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(2.4,2.4,2.5,2.6,2.4,2.6,2.4,2.3,2.4,2.4,2.4,2.4,2.4,2.4,2.4,2.4,2.5,2.1,2.1,2,2,2,1.9,1.9,2,1.8,1.6,1.3,1.4,1.4,1.5,1.7,1.6,1.5,1.6,1.5,1.1,1.1,1.1,1.4,1.3,1.4,1.3,1.1,1,0.9,0.8,0.8,0.8,0.8,1,1.1,1,0.9,1.1,1.2,1.2,1.4,1.5,1.7,1.9,1.9,1.9,1.7,1.7,2.1,2,2,2.5,2.4,2.5,2.5,2,1.9,2.2,2.7,3.1,2.8,2.6,2.3,2.2,2.2,2,2,2.6,2.5,2.5,2.3,2,1.9,2,2.1,2.1,2.3,2.3,2.3,2.1,2.4,2.5,2.1,1.8,1.9,1.9,2.1,2.2,2,2.2,2,1.9,1.6,1.7,2,2.5,2.4,2.3,2.3,2.1,2.4,2.2,2.4,1.9,2.1,2.1,2.1,2,2.1,2.2,2.2,2.6,2.5,2.3,2.2,2.4,2.3,2.2,2.5,2.5,2.5,2.4,2.3,1.7,1.6,1.9,1.9,1.8,1.8,1.9,1.9,1.9,1.9,1.8,1.7,2.1,2.6,3.1,3.1,3.2,3.3,3.6,3.3,3.7,4,4,3.8,3.6,3.2,2.1,1.6,1.1,1.2,0.6,0.6,0,-0.1,-0.6,-0.2,-0.3,-0.1,0.5,0.9)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '2'
> par7 = '1'
> par6 = '2'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '1'
> par1 = '24'
> #'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      ma1     sar1     sar2
      0.6897  -0.1971  -0.5513  -0.5661  -0.2796
s.e.  0.2083   0.0852   0.1994   0.0815   0.0829

sigma^2 estimated as 0.02939:  log likelihood = 51.09,  aic = -90.19
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 157 
End = 180 
Frequency = 1 
 [1] 2.992939 2.952078 2.897193 2.808799 2.810845 2.813148 2.898903 2.983836
 [9] 2.925135 2.669963 2.302983 2.302964 2.391527 2.414660 2.417778 2.467822
[17] 2.466664 2.465360 2.444767 2.424639 2.346049 2.350731 2.418712 2.418723

$se
Time Series:
Start = 157 
End = 180 
Frequency = 1 
 [1] 0.1714353 0.2597723 0.3147680 0.3535840 0.3852625 0.4136901 0.4402919
 [8] 0.4655255 0.4895573 0.5125008 0.5344673 0.5555639 0.5582383 0.5597519
[15] 0.5620698 0.5653101 0.5690363 0.5728865 0.5767099 0.5804782 0.5842022
[22] 0.5878945 0.5915622 0.5952078

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 157 
End = 180 
Frequency = 1 
 [1] 2.656926 2.442924 2.280248 2.115774 2.055730 2.002316 2.035931 2.071406
 [9] 1.965602 1.665461 1.255427 1.214059 1.297380 1.317547 1.316121 1.359814
[17] 1.351353 1.342502 1.314416 1.286902 1.201012 1.198458 1.259250 1.252115
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 157 
End = 180 
Frequency = 1 
 [1] 3.328952 3.461232 3.514139 3.501823 3.565959 3.623981 3.761875 3.896266
 [9] 3.884667 3.674464 3.350539 3.391869 3.485674 3.511774 3.519434 3.575830
[17] 3.581975 3.588217 3.575118 3.562376 3.491085 3.503004 3.578174 3.585330
> 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$pred))
  [1] 2.400000 2.400000 2.500000 2.600000 2.400000 2.600000 2.400000 2.300000
  [9] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
 [17] 2.500000 2.100000 2.100000 2.000000 2.000000 2.000000 1.900000 1.900000
 [25] 2.000000 1.800000 1.600000 1.300000 1.400000 1.400000 1.500000 1.700000
 [33] 1.600000 1.500000 1.600000 1.500000 1.100000 1.100000 1.100000 1.400000
 [41] 1.300000 1.400000 1.300000 1.100000 1.000000 0.900000 0.800000 0.800000
 [49] 0.800000 0.800000 1.000000 1.100000 1.000000 0.900000 1.100000 1.200000
 [57] 1.200000 1.400000 1.500000 1.700000 1.900000 1.900000 1.900000 1.700000
 [65] 1.700000 2.100000 2.000000 2.000000 2.500000 2.400000 2.500000 2.500000
 [73] 2.000000 1.900000 2.200000 2.700000 3.100000 2.800000 2.600000 2.300000
 [81] 2.200000 2.200000 2.000000 2.000000 2.600000 2.500000 2.500000 2.300000
 [89] 2.000000 1.900000 2.000000 2.100000 2.100000 2.300000 2.300000 2.300000
 [97] 2.100000 2.400000 2.500000 2.100000 1.800000 1.900000 1.900000 2.100000
[105] 2.200000 2.000000 2.200000 2.000000 1.900000 1.600000 1.700000 2.000000
[113] 2.500000 2.400000 2.300000 2.300000 2.100000 2.400000 2.200000 2.400000
[121] 1.900000 2.100000 2.100000 2.100000 2.000000 2.100000 2.200000 2.200000
[129] 2.600000 2.500000 2.300000 2.200000 2.400000 2.300000 2.200000 2.500000
[137] 2.500000 2.500000 2.400000 2.300000 1.700000 1.600000 1.900000 1.900000
[145] 1.800000 1.800000 1.900000 1.900000 1.900000 1.900000 1.800000 1.700000
[153] 2.100000 2.600000 3.100000 3.100000 2.992939 2.952078 2.897193 2.808799
[161] 2.810845 2.813148 2.898903 2.983836 2.925135 2.669963 2.302983 2.302964
[169] 2.391527 2.414660 2.417778 2.467822 2.466664 2.465360 2.444767 2.424639
[177] 2.346049 2.350731 2.418712 2.418723
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 157 
End = 180 
Frequency = 1 
 [1] 0.05727991 0.08799642 0.10864584 0.12588441 0.13706290 0.14705591
 [7] 0.15188226 0.15601576 0.16736232 0.19195051 0.23207609 0.24123864
[13] 0.23342342 0.23181393 0.23247370 0.22907246 0.23069065 0.23237439
[19] 0.23589565 0.23940810 0.24901536 0.25009007 0.24457736 0.24608351
> postscript(file="/var/wessaorg/rcomp/tmp/1zvyl1323214957.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2bq5k1323214957.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/3yh6y1323214957.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/4ai3h1323214957.tab") 
> 
> try(system("convert tmp/1zvyl1323214957.ps tmp/1zvyl1323214957.png",intern=TRUE))
character(0)
> try(system("convert tmp/2bq5k1323214957.ps tmp/2bq5k1323214957.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.830   0.309   2.132