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(1.71,0.81,0.71,1.01,0.01,0.71,1.51,2.41,2.31,3.61,3.81,4.41,4.91,6.51,7.21,7.11,7.61,7.51,6.81,5.81,6.11,5.31,5.21,4.81,4.61,3.91,3.11,2.91,3.01,3.01,3.01,3.51,3.51,3.51,3.41,3.81,3.71,3.41,3.61,4.01,4.11,4.21,4.51,4.31,3.91,4.51,4.51,4.51,4.01,3.91,4.71,4.61,4.41,4.41,4.01,4.11,4.51,4.01,3.71,3.61)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '0'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '1'
> par1 = '24'
> 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
      0.8785  -0.5092  0.0932  -0.8359  0.8937  0.1121
s.e.  0.6599   0.6477  0.3925   0.6469  0.6393  0.6431

sigma^2 estimated as 0.2620:  log likelihood = -25.35,  aic = 64.69
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 3.779848 3.858106 3.849590 3.827407 3.819546 3.823142 3.828236 3.830148
 [9] 3.829570 3.828562 3.828150 3.828247 3.828448 3.828537 3.828522 3.828482
[17] 3.828463 3.828465 3.828473 3.828477 3.828477 3.828475 3.828474 3.828474
[25] 3.828474 3.828475 3.828475 3.828475

$se
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 0.5262695 0.7695412 1.0874435 1.5026014 1.9048456 2.2359417 2.5043365
 [8] 2.7363126 2.9499573 3.1521492 3.3439169 3.5253671 3.6974245 3.8615020
[15] 4.0188567 4.1703635 4.3166156 4.4580799 4.5951764 4.7282882 4.8577521
[22] 4.9838566 5.1068503 5.2269511 5.3443532 5.4592307 5.5717400 5.6820221

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1]  2.74835941  2.34980504  1.71820085  0.88230813  0.08604906 -0.55930364
 [7] -1.08026324 -1.53302427 -1.95234679 -2.34965044 -2.72592727 -3.08147267
[13] -3.41850412 -3.74000701 -4.04843740 -4.34543075 -4.63210382 -4.90937164
[19] -5.17807288 -5.43896802 -5.69271744 -5.93988391 -6.18095245 -6.41635000
[25] -6.64645775 -6.87161744 -7.09213578 -7.30828873
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1]  4.811336  5.366406  5.980980  6.772506  7.553044  8.205588  8.736736
 [8]  9.193321  9.611486 10.006775 10.382227 10.737966 11.075400 11.397081
[15] 11.705481 12.002394 12.289029 12.566301 12.835018 13.095922 13.349671
[22] 13.596834 13.837901 14.073298 14.303407 14.528567 14.749085 14.965238
> 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$pred))
 [1] 1.710000 0.810000 0.710000 1.010000 0.010000 0.710000 1.510000 2.410000
 [9] 2.310000 3.610000 3.810000 4.410000 4.910000 6.510000 7.210000 7.110000
[17] 7.610000 7.510000 6.810000 5.810000 6.110000 5.310000 5.210000 4.810000
[25] 4.610000 3.910000 3.110000 2.910000 3.010000 3.010000 3.010000 3.510000
[33] 3.779848 3.858106 3.849590 3.827407 3.819546 3.823142 3.828236 3.830148
[41] 3.829570 3.828562 3.828150 3.828247 3.828448 3.828537 3.828522 3.828482
[49] 3.828463 3.828465 3.828473 3.828477 3.828477 3.828475 3.828474 3.828474
[57] 3.828474 3.828475 3.828475 3.828475
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 0.1392303 0.1994609 0.2824829 0.3925899 0.4987099 0.5848440 0.6541750
 [8] 0.7144142 0.7703104 0.8233246 0.8735073 0.9208829 0.9657764 1.0086104
[15] 1.0497150 1.0892996 1.1275062 1.1644562 1.2002636 1.2350312 1.2688473
[22] 1.3017864 1.3339127 1.3652831 1.3959485 1.4259545 1.4553420 1.4841478
> postscript(file="/var/www/html/rcomp/tmp/1pl881260551235.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2qey71260551235.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/304qh1260551235.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/42c9b1260551235.tab") 
> system("convert tmp/1pl881260551235.ps tmp/1pl881260551235.png")
> system("convert tmp/2qey71260551235.ps tmp/2qey71260551235.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.727   0.325   0.882