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(7.1,6.9,6.8,7.5,7.6,7.8,8.0,8.1,8.2,8.3,8.2,8.0,7.9,7.6,7.6,8.3,8.4,8.4,8.4,8.4,8.6,8.9,8.8,8.3,7.5,7.2,7.4,8.8,9.3,9.3,8.7,8.2,8.3,8.5,8.6,8.5,8.2,8.1,7.9,8.6,8.7,8.7,8.5,8.4,8.5,8.7,8.7,8.6,8.5,8.3,8.0,8.2,8.1,8.1,8.0,7.9,7.9,8.0,8.0,7.9,8.0,7.7,7.2,7.5,7.3,7.0,7.0,7.0,7.2,7.3,7.1,6.8,6.4,6.1,6.5,7.7,7.9,7.5,6.9,6.6,6.9,7.7,8.0,8.0,7.7,7.3,7.4,8.1,8.3,8.2)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '1'
> par7 = '0'
> par6 = '3'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> 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
      0.8433  -0.4999  -0.1498  -0.2816  0.2591  -0.3008  0.5573  -0.9999
s.e.  0.5164   0.6048   0.4465   0.5021  0.3238   0.1912  0.2467   0.4278

sigma^2 estimated as 0.02143:  log likelihood = 19.01,  aic = -20.02
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 63 
End = 90 
Frequency = 1 
 [1] 7.389074 7.602202 7.559209 7.667821 7.690357 7.657536 7.674091 7.732435
 [9] 7.663564 7.517270 7.529324 7.290213 7.068446 7.441981 7.436270 7.519258
[17] 7.511743 7.475681 7.529224 7.622831 7.557107 7.386638 7.321532 7.085583
[25] 6.901384 7.373691 7.407335 7.488833

$se
Time Series:
Start = 63 
End = 90 
Frequency = 1 
 [1] 0.1563839 0.2903517 0.4038245 0.4488002 0.4578727 0.4594678 0.4641119
 [8] 0.4806128 0.5102106 0.5406388 0.5616367 0.5734846 0.6107683 0.6709559
[15] 0.7434593 0.7929576 0.8188923 0.8343974 0.8511653 0.8759168 0.9088263
[22] 0.9436036 0.9733621 0.9957760 1.0341772 1.0844027 1.1409112 1.1850222

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 63 
End = 90 
Frequency = 1 
 [1] 7.082561 7.033113 6.767713 6.788172 6.792926 6.756979 6.764432 6.790434
 [9] 6.663552 6.457618 6.428517 6.166183 5.871340 6.126907 5.979090 5.965061
[17] 5.906715 5.840262 5.860940 5.906034 5.775808 5.537175 5.413743 5.133862
[25] 4.874397 5.248262 5.171149 5.166189
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 63 
End = 90 
Frequency = 1 
 [1] 7.695586 8.171292 8.350705 8.547469 8.587787 8.558093 8.583750 8.674436
 [9] 8.663577 8.576922 8.630132 8.414243 8.265551 8.757054 8.893450 9.073454
[17] 9.116772 9.111100 9.197508 9.339628 9.338407 9.236101 9.229322 9.037304
[25] 8.928372 9.499120 9.643521 9.811476
> 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$pred))
 [1] 7.100000 6.900000 6.800000 7.500000 7.600000 7.800000 8.000000 8.100000
 [9] 8.200000 8.300000 8.200000 8.000000 7.900000 7.600000 7.600000 8.300000
[17] 8.400000 8.400000 8.400000 8.400000 8.600000 8.900000 8.800000 8.300000
[25] 7.500000 7.200000 7.400000 8.800000 9.300000 9.300000 8.700000 8.200000
[33] 8.300000 8.500000 8.600000 8.500000 8.200000 8.100000 7.900000 8.600000
[41] 8.700000 8.700000 8.500000 8.400000 8.500000 8.700000 8.700000 8.600000
[49] 8.500000 8.300000 8.000000 8.200000 8.100000 8.100000 8.000000 7.900000
[57] 7.900000 8.000000 8.000000 7.900000 8.000000 7.700000 7.389074 7.602202
[65] 7.559209 7.667821 7.690357 7.657536 7.674091 7.732435 7.663564 7.517270
[73] 7.529324 7.290213 7.068446 7.441981 7.436270 7.519258 7.511743 7.475681
[81] 7.529224 7.622831 7.557107 7.386638 7.321532 7.085583 6.901384 7.373691
[89] 7.407335 7.488833
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 63 
End = 90 
Frequency = 1 
 [1] 0.02116421 0.03819311 0.05342154 0.05853035 0.05953856 0.06000204
 [7] 0.06047777 0.06215542 0.06657615 0.07191956 0.07459324 0.07866500
[13] 0.08640773 0.09015824 0.09997745 0.10545690 0.10901495 0.11161490
[19] 0.11304821 0.11490701 0.12026113 0.12774467 0.13294513 0.14053551
[25] 0.14985069 0.14706375 0.15402452 0.15823857
> postscript(file="/var/www/html/rcomp/tmp/1xwd91261127277.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2jtdr1261127277.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/3qz121261127277.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/417nn1261127277.tab") 
> 
> try(system("convert tmp/1xwd91261127277.ps tmp/1xwd91261127277.png",intern=TRUE))
character(0)
> try(system("convert tmp/2jtdr1261127277.ps tmp/2jtdr1261127277.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.777   0.322   2.019