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(-2.0,2.6,0.2,0.1,-0.1,0.1,-1.6,2.3,-0.3,0.0,0.1,0.4,-1.9,2.4,0.0,0.4,0.1,0.2,-1.3,2.1,-0.1,0.3,0.3,0.2,-1.9,2.7,0.0,-0.2,0.2,0.1,-1.5,2.1,-0.3,-0.2,0.2,0.3,-2.0,2.6,0.0,0.5,-0.1,0.2,-1.6,2.1,-0.2,0.0,0.2,0.2,-2.2,2.7,-0.3,0.4,-0.1,0.0,-1.6,2.2,-0.3,0.0,0.1,0.1,-1.9,2.5,0.1,-0.1,0.3,0.1,-1.9,2.5,-0.3,0.2,0.2,0.1,-2.4,3.1,-0.3,0.2,0.1,0.2,-1.8,2.4,-0.4,0.0,0.0,0.2,-2.4,3.2,0.0,0.1,0.1,0.1,-1.8,2.5,-0.6,0.0,0.0,0.4,-2.5,3.1,0.2,-0.3,0.3,0.4,-1.8,2.6,-0.3,0.3,0.0,0.4,-2.9,3.6,-0.1,0.3,0.0,0.3,-2.1,2.6,-0.2,0.0,-0.2,0.3,-3.1,3.4,-0.1,0.1,0.3,0.1,-2.5,3.1,-0.1,0.1,0.0)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '1'
> par7 = '0'
> par6 = '1'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> par2 = '1'
> par1 = '10'
> #'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     sar1
      -0.3737  -0.5171
s.e.   0.0906   0.0868

sigma^2 estimated as 0.03835:  log likelihood = 21.11,  aic = -36.23
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 122 
End = 131 
Frequency = 1 
 [1]  3.493492999 -0.001690708  0.010983119  0.147190005  0.354673191
 [6] -1.945983694  2.600414079 -0.251862860  0.155182183 -0.096605373

$se
Time Series:
Start = 122 
End = 131 
Frequency = 1 
 [1] 0.1958412 0.2090693 0.2108506 0.2110982 0.2111327 0.2111376 0.2111382
 [8] 0.2111383 0.2111384 0.2111384

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 122 
End = 131 
Frequency = 1 
 [1]  3.1096442 -0.4114666 -0.4022841 -0.2665625 -0.0591470 -2.3598133
 [7]  2.1865831 -0.6656940 -0.2586490 -0.5104366
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 122 
End = 131 
Frequency = 1 
 [1]  3.8773418  0.4080852  0.4242504  0.5609425  0.7684934 -1.5321540
 [7]  3.0142450  0.1619683  0.5690134  0.3172258
> 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$pred))
  [1] -2.000000000  2.600000000  0.200000000  0.100000000 -0.100000000
  [6]  0.100000000 -1.600000000  2.300000000 -0.300000000  0.000000000
 [11]  0.100000000  0.400000000 -1.900000000  2.400000000  0.000000000
 [16]  0.400000000  0.100000000  0.200000000 -1.300000000  2.100000000
 [21] -0.100000000  0.300000000  0.300000000  0.200000000 -1.900000000
 [26]  2.700000000  0.000000000 -0.200000000  0.200000000  0.100000000
 [31] -1.500000000  2.100000000 -0.300000000 -0.200000000  0.200000000
 [36]  0.300000000 -2.000000000  2.600000000  0.000000000  0.500000000
 [41] -0.100000000  0.200000000 -1.600000000  2.100000000 -0.200000000
 [46]  0.000000000  0.200000000  0.200000000 -2.200000000  2.700000000
 [51] -0.300000000  0.400000000 -0.100000000  0.000000000 -1.600000000
 [56]  2.200000000 -0.300000000  0.000000000  0.100000000  0.100000000
 [61] -1.900000000  2.500000000  0.100000000 -0.100000000  0.300000000
 [66]  0.100000000 -1.900000000  2.500000000 -0.300000000  0.200000000
 [71]  0.200000000  0.100000000 -2.400000000  3.100000000 -0.300000000
 [76]  0.200000000  0.100000000  0.200000000 -1.800000000  2.400000000
 [81] -0.400000000  0.000000000  0.000000000  0.200000000 -2.400000000
 [86]  3.200000000  0.000000000  0.100000000  0.100000000  0.100000000
 [91] -1.800000000  2.500000000 -0.600000000  0.000000000  0.000000000
 [96]  0.400000000 -2.500000000  3.100000000  0.200000000 -0.300000000
[101]  0.300000000  0.400000000 -1.800000000  2.600000000 -0.300000000
[106]  0.300000000  0.000000000  0.400000000 -2.900000000  3.600000000
[111] -0.100000000  0.300000000  0.000000000  0.300000000 -2.100000000
[116]  2.600000000 -0.200000000  0.000000000 -0.200000000  0.300000000
[121] -3.100000000  3.493492999 -0.001690708  0.010983119  0.147190005
[126]  0.354673191 -1.945983694  2.600414079 -0.251862860  0.155182183
[131] -0.096605373
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 122 
End = 131 
Frequency = 1 
 [1]    0.05605886 -123.65782458   19.19770026    1.43418841    0.59528815
 [6]   -0.10849915    0.08119409   -0.83830677    1.36058374   -2.18557572
> postscript(file="/var/www/html/rcomp/tmp/1gvzk1292532389.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/html/rcomp/tmp/2c5xs1292532389.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/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/3uxbp1292532389.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/html/rcomp/tmp/4xg9v1292532389.tab") 
> 
> try(system("convert tmp/1gvzk1292532389.ps tmp/1gvzk1292532389.png",intern=TRUE))
character(0)
> try(system("convert tmp/2c5xs1292532389.ps tmp/2c5xs1292532389.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.646   0.383   1.623