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(9.769,9.321,9.939,9.336,10.195,9.464,10.010,10.213,9.563,9.890,9.305,9.391,9.928,8.686,9.843,9.627,10.074,9.503,10.119,10.000,9.313,9.866,9.172,9.241,9.659,8.904,9.755,9.080,9.435,8.971,10.063,9.793,9.454,9.759,8.820,9.403,9.676,8.642,9.402,9.610,9.294,9.448,10.319,9.548,9.801,9.596,8.923,9.746,9.829,9.125,9.782,9.441,9.162,9.915,10.444,10.209,9.985,9.842,9.429,10.132,9.849,9.172,10.313,9.819,9.955,10.048,10.082,10.541,10.208,10.233,9.439,9.963,10.158,9.225,10.474,9.757,10.490,10.281,10.444,10.640,10.695,10.786,9.832,9.747,10.411,9.511,10.402,9.701,10.540,10.112,10.915,11.183,10.384,10.834,9.886,10.216)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '1'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> par2 = '-0.8'
> 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      ma1    sar1     sma1
      0.9937  -0.8286  0.4595  -1.0000
s.e.  0.0253   0.0555  0.1503   0.1611

sigma^2 estimated as 1.145e-05:  log likelihood = 300.71,  aic = -591.42
Warning messages:
1: In log(s2) : NaNs produced
2: In log(s2) : NaNs produced
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 85 
End = 96 
Frequency = 1 
 [1] 0.1542143 0.1661313 0.1517885 0.1591663 0.1524144 0.1550242 0.1505491
 [8] 0.1497677 0.1514999 0.1500045 0.1606106 0.1588085

$se
Time Series:
Start = 85 
End = 96 
Frequency = 1 
 [1] 0.003563909 0.003607833 0.003650152 0.003690927 0.003730215 0.003768070
 [7] 0.003804539 0.003839669 0.003873500 0.003906073 0.003937423 0.003967585

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 85 
End = 96 
Frequency = 1 
 [1] 0.1472290 0.1590599 0.1446342 0.1519321 0.1451032 0.1476388 0.1430922
 [8] 0.1422420 0.1439078 0.1423486 0.1528933 0.1510320
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 85 
End = 96 
Frequency = 1 
 [1] 0.1611996 0.1732026 0.1589428 0.1664005 0.1597256 0.1624096 0.1580060
 [8] 0.1572935 0.1590919 0.1576604 0.1683280 0.1665849
> 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$pred))
 [1]  9.769000  9.321000  9.939000  9.336000 10.195000  9.464000 10.010000
 [8] 10.213000  9.563000  9.890000  9.305000  9.391000  9.928000  8.686000
[15]  9.843000  9.627000 10.074000  9.503000 10.119000 10.000000  9.313000
[22]  9.866000  9.172000  9.241000  9.659000  8.904000  9.755000  9.080000
[29]  9.435000  8.971000 10.063000  9.793000  9.454000  9.759000  8.820000
[36]  9.403000  9.676000  8.642000  9.402000  9.610000  9.294000  9.448000
[43] 10.319000  9.548000  9.801000  9.596000  8.923000  9.746000  9.829000
[50]  9.125000  9.782000  9.441000  9.162000  9.915000 10.444000 10.209000
[57]  9.985000  9.842000  9.429000 10.132000  9.849000  9.172000 10.313000
[64]  9.819000  9.955000 10.048000 10.082000 10.541000 10.208000 10.233000
[71]  9.439000  9.963000 10.158000  9.225000 10.474000  9.757000 10.490000
[78] 10.281000 10.444000 10.640000 10.695000 10.786000  9.832000  9.747000
[85] 10.347708  9.428350 10.554835  9.946861 10.500682 10.280180 10.663565
[92] 10.733149 10.579977 10.711981  9.835175  9.974887
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 85 
End = 96 
Frequency = 1 
 [1] 0.03043557 0.02850862 0.03173910 0.03054521 0.03233406 0.03209983
 [7] 0.03344878 0.03396267 0.03386470 0.03452782 0.03239154 0.03304597
> postscript(file="/var/www/rcomp/tmp/1l2us1293031741.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2rm941293031741.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/3g56y1293031741.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/42n5m1293031741.tab") 
> 
> try(system("convert tmp/1l2us1293031741.ps tmp/1l2us1293031741.png",intern=TRUE))
character(0)
> try(system("convert tmp/2rm941293031741.ps tmp/2rm941293031741.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.200   0.470   1.641