.86,219.75,220.89,224.02,222.27,217.27,213.23,212.44,207.87,199.46,198.19,199.77,200.10,195.76,191.27,195.79,192.7)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '1'
> par7 = '1'
> par6 = '3'
> par5 = '4'
> par4 = '0'
> par3 = '2'
> par2 = '-1.0'
> par1 = '0'
> par1 <- 26
> 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     ar3      ma1    sar1     sma1
      0.1651  -0.2918  0.4201  -0.9367  0.9975  -0.9184
s.e.  0.1583   0.1667  0.1686   0.0684  0.0292   0.4641

sigma^2 estimated as 7.714e-10:  log likelihood = 457.69,  aic = -901.38
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 54 
End = 79 
Frequency = 1 
 [1] 0.005350683 0.005222214 0.005137227 0.005026582 0.004848110 0.004714261
 [7] 0.004622874 0.004505887 0.004322245 0.004182901 0.004085583 0.003963159
[13] 0.003774322 0.003629421 0.003526559 0.003398778 0.003204630 0.003054302
[19] 0.002945995 0.002812797 0.002613361 0.002457678 0.002343915 0.002205296
[25] 0.002000616 0.001839590

$se
Time Series:
Start = 54 
End = 79 
Frequency = 1 
 [1] 2.817388e-05 4.485264e-05 5.388447e-05 6.765462e-05 8.524615e-05
 [6] 9.912321e-05 1.129040e-04 1.286903e-04 1.448795e-04 1.604674e-04
[11] 1.765608e-04 1.930225e-04 2.103906e-04 2.280362e-04 2.456743e-04
[16] 2.636030e-04 2.828577e-04 3.023401e-04 3.217000e-04 3.415441e-04
[21] 3.627294e-04 3.840771e-04 4.053903e-04 4.272502e-04 4.503850e-04
[26] 4.737122e-04

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 54 
End = 79 
Frequency = 1 
 [1] 0.0052954618 0.0051343026 0.0050316130 0.0048939794 0.0046810275
 [6] 0.0045199792 0.0044015817 0.0042536536 0.0040382809 0.0038683848
[11] 0.0037395237 0.0035848345 0.0033619559 0.0031824700 0.0030450375
[16] 0.0028821166 0.0026502285 0.0024617149 0.0023154627 0.0021433703
[21] 0.0019024111 0.0017048867 0.0015493496 0.0013678861 0.0011178610
[26] 0.0009111144
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 54 
End = 79 
Frequency = 1 
 [1] 0.005405903 0.005310125 0.005242840 0.005159186 0.005015192 0.004908542
 [7] 0.004844165 0.004758120 0.004606209 0.004497417 0.004431642 0.004341483
[13] 0.004186687 0.004076372 0.004008081 0.003915440 0.003759031 0.003646888
[19] 0.003576527 0.003482223 0.003324310 0.003210469 0.003138480 0.003042707
[25] 0.002883370 0.002768066
> 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$pred))
 [1] 100.0000 100.4200 100.5000 101.1400 101.9800 102.3100 103.2700 103.8000
 [9] 103.4600 105.0600 106.0800 106.7400 107.3500 108.9600 109.8500 109.8100
[17] 109.9900 111.6000 112.7400 112.7800 113.6600 115.3700 116.2600 116.2400
[25] 116.7300 118.7600 119.7800 120.2300 121.4800 124.0700 125.8200 126.9200
[33] 128.4800 131.4400 133.5100 134.5800 136.6800 140.1000 142.4500 143.9100
[41] 146.1900 149.8400 152.3100 153.6200 155.7900 159.8900 163.2100 165.3200
[49] 167.6800 171.7900 175.3800 177.8100 181.0900 186.8920 191.4897 194.6576
[57] 198.9423 206.2659 212.1223 216.3157 221.9319 231.3613 239.0685 244.7631
[65] 252.3240 264.9483 275.5260 283.5625 294.2234 312.0485 327.4071 339.4439
[73] 355.5180 382.6490 406.8882 426.6367 453.4538 499.8461 543.5993
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 54 
End = 79 
Frequency = 1 
 [1] 0.005320383 0.008735877 0.010709185 0.013824050 0.018210991 0.021930016
 [7] 0.025650789 0.030254069 0.035876536 0.041481760 0.047214771 0.053844183
[13] 0.062579830 0.071653854 0.080680213 0.091461592 0.106729564 0.122816881
[19] 0.138935491 0.159349082 0.190668267 0.225280128 0.261651941 0.312343424
[25] 0.402898944 0.519926131
> postscript(file="/var/www/rcomp/tmp/10g9n1292679994.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2wppv1292679994.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/3v03s1292679994.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/4h02g1292679994.tab") 
> 
> try(system("convert tmp/10g9n1292679994.ps tmp/10g9n1292679994.png",intern=TRUE))
character(0)
> try(system("convert tmp/2wppv1292679994.ps tmp/2wppv1292679994.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.840   0.430   1.253