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(35.36,31.19,35.29,33.80,36.38,37.77,34.88,37.07,35.56,34.18,32.05,32.35,34.79,33.75,33.76,36.80,36.57,34.14,33.85,35.10,33.92,33.34,30.69,32.32,32.47,34.71,37.19,35.58,36.04,35.63,32.74,33.31,28.40,27.37,28.20,29.23,28.05,27.70,28.05,28.01,30.73,30.82,30.48,30.92,31.20,31.41,31.96,36.95,35.64,37.18,38.69,39.97,40.36,40.79,42.92,41.21,44.15,44.70,47.42,45.14,46.08,50.59,48.63,47.46,47.30,49.02,51.77,54.15,56.10,52.58,52.56,51.27,57.72,53.46,55.48,59.33,57.32,56.44,58.80,55.64,53.62,54.87,56.15,55.35,52.38,51.27,53.95,56.09,56.34,60.65,58.35,57.18,58.87,66.20,62.25,62.62,54.73,56.20,52.54,63.06,63.53,60.95,53.83,51.20,44.57,44.15,44.04,42.28,38.42,35.41,37.01,39.19,46.50,44.79,47.01,49.15,50.85,54.09,55.40,56.16,54.37,52.34,56.13,51.29,42.95,28.88,38.47,34.83,41.17,40.80,40.00,44.00)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '1'
> par7 = '0'
> par6 = '3'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '1'
> par1 = '10'
> #'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     ar2      ar3     sar1    sma1
      -0.0504  0.0884  -0.1995  -0.6499  0.6050
s.e.   0.0904  0.0905   0.0976   0.6798  0.7038

sigma^2 estimated as 7.312:  log likelihood = -292.16,  aic = 596.33
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 123 
End = 132 
Frequency = 1 
 [1] 51.98427 52.36937 52.43397 52.38678 52.13853 51.86029 51.54496 51.29511
 [9] 51.33727 51.22954

$se
Time Series:
Start = 123 
End = 132 
Frequency = 1 
 [1] 2.704062 3.728976 4.671409 5.184940 5.683243 6.103025 6.539420 6.938111
 [9] 7.325651 7.684813

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 123 
End = 132 
Frequency = 1 
 [1] 46.68431 45.06058 43.27801 42.22430 40.99938 39.89836 38.72769 37.69641
 [9] 36.97899 36.16730
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 123 
End = 132 
Frequency = 1 
 [1] 57.28423 59.67816 61.58993 62.54926 63.27769 63.82221 64.36222 64.89380
 [9] 65.69554 66.29177
> 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$pred))
  [1] 35.36000 31.19000 35.29000 33.80000 36.38000 37.77000 34.88000 37.07000
  [9] 35.56000 34.18000 32.05000 32.35000 34.79000 33.75000 33.76000 36.80000
 [17] 36.57000 34.14000 33.85000 35.10000 33.92000 33.34000 30.69000 32.32000
 [25] 32.47000 34.71000 37.19000 35.58000 36.04000 35.63000 32.74000 33.31000
 [33] 28.40000 27.37000 28.20000 29.23000 28.05000 27.70000 28.05000 28.01000
 [41] 30.73000 30.82000 30.48000 30.92000 31.20000 31.41000 31.96000 36.95000
 [49] 35.64000 37.18000 38.69000 39.97000 40.36000 40.79000 42.92000 41.21000
 [57] 44.15000 44.70000 47.42000 45.14000 46.08000 50.59000 48.63000 47.46000
 [65] 47.30000 49.02000 51.77000 54.15000 56.10000 52.58000 52.56000 51.27000
 [73] 57.72000 53.46000 55.48000 59.33000 57.32000 56.44000 58.80000 55.64000
 [81] 53.62000 54.87000 56.15000 55.35000 52.38000 51.27000 53.95000 56.09000
 [89] 56.34000 60.65000 58.35000 57.18000 58.87000 66.20000 62.25000 62.62000
 [97] 54.73000 56.20000 52.54000 63.06000 63.53000 60.95000 53.83000 51.20000
[105] 44.57000 44.15000 44.04000 42.28000 38.42000 35.41000 37.01000 39.19000
[113] 46.50000 44.79000 47.01000 49.15000 50.85000 54.09000 55.40000 56.16000
[121] 54.37000 52.34000 51.98427 52.36937 52.43397 52.38678 52.13853 51.86029
[129] 51.54496 51.29511 51.33727 51.22954
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 123 
End = 132 
Frequency = 1 
 [1] 0.05201694 0.07120528 0.08909128 0.09897422 0.10900273 0.11768205
 [7] 0.12686828 0.13525872 0.14269655 0.15000746
> postscript(file="/var/www/html/rcomp/tmp/1f9a41293457757.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/html/rcomp/tmp/2t1qd1293457757.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/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/3ik5p1293457757.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/43k4v1293457757.tab") 
> 
> try(system("convert tmp/1f9a41293457757.ps tmp/1f9a41293457757.png",intern=TRUE))
character(0)
> try(system("convert tmp/2t1qd1293457757.ps tmp/2t1qd1293457757.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.971   0.333   2.174