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(8.3,8.2,8,7.9,7.6,7.6,8.3,8.4,8.4,8.4,8.4,8.6,8.9,8.8,8.3,7.5,7.2,7.4,8.8,9.3,9.3,8.7,8.2,8.3,8.5,8.6,8.5,8.2,8.1,7.9,8.6,8.7,8.7,8.5,8.4,8.5,8.7,8.7,8.6,8.5,8.3,8,8.2,8.1,8.1,8,7.9,7.9,8,8,7.9,8,7.7,7.2,7.5,7.3,7,7,7,7.2,7.3,7.1,6.8,6.4,6.1,6.5,7.7,7.9,7.5,6.9,6.6,6.9)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '1'
> par7 = '1'
> par6 = '3'
> par5 = '12'
> par4 = '1'
> par3 = '2'
> par2 = '1'
> par1 = '12'
> par1 <- as.numeric(par1) #cut off periods
> par1 <- 28
> 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
> par6 <- 3
> par7 <- as.numeric(par7) #q
> par7 <- 3
> 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      ar3      ma1      ma2     ma3    sar1     sma1
      0.5066  0.1102  -0.6667  -1.3625  -0.1944  0.5996  0.2708  -0.8547
s.e.  0.3930  0.4815   0.3278   0.4400   0.8237  0.4196  0.3526   0.4752

sigma^2 estimated as 0.02039:  log likelihood = 4.91,  aic = 8.18
Warning message:
In log(s2) : NaNs produced
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1] 8.214035 8.436417 8.681640 8.957675 8.974898 8.603594 8.091009 7.737529
 [9] 7.630272 7.720204 8.463761 8.554782 8.468367 8.242435 8.099438 8.263640
[17] 8.464926 8.407260 8.117143 7.746543 7.443491 7.302281 7.956054 8.081225
[25] 8.122306 8.015409 7.913134 8.018541

$se
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1] 0.1535683 0.2371677 0.2698939 0.2699199 0.2778542 0.2882573 0.2882977
 [8] 0.3003381 0.3371276 0.3720710 0.3880244 0.3902232 0.4009531 0.4189783
[15] 0.4435967 0.4654430 0.4844321 0.4997464 0.5160144 0.5357117 0.5617719
[22] 0.5929649 0.6261833 0.6576469 0.7057959 0.7546483 0.7969509 0.8287653

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1] 7.913042 7.971569 8.152648 8.428632 8.430304 8.038610 7.525945 7.148866
 [9] 6.969502 6.990945 7.703233 7.789944 7.682499 7.421237 7.229988 7.351372
[17] 7.515439 7.427758 7.105754 6.696548 6.342419 6.140070 6.728735 6.792237
[25] 6.738946 6.536299 6.351110 6.394161
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1] 8.515029 8.901266 9.210632 9.486718 9.519493 9.168578 8.656073 8.326191
 [9] 8.291042 8.449464 9.224289 9.319619 9.254235 9.063632 8.968887 9.175908
[17] 9.414413 9.386763 9.128531 8.796538 8.544564 8.464492 9.183373 9.370212
[25] 9.505666 9.494520 9.475158 9.642921
> 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$pred))
 [1] 8.300000 8.200000 8.000000 7.900000 7.600000 7.600000 8.300000 8.400000
 [9] 8.400000 8.400000 8.400000 8.600000 8.900000 8.800000 8.300000 7.500000
[17] 7.200000 7.400000 8.800000 9.300000 9.300000 8.700000 8.200000 8.300000
[25] 8.500000 8.600000 8.500000 8.200000 8.100000 7.900000 8.600000 8.700000
[33] 8.700000 8.500000 8.400000 8.500000 8.700000 8.700000 8.600000 8.500000
[41] 8.300000 8.000000 8.200000 8.100000 8.214035 8.436417 8.681640 8.957675
[49] 8.974898 8.603594 8.091009 7.737529 7.630272 7.720204 8.463761 8.554782
[57] 8.468367 8.242435 8.099438 8.263640 8.464926 8.407260 8.117143 7.746543
[65] 7.443491 7.302281 7.956054 8.081225 8.122306 8.015409 7.913134 8.018541
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 45 
End = 72 
Frequency = 1 
 [1] 0.01869584 0.02811237 0.03108789 0.03013281 0.03095903 0.03350429
 [7] 0.03563186 0.03881576 0.04418291 0.04819445 0.04584539 0.04561463
[13] 0.04734715 0.05083186 0.05476883 0.05632421 0.05722815 0.05944224
[19] 0.06357095 0.06915494 0.07547155 0.08120269 0.07870526 0.08137961
[25] 0.08689600 0.09414969 0.10071242 0.10335613
> postscript(file="/var/www/html/rcomp/tmp/1t22w1261039867.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/28y171261039867.ps",horizontal=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/31m4i1261039867.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/4ob401261039867.tab") 
> try(system("convert tmp/1t22w1261039867.ps tmp/1t22w1261039867.png",intern=TRUE))
character(0)
> try(system("convert tmp/28y171261039867.ps tmp/28y171261039867.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  2.088   0.331   2.256