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(0.072,0.073,0.073,0.073,0.074,0.073,0.074,0.074,0.076,0.076,0.077,0.077,0.078,0.078,0.080,0.081,0.081,0.082,0.081,0.081,0.081,0.080,0.082,0.084,0.084,0.085,0.086,0.085,0.083,0.078,0.078,0.080,0.086,0.089,0.089,0.086,0.083,0.083,0.083,0.084,0.085,0.084,0.086,0.085,0.085,0.085,0.085,0.085,0.085,0.085,0.085,0.086,0.086,0.086,0.086,0.084,0.080,0.079,0.080,0.080,0.080,0.080,0.079,0.079,0.079,0.080,0.079,0.075,0.072,0.070,0.069,0.071,0.071,0.072,0.071,0.069,0.068,0.067,0.067,0.069,0.073,0.074,0.073,0.071,0.070,0.071,0.075,0.077,0.078,0.077,0.077,0.078,0.080,0.081,0.081,0.080,0.081,0.082,0.083,0.084,0.085,0.085,0.085,0.085,0.085,0.083,0.082,0.081,0.079,0.076,0.073,0.071,0.070,0.070,0.070,0.070,0.069,0.068,0.067,0.066)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '1'
> par7 = '1'
> par6 = '2'
> par5 = '12'
> par4 = '0'
> par3 = '2'
> 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
      0.5694  -0.2492  -1.0000  0.0355
s.e.  0.1005   0.0997   0.0505  0.1080

sigma^2 estimated as 2.046e-06:  log likelihood = 480.24,  aic = -950.49
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 97 
End = 120 
Frequency = 1 
 [1] 0.07948539 0.07953832 0.07986840 0.08010083 0.08024009 0.08028210
 [7] 0.08035908 0.08047780 0.08063572 0.08075866 0.08084548 0.08089629
[13] 0.08096421 0.08105235 0.08115040 0.08124500 0.08133628 0.08142410
[19] 0.08151316 0.08160371 0.08169565 0.08178634 0.08187575 0.08196389

$se
Time Series:
Start = 97 
End = 120 
Frequency = 1 
 [1] 0.001437959 0.002688356 0.003605298 0.004267578 0.004800093 0.005277008
 [7] 0.005726820 0.006156084 0.006565921 0.006958042 0.007335016 0.007699314
[13] 0.008068063 0.008434957 0.008793310 0.009141675 0.009481441 0.009814236
[19] 0.010141089 0.010462572 0.010779091 0.011091028 0.011398751 0.011702600

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 97 
End = 120 
Frequency = 1 
 [1] 0.07666699 0.07426914 0.07280202 0.07173638 0.07083190 0.06993916
 [7] 0.06913451 0.06841187 0.06776651 0.06712090 0.06646884 0.06580563
[13] 0.06515081 0.06451984 0.06391551 0.06332731 0.06275266 0.06218820
[19] 0.06163663 0.06109707 0.06056863 0.06004793 0.05953420 0.05902679
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 97 
End = 120 
Frequency = 1 
 [1] 0.08230379 0.08480750 0.08693478 0.08846529 0.08964827 0.09062503
 [7] 0.09158364 0.09254373 0.09350493 0.09439642 0.09522211 0.09598694
[13] 0.09677762 0.09758487 0.09838529 0.09916268 0.09991990 0.10066000
[19] 0.10138970 0.10211035 0.10282266 0.10352476 0.10421731 0.10490098
> 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$pred))
  [1] 0.07200000 0.07300000 0.07300000 0.07300000 0.07400000 0.07300000
  [7] 0.07400000 0.07400000 0.07600000 0.07600000 0.07700000 0.07700000
 [13] 0.07800000 0.07800000 0.08000000 0.08100000 0.08100000 0.08200000
 [19] 0.08100000 0.08100000 0.08100000 0.08000000 0.08200000 0.08400000
 [25] 0.08400000 0.08500000 0.08600000 0.08500000 0.08300000 0.07800000
 [31] 0.07800000 0.08000000 0.08600000 0.08900000 0.08900000 0.08600000
 [37] 0.08300000 0.08300000 0.08300000 0.08400000 0.08500000 0.08400000
 [43] 0.08600000 0.08500000 0.08500000 0.08500000 0.08500000 0.08500000
 [49] 0.08500000 0.08500000 0.08500000 0.08600000 0.08600000 0.08600000
 [55] 0.08600000 0.08400000 0.08000000 0.07900000 0.08000000 0.08000000
 [61] 0.08000000 0.08000000 0.07900000 0.07900000 0.07900000 0.08000000
 [67] 0.07900000 0.07500000 0.07200000 0.07000000 0.06900000 0.07100000
 [73] 0.07100000 0.07200000 0.07100000 0.06900000 0.06800000 0.06700000
 [79] 0.06700000 0.06900000 0.07300000 0.07400000 0.07300000 0.07100000
 [85] 0.07000000 0.07100000 0.07500000 0.07700000 0.07800000 0.07700000
 [91] 0.07700000 0.07800000 0.08000000 0.08100000 0.08100000 0.08000000
 [97] 0.07948539 0.07953832 0.07986840 0.08010083 0.08024009 0.08028210
[103] 0.08035908 0.08047780 0.08063572 0.08075866 0.08084548 0.08089629
[109] 0.08096421 0.08105235 0.08115040 0.08124500 0.08133628 0.08142410
[115] 0.08151316 0.08160371 0.08169565 0.08178634 0.08187575 0.08196389
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 97 
End = 120 
Frequency = 1 
 [1] 0.01809085 0.03379951 0.04514048 0.05327757 0.05982163 0.06573082
 [7] 0.07126537 0.07649419 0.08142696 0.08615846 0.09072884 0.09517513
[13] 0.09964974 0.10406801 0.10835819 0.11251986 0.11657087 0.12053232
[19] 0.12441045 0.12821196 0.13194205 0.13560978 0.13922011 0.14277752
> postscript(file="/var/www/rcomp/tmp/1gu1q1324639806.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2ftrc1324639806.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/3ogop1324639806.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/4rhi21324639806.tab") 
> 
> try(system("convert tmp/1gu1q1324639806.ps tmp/1gu1q1324639806.png",intern=TRUE))
character(0)
> try(system("convert tmp/2ftrc1324639806.ps tmp/2ftrc1324639806.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.460   0.090   1.553