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(01.303763,01.416094,01.052458,01.312283,01.309429,01.492409,01.026556,01.005406,01.334886,01.393873,01.128092,01.122787,01.213104,01.253528,01.094796,00.912944,01.195130,00.927499,00.965333,01.198078,00.966362,00.973685,00.994801,00.826262,00.688888,00.781307,00.604791,01.086240,00.774026,01.026032,00.676435,00.830525,00.791624,00.752391,00.670202,00.880336,00.914297,00.961042,00.930194,00.867966,00.989160,00.997288,00.798744,00.975379,00.934721,00.973234,00.815300,00.940209,00.794493,00.931340,00.922050,00.784517,00.822098,00.891026,00.807306,00.951441,01.147907,01.172609,01.281051,01.165962,00.978911,01.410951,01.197838,01.288368,01.102253,01.197657,01.299984,01.198611,01.299252,01.097604,01.399770,01.398396,01.401880,01.699717,01.397610,01.500135,01.400136,01.400427,01.341477,01.338580,01.482977,01.163253,01.328468,01.234550,01.484741,01.336579,01.339292,01.405225,01.333491,01.149740)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> 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#output/
> #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     ma1     sma1
      -0.0718  -0.562  -0.7237
s.e.   0.1934   0.159   0.1862

sigma^2 estimated as 0.02587:  log likelihood = 21.96,  aic = -35.93
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 79 
End = 90 
Frequency = 1 
 [1] 1.353462 1.422165 1.489431 1.443948 1.495282 1.498667 1.437499 1.657670
 [9] 1.469182 1.536859 1.482492 1.529326

$se
Time Series:
Start = 79 
End = 90 
Frequency = 1 
 [1] 0.1616446 0.1721411 0.1845582 0.1960122 0.2068451 0.2171355 0.2268820
 [8] 0.2362590 0.2452777 0.2539764 0.2623869 0.2705360

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 79 
End = 90 
Frequency = 1 
 [1] 1.0366382 1.0847689 1.1276965 1.0597646 1.0898660 1.0730815 0.9928098
 [8] 1.1946022 0.9884373 1.0390648 0.9682136 0.9990757
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 79 
End = 90 
Frequency = 1 
 [1] 1.670285 1.759562 1.851165 1.828132 1.900699 1.924253 1.882187 2.120737
 [9] 1.949926 2.034652 1.996770 2.059577
> 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$pred))
 [1] 1.303763 1.416094 1.052458 1.312283 1.309429 1.492409 1.026556 1.005406
 [9] 1.334886 1.393873 1.128092 1.122787 1.213104 1.253528 1.094796 0.912944
[17] 1.195130 0.927499 0.965333 1.198078 0.966362 0.973685 0.994801 0.826262
[25] 0.688888 0.781307 0.604791 1.086240 0.774026 1.026032 0.676435 0.830525
[33] 0.791624 0.752391 0.670202 0.880336 0.914297 0.961042 0.930194 0.867966
[41] 0.989160 0.997288 0.798744 0.975379 0.934721 0.973234 0.815300 0.940209
[49] 0.794493 0.931340 0.922050 0.784517 0.822098 0.891026 0.807306 0.951441
[57] 1.147907 1.172609 1.281051 1.165962 0.978911 1.410951 1.197838 1.288368
[65] 1.102253 1.197657 1.299984 1.198611 1.299252 1.097604 1.399770 1.398396
[73] 1.401880 1.699717 1.397610 1.500135 1.400136 1.400427 1.353462 1.422165
[81] 1.489431 1.443948 1.495282 1.498667 1.437499 1.657670 1.469182 1.536859
[89] 1.482492 1.529326
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 79 
End = 90 
Frequency = 1 
 [1] 0.1194305 0.1210415 0.1239119 0.1357473 0.1383318 0.1448857 0.1578311
 [8] 0.1425248 0.1669485 0.1652569 0.1769904 0.1768988
> postscript(file="/var/www/rcomp/tmp/1ymmz1293630079.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2pav11293630079.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/36k9g1293630079.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/4r3qm1293630079.tab") 
> 
> try(system("convert tmp/1ymmz1293630079.ps tmp/1ymmz1293630079.png",intern=TRUE))
character(0)
> try(system("convert tmp/2pav11293630079.ps tmp/2pav11293630079.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.810   0.430   1.233