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(6.9,6.8,6.7,6.6,6.5,6.5,7.0,7.5,7.6,7.6,7.6,7.8,8.0,8.0,8.0,7.9,7.9,8.0,8.5,9.2,9.4,9.5,9.5,9.6,9.7,9.7,9.6,9.5,9.4,9.3,9.6,10.2,10.2,10.1,9.9,9.8,9.8,9.7,9.5,9.3,9.1,9.0,9.5,10.0,10.2,10.1,10.0,9.9,10.0,9.9,9.7,9.5,9.2,9.0,9.3,9.8,9.8,9.6,9.4,9.3,9.2,9.2,9.0,8.8,8.7,8.7,9.1,9.7,9.8,9.6,9.4,9.4,9.5,9.4,9.3,9.2,9.0,8.9,9.2,9.8,9.9,9.6,9.2,9.1,9.1,9.0,8.9,8.7,8.5,8.3,8.5,8.7,8.4,8.1,7.8,7.7,7.5,7.2,6.8,6.7,6.4,6.3,6.8,7.3,7.1,7.0,6.8,6.6,6.3,6.1,6.1,6.3,6.3,6.0,6.2,6.4,6.8,7.5,7.5,7.6,7.6,7.4,7.3,7.1,6.9,6.8,7.5,7.6,7.8,8.0,8.1,8.2,8.3,8.2,8.0,7.9,7.6,7.6,8.3,8.4,8.4,8.4,8.4,8.6,8.9,8.8,8.3,7.5,7.2,7.4,8.8,9.3,9.3,8.7,8.2,8.3,8.5,8.6,8.5,8.2,8.1,7.9,8.6,8.7,8.7,8.5,8.4,8.5,8.7,8.7,8.6,8.5,8.3,8.0,8.2,8.1,8.1,8.0,7.9,7.9)
> 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
      -0.0264  -0.0545  -0.4811  0.5618  0.2959  0.2972  0.0828  -0.4730
s.e.   0.4348   0.2988   0.2774  0.4443  0.2252  0.2507  0.3172   0.3032

sigma^2 estimated as 0.02552:  log likelihood = 56.32,  aic = -94.64
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 153 
End = 180 
Frequency = 1 
 [1]  9.356166  9.187114  9.023894  9.186768  9.507065  9.461925  9.074627
 [8]  8.482219  8.175536  8.283402  9.408665  9.785271  9.841623  9.765753
[15]  9.660046  9.814285 10.080973 10.007962  9.636537  9.089516  8.796775
[22]  8.891948  9.980237 10.340300 10.400045 10.338989 10.240716 10.392159

$se
Time Series:
Start = 153 
End = 180 
Frequency = 1 
 [1] 0.1597583 0.2927396 0.4062077 0.4752088 0.5173038 0.5510748 0.5895425
 [8] 0.6328378 0.6752011 0.7116230 0.7433441 0.7732866 0.8354523 0.9149876
[15] 0.9968732 1.0637788 1.1178179 1.1668135 1.2176160 1.2701793 1.3215140
[22] 1.3690024 1.4132677 1.4559620 1.5227885 1.6023525 1.6845483 1.7564812

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 153 
End = 180 
Frequency = 1 
 [1] 9.043039 8.613344 8.227727 8.255359 8.493149 8.381818 7.919123 7.241857
 [9] 6.852141 6.888621 7.951711 8.269629 8.204137 7.972377 7.706174 7.729278
[17] 7.890050 7.721008 7.250010 6.599964 6.206607 6.208703 7.210233 7.486614
[25] 7.415380 7.198378 6.939002 6.949455
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 153 
End = 180 
Frequency = 1 
 [1]  9.669292  9.760883  9.820061 10.118177 10.520980 10.542031 10.230130
 [8]  9.722581  9.498930  9.678183 10.865619 11.300912 11.479110 11.559129
[15] 11.613917 11.899291 12.271896 12.294917 12.023065 11.579067 11.386942
[22] 11.575193 12.750242 13.193985 13.384710 13.479600 13.542431 13.834862
> 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$pred))
  [1]  6.900000  6.800000  6.700000  6.600000  6.500000  6.500000  7.000000
  [8]  7.500000  7.600000  7.600000  7.600000  7.800000  8.000000  8.000000
 [15]  8.000000  7.900000  7.900000  8.000000  8.500000  9.200000  9.400000
 [22]  9.500000  9.500000  9.600000  9.700000  9.700000  9.600000  9.500000
 [29]  9.400000  9.300000  9.600000 10.200000 10.200000 10.100000  9.900000
 [36]  9.800000  9.800000  9.700000  9.500000  9.300000  9.100000  9.000000
 [43]  9.500000 10.000000 10.200000 10.100000 10.000000  9.900000 10.000000
 [50]  9.900000  9.700000  9.500000  9.200000  9.000000  9.300000  9.800000
 [57]  9.800000  9.600000  9.400000  9.300000  9.200000  9.200000  9.000000
 [64]  8.800000  8.700000  8.700000  9.100000  9.700000  9.800000  9.600000
 [71]  9.400000  9.400000  9.500000  9.400000  9.300000  9.200000  9.000000
 [78]  8.900000  9.200000  9.800000  9.900000  9.600000  9.200000  9.100000
 [85]  9.100000  9.000000  8.900000  8.700000  8.500000  8.300000  8.500000
 [92]  8.700000  8.400000  8.100000  7.800000  7.700000  7.500000  7.200000
 [99]  6.800000  6.700000  6.400000  6.300000  6.800000  7.300000  7.100000
[106]  7.000000  6.800000  6.600000  6.300000  6.100000  6.100000  6.300000
[113]  6.300000  6.000000  6.200000  6.400000  6.800000  7.500000  7.500000
[120]  7.600000  7.600000  7.400000  7.300000  7.100000  6.900000  6.800000
[127]  7.500000  7.600000  7.800000  8.000000  8.100000  8.200000  8.300000
[134]  8.200000  8.000000  7.900000  7.600000  7.600000  8.300000  8.400000
[141]  8.400000  8.400000  8.400000  8.600000  8.900000  8.800000  8.300000
[148]  7.500000  7.200000  7.400000  8.800000  9.300000  9.356166  9.187114
[155]  9.023894  9.186768  9.507065  9.461925  9.074627  8.482219  8.175536
[162]  8.283402  9.408665  9.785271  9.841623  9.765753  9.660046  9.814285
[169] 10.080973 10.007962  9.636537  9.089516  8.796775  8.891948  9.980237
[176] 10.340300 10.400045 10.338989 10.240716 10.392159
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 153 
End = 180 
Frequency = 1 
 [1] 0.01707519 0.03186415 0.04501468 0.05172752 0.05441257 0.05824130
 [7] 0.06496604 0.07460758 0.08258800 0.08590951 0.07900632 0.07902558
[13] 0.08488969 0.09369351 0.10319550 0.10839086 0.11088393 0.11658852
[19] 0.12635410 0.13974114 0.15022710 0.15395979 0.14160662 0.14080462
[25] 0.14642134 0.15498154 0.16449516 0.16901986
> postscript(file="/var/www/html/rcomp/tmp/1qvzu1260543018.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2g0pt1260543019.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/3f0y61260543019.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/4fsxf1260543019.tab") 
> system("convert tmp/1qvzu1260543018.ps tmp/1qvzu1260543018.png")
> system("convert tmp/2g0pt1260543019.ps tmp/2g0pt1260543019.png")
> 
> 
> proc.time()
   user  system elapsed 
  3.172   0.332   5.709