R version 3.0.2 (2013-09-25) -- "Frisbee Sailing"
Copyright (C) 2013 The R Foundation for Statistical Computing
Platform: i686-pc-linux-gnu (32-bit)

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> x <- c(4,5,7,5,6,5,3,7,7,11,13,13,9,7,6,3,5,1,5,2,9,4,4,10,8,6,7,0,7,4,5,11,2,4,5,12,10,6,6,8,3,10,2,5,4,3,8,5,7,1,7,4,8,7,10,2,6,6,11,8,8,6,11,15,9,5,10,4,9,3,7,7,9,15,11,10,6,5,6,6,14,11,1,9,13,10,11,7,6,4,6,8,6,7,12,20,10,14,11,13,7,9,8,7,9,10,12,13,11,11,14,10,9,12,8,13,14,15,14,14,15,14,21,10,8,12,13,6,12,12)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '3'
> par5 = '1'
> par4 = '0'
> par3 = '1'
> par2 = '1'
> par1 = '24'
> par10 <- 'FALSE'
> par9 <- '0'
> par8 <- '0'
> par7 <- '0'
> par6 <- '3'
> par5 <- '1'
> par4 <- '0'
> par3 <- '1'
> par2 <- '1'
> par1 <- '24'
> #'GNU S' R Code compiled by R2WASP v. 1.2.327 ()
> #Author: root
> #To cite this work: Wessa P., (2013), ARIMA Forecasting (v1.0.9) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_arimaforecasting.wasp/
> #Source of accompanying publication: 
> #
> 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      ar3
      -0.5629  -0.2547  -0.1979
s.e.   0.0954   0.1072   0.0946

sigma^2 estimated as 12.76:  log likelihood = -282.86,  aic = 573.72
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 107 
End = 130 
Frequency = 1 
 [1] 9.125519 8.967247 9.081199 9.230431 9.148720 9.134151 9.133634 9.153807
 [9] 9.145466 9.145125 9.143449 9.146130 9.145115 9.145335 9.144939 9.145307
[17] 9.145157 9.145226 9.145153 9.145206 9.145181 9.145196 9.145184 9.145192

$se
Time Series:
Start = 107 
End = 130 
Frequency = 1 
 [1] 3.571724 3.897993 4.286468 4.529408 4.945176 5.238657 5.540361 5.802222
 [9] 6.075035 6.325550 6.571212 6.804002 7.032025 7.251393 7.465150 7.672322
[17] 7.874463 8.071314 8.263617 8.451448 8.635256 8.815196 8.991559 9.164513

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 107 
End = 130 
Frequency = 1 
 [1]  2.1249396  1.3271802  0.6797223  0.3527909 -0.5438254 -1.1336169
 [7] -1.7254736 -2.2185480 -2.7616033 -3.2529525 -3.7361268 -4.1897138
[13] -4.6376530 -5.0673951 -5.4867537 -5.8924449 -6.2887892 -6.6745485
[19] -7.0515368 -7.4196313 -7.7799202 -8.1325876 -8.4782715 -8.8172532
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 107 
End = 130 
Frequency = 1 
 [1] 16.12610 16.60731 17.48268 18.10807 18.84127 19.40192 19.99274 20.52616
 [9] 21.05254 21.54320 22.02303 22.48197 22.92788 23.35807 23.77663 24.18306
[17] 24.57910 24.96500 25.34184 25.71004 26.07028 26.42298 26.76864 27.10764
> 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$pred))
  [1]  4.000000  5.000000  7.000000  5.000000  6.000000  5.000000  3.000000
  [8]  7.000000  7.000000 11.000000 13.000000 13.000000  9.000000  7.000000
 [15]  6.000000  3.000000  5.000000  1.000000  5.000000  2.000000  9.000000
 [22]  4.000000  4.000000 10.000000  8.000000  6.000000  7.000000  0.000000
 [29]  7.000000  4.000000  5.000000 11.000000  2.000000  4.000000  5.000000
 [36] 12.000000 10.000000  6.000000  6.000000  8.000000  3.000000 10.000000
 [43]  2.000000  5.000000  4.000000  3.000000  8.000000  5.000000  7.000000
 [50]  1.000000  7.000000  4.000000  8.000000  7.000000 10.000000  2.000000
 [57]  6.000000  6.000000 11.000000  8.000000  8.000000  6.000000 11.000000
 [64] 15.000000  9.000000  5.000000 10.000000  4.000000  9.000000  3.000000
 [71]  7.000000  7.000000  9.000000 15.000000 11.000000 10.000000  6.000000
 [78]  5.000000  6.000000  6.000000 14.000000 11.000000  1.000000  9.000000
 [85] 13.000000 10.000000 11.000000  7.000000  6.000000  4.000000  6.000000
 [92]  8.000000  6.000000  7.000000 12.000000 20.000000 10.000000 14.000000
 [99] 11.000000 13.000000  7.000000  9.000000  8.000000  7.000000  9.000000
[106] 10.000000  9.125519  8.967247  9.081199  9.230431  9.148720  9.134151
[113]  9.133634  9.153807  9.145466  9.145125  9.143449  9.146130  9.145115
[120]  9.145335  9.144939  9.145307  9.145157  9.145226  9.145153  9.145206
[127]  9.145181  9.145196  9.145184  9.145192
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 107 
End = 130 
Frequency = 1 
 [1] 0.3913996 0.4346923 0.4720156 0.4907039 0.5405320 0.5735242 0.6065889
 [8] 0.6338589 0.6642674 0.6916854 0.7186798 0.7439214 0.7689378 0.7929062
[15] 0.8163148 0.8389355 0.8610527 0.8825712 0.9036062 0.9241397 0.9442411
[22] 0.9639154 0.9832016 1.0021127
> postscript(file="/var/wessaorg/rcomp/tmp/1t2g11386165540.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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.spe <- array(0, dim=fx)
> perf.scalederr <- array(0, dim=fx)
> perf.mase <- array(0, dim=fx)
> perf.mase1 <- array(0, dim=fx)
> perf.mape <- array(0, dim=fx)
> perf.smape <- array(0, dim=fx)
> perf.mape1 <- array(0, dim=fx)
> perf.smape1 <- 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)
> perf.scaleddenom <- 0
> for (i in 2:fx) {
+ perf.scaleddenom = perf.scaleddenom + abs(x[nx+i] - x[nx+i-1])
+ }
> perf.scaleddenom = perf.scaleddenom / (fx-1)
> for (i in 1:fx) {
+ locSD <- (ub[i] - forecast$pred[i]) / 1.96
+ perf.scalederr[i] = (x[nx+i] - forecast$pred[i]) / perf.scaleddenom
+ perf.pe[i] = (x[nx+i] - forecast$pred[i]) / x[nx+i]
+ perf.spe[i] = 2*(x[nx+i] - forecast$pred[i]) / (x[nx+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.smape[1] = abs(perf.spe[1])
> perf.mape1[1] = perf.mape[1]
> perf.smape1[1] = perf.smape[1]
> perf.mse[1] = perf.se[1]
> perf.mase[1] = abs(perf.scalederr[1])
> perf.mase1[1] = perf.mase[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.smape[i] = perf.smape[i-1] + abs(perf.spe[i])
+ perf.smape1[i] = perf.smape[i] / i
+ perf.mse[i] = perf.mse[i-1] + perf.se[i]
+ perf.mse1[i] = perf.mse[i] / i
+ perf.mase[i] = perf.mase[i-1] + abs(perf.scalederr[i])
+ perf.mase1[i] = perf.mase[i] / i
+ }
> perf.rmse = sqrt(perf.mse1)
> postscript(file="/var/wessaorg/rcomp/tmp/20v381386165540.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/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/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/wessaorg/rcomp/tmp/3tkr61386165540.tab") 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Univariate ARIMA Extrapolation Forecast Performance',10,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,'sMAPE',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.element(a,'ScaledE',1,header=TRUE)
> a<-table.element(a,'MASE',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.smape1[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.element(a,round(perf.scalederr[i],4))
+ a<-table.element(a,round(perf.mase1[i],4))
+ a<-table.row.end(a)
+ }
> a<-table.end(a)
> table.save(a,file="/var/wessaorg/rcomp/tmp/4e73v1386165541.tab") 
> 
> try(system("convert tmp/1t2g11386165540.ps tmp/1t2g11386165540.png",intern=TRUE))
character(0)
> try(system("convert tmp/20v381386165540.ps tmp/20v381386165540.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  2.833   0.599   3.395