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)

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> x <- c(5,4,5,6,6,6,7,8,7,8,7,8,8,9,9,8,9,9,10,11,12,13,13,13,14,14,15,15,16,16,17,18,19,20,22,20,22,25,24,25,28,26,27,26,25,27,28,30,31,32,34,34,33,32,34,36,37,40,38,38,36,40,40,42,44,45,47,49,47,49,52,50,50,57,58,58,58,61,61,64,68,40,34,46,36,34,45,55,50,56,72,76,78,77,90,88,97,93,84,67,72,75,71,75,90,78,73,62,65,61,58,33,39,56,79,82,79,73,87,85,83,82,83,92,95,97,87,84,84,89,103,106,109,106,105,115,120,124,121,131,139,133,119,123,120,128,134,126,115,106,99,100,99,99,100,100,108,109,115,114,108,113,118,122,118,121,118,121,121,112,119,116,110,111,106,108)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '1'
> par7 = '0'
> par6 = '0'
> par5 = '1'
> par4 = '0'
> par3 = '1'
> par2 = '0.2'
> par1 = '20'
> #'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:
        sar1
      0.0811
s.e.  0.0802

sigma^2 estimated as 0.002452:  log likelihood = 245.92,  aic = -487.84
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 157 
End = 176 
Frequency = 1 
 [1] 2.511886 2.511886 2.511886 2.511886 2.511886 2.511886 2.511886 2.511886
 [9] 2.511886 2.511886 2.511886 2.511886 2.511886 2.511886 2.511886 2.511886
[17] 2.511886 2.511886 2.511886 2.511886

$se
Time Series:
Start = 157 
End = 176 
Frequency = 1 
 [1] 0.04951270 0.07291498 0.09064557 0.10544898 0.11841700 0.13009882
 [7] 0.14081484 0.15077114 0.16010951 0.16893246 0.17731693 0.18532245
[13] 0.19299619 0.20037626 0.20749401 0.21437557 0.22104299 0.22751510
[19] 0.23380812 0.23993615

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 157 
End = 176 
Frequency = 1 
 [1] 2.414842 2.368973 2.334221 2.305206 2.279789 2.256893 2.235889 2.216375
 [9] 2.198072 2.180779 2.164345 2.148654 2.133614 2.119149 2.105198 2.091710
[17] 2.078642 2.065957 2.053623 2.041612
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 157 
End = 176 
Frequency = 1 
 [1] 2.608931 2.654800 2.689552 2.718566 2.743984 2.766880 2.787884 2.807398
 [9] 2.825701 2.842994 2.859428 2.875118 2.890159 2.904624 2.918575 2.932063
[17] 2.945131 2.957816 2.970150 2.982161
> 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$pred))
  [1]   5   4   5   6   6   6   7   8   7   8   7   8   8   9   9   8   9   9
 [19]  10  11  12  13  13  13  14  14  15  15  16  16  17  18  19  20  22  20
 [37]  22  25  24  25  28  26  27  26  25  27  28  30  31  32  34  34  33  32
 [55]  34  36  37  40  38  38  36  40  40  42  44  45  47  49  47  49  52  50
 [73]  50  57  58  58  58  61  61  64  68  40  34  46  36  34  45  55  50  56
 [91]  72  76  78  77  90  88  97  93  84  67  72  75  71  75  90  78  73  62
[109]  65  61  58  33  39  56  79  82  79  73  87  85  83  82  83  92  95  97
[127]  87  84  84  89 103 106 109 106 105 115 120 124 121 131 139 133 119 123
[145] 120 128 134 126 115 106  99 100  99  99 100 100 100 100 100 100 100 100
[163] 100 100 100 100 100 100 100 100 100 100 100 100 100 100
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 157 
End = 176 
Frequency = 1 
 [1] 0.1064721 0.1626220 0.2078274 0.2474024 0.2834872 0.3171580 0.3490410
 [8] 0.3795372 0.4089218 0.4373929 0.4650987 0.4921534 0.5186471 0.5446526
[15] 0.5702293 0.5954266 0.6202861 0.6448431 0.6691280 0.6931670
> postscript(file="/var/www/rcomp/tmp/10tmh1292848755.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/27cjt1292848755.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/3dvg51292848755.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/4r6z51292848756.tab") 
> 
> try(system("convert tmp/10tmh1292848755.ps tmp/10tmh1292848755.png",intern=TRUE))
character(0)
> try(system("convert tmp/27cjt1292848755.ps tmp/27cjt1292848755.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.750   0.330   1.063