R version 2.13.0 (2011-04-13)
Copyright (C) 2011 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(1.579,2.146,2.462,3.695,4.831,5.134,6.250,5.760,6.249,2.917,1.741,2.359,1.511,2.059,2.635,2.867,4.403,5.720,4.502,5.749,5.627,2.846,1.762,2.429,1.169,2.154,2.249,2.687,4.359,5.382,4.459,6.398,4.596,3.024,1.887,2.070,1.351,2.218,2.461,3.028,4.784,4.975,4.607,6.249,4.809,3.157,1.910,2.228,1.594,2.467,2.222,3.607,4.685,4.962,5.770,5.480,5.000,3.228,1.993,2.288,1.580,2.111,2.192,3.601,4.665,4.876,5.813,5.589,5.331,3.075,2.002,2.306,1.507,1.992,2.487,3.490,4.647,5.594,5.611,5.788,6.204,3.013,1.931,2.549,1.504,2.090,2.702,2.939,4.500,6.208,6.415,5.657,5.964,3.163,1.997,2.422,1.376,2.202,2.683,3.303,5.202,5.231,4.880,7.998,4.977,3.531,2.025,2.205,1.442,2.238,2.179,3.218,5.139,4.990,4.914,6.084,5.672,3.548,1.793,2.086,1.262,1.743,1.964,3.258,4.966,4.944,5.907,5.561,5.321,3.582,1.757,1.894)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '2'
> par7 = '1'
> par6 = '3'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> 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     ar3      ma1    sar1     sar2     sma1
      0.4723  0.2162  0.2240  -0.7978  0.3011  -0.2101  -1.0000
s.e.  0.1539  0.1047  0.1051   0.1203  0.1121   0.1241   0.1201

sigma^2 estimated as 0.1268:  log likelihood = -54.95,  aic = 125.91
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 121 
End = 132 
Frequency = 1 
 [1] 1.592306 2.168779 2.266039 3.249009 4.748596 5.216711 5.329922 5.641588
 [9] 5.631965 3.196695 1.850602 2.261454

$se
Time Series:
Start = 121 
End = 132 
Frequency = 1 
 [1] 0.3739025 0.3931875 0.3938483 0.3996417 0.3997563 0.4004898 0.4015076
 [8] 0.4020447 0.4026134 0.4030984 0.4035485 0.4038298

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 121 
End = 132 
Frequency = 1 
 [1] 0.8594572 1.3981313 1.4940964 2.4657113 3.9650741 4.4317515 4.5429667
 [8] 4.8535800 4.8428425 2.4066217 1.0596467 1.4699479
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 121 
End = 132 
Frequency = 1 
 [1] 2.325155 2.939426 3.037982 4.032307 5.532119 6.001671 6.116876 6.429595
 [9] 6.421087 3.986767 2.641557 3.052961
> 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$pred))
  [1] 1.579000 2.146000 2.462000 3.695000 4.831000 5.134000 6.250000 5.760000
  [9] 6.249000 2.917000 1.741000 2.359000 1.511000 2.059000 2.635000 2.867000
 [17] 4.403000 5.720000 4.502000 5.749000 5.627000 2.846000 1.762000 2.429000
 [25] 1.169000 2.154000 2.249000 2.687000 4.359000 5.382000 4.459000 6.398000
 [33] 4.596000 3.024000 1.887000 2.070000 1.351000 2.218000 2.461000 3.028000
 [41] 4.784000 4.975000 4.607000 6.249000 4.809000 3.157000 1.910000 2.228000
 [49] 1.594000 2.467000 2.222000 3.607000 4.685000 4.962000 5.770000 5.480000
 [57] 5.000000 3.228000 1.993000 2.288000 1.580000 2.111000 2.192000 3.601000
 [65] 4.665000 4.876000 5.813000 5.589000 5.331000 3.075000 2.002000 2.306000
 [73] 1.507000 1.992000 2.487000 3.490000 4.647000 5.594000 5.611000 5.788000
 [81] 6.204000 3.013000 1.931000 2.549000 1.504000 2.090000 2.702000 2.939000
 [89] 4.500000 6.208000 6.415000 5.657000 5.964000 3.163000 1.997000 2.422000
 [97] 1.376000 2.202000 2.683000 3.303000 5.202000 5.231000 4.880000 7.998000
[105] 4.977000 3.531000 2.025000 2.205000 1.442000 2.238000 2.179000 3.218000
[113] 5.139000 4.990000 4.914000 6.084000 5.672000 3.548000 1.793000 2.086000
[121] 1.592306 2.168779 2.266039 3.249009 4.748596 5.216711 5.329922 5.641588
[129] 5.631965 3.196695 1.850602 2.261454
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 121 
End = 132 
Frequency = 1 
 [1] 0.23481823 0.18129441 0.17380474 0.12300418 0.08418410 0.07677054
 [7] 0.07533086 0.07126446 0.07148720 0.12609851 0.21806340 0.17857084
> postscript(file="/var/wessaorg/rcomp/tmp/1tlok1324636954.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/wessaorg/rcomp/tmp/2lcws1324636954.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/3whba1324636954.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/wessaorg/rcomp/tmp/48r8q1324636954.tab") 
> 
> try(system("convert tmp/1tlok1324636954.ps tmp/1tlok1324636954.png",intern=TRUE))
character(0)
> try(system("convert tmp/2lcws1324636954.ps tmp/2lcws1324636954.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  3.732   0.672   4.420