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(15,14.4,13,13.7,13.6,15.2,12.9,14,14.1,13.2,11.3,13.3,14.4,13.3,11.6,13.2,13.1,14.6,14,14.3,13.8,13.7,11,14.4,15.6,13.7,12.6,13.2,13.3,14.3,14,13.4,13.9,13.7,10.5,14.5,15,13.5,13.5,13.2,13.8,16.2,14.7,13.9,16,14.4,12.3,15.9,15.9,15.5,15.1,14.5,15.1,17.4,16.2,15.6,17.2,14.9,13.8,17.5,16.2,17.5,16.6,16.2,16.6,19.6,15.9,18,18.3,16.3,14.9,18.2,18.4,18.5,16,17.4,17.2,19.6,17.2,18.3,19.3,18.1,16.2,18.4,20.5,19,16.5,18.7,19,19.2,20.5,19.3,20.6,20.1,16.1,20.4,19.7,15.6,14.4,13.7,14.1,15,14.2,13.6,15.4,14.8,12.5,16.2,16.1,16,15.8,15.2,15.7,18.9,17.4,17,19.8,17.7,16,19.6,19.7)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '2'
> par7 = '1'
> par6 = '3'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> par1 = '12'
> #'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      ma1    sar1     sar2     sma1
      -0.3285  0.0956  0.4417  -0.1447  0.3865  -0.3474  -1.0000
s.e.   0.1920  0.1290  0.0933   0.2118  0.1195   0.1235   0.2589

sigma^2 estimated as 0.4595:  log likelihood = -113.68,  aic = 243.37
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 110 
End = 121 
Frequency = 1 
 [1] 14.05248 13.13139 12.79959 12.96461 14.95086 12.96267 13.18493 14.40122
 [9] 13.31059 11.65644 14.82335 15.33790

$se
Time Series:
Start = 110 
End = 121 
Frequency = 1 
 [1] 0.7192289 0.8121388 0.9846790 1.2587821 1.3838641 1.5719322 1.7501759
 [8] 1.8790186 2.0389081 2.1746397 2.2964807 2.4290321

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 110 
End = 121 
Frequency = 1 
 [1] 12.642793 11.539598 10.869616 10.497401 12.238483  9.881681  9.754583
 [8] 10.718348  9.314327  7.394149 10.322249 10.577001
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 110 
End = 121 
Frequency = 1 
 [1] 15.46217 14.72318 14.72956 15.43183 17.66323 16.04366 16.61527 18.08410
 [9] 17.30685 15.91874 19.32445 20.09881
> 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$pred))
  [1] 15.00000 14.40000 13.00000 13.70000 13.60000 15.20000 12.90000 14.00000
  [9] 14.10000 13.20000 11.30000 13.30000 14.40000 13.30000 11.60000 13.20000
 [17] 13.10000 14.60000 14.00000 14.30000 13.80000 13.70000 11.00000 14.40000
 [25] 15.60000 13.70000 12.60000 13.20000 13.30000 14.30000 14.00000 13.40000
 [33] 13.90000 13.70000 10.50000 14.50000 15.00000 13.50000 13.50000 13.20000
 [41] 13.80000 16.20000 14.70000 13.90000 16.00000 14.40000 12.30000 15.90000
 [49] 15.90000 15.50000 15.10000 14.50000 15.10000 17.40000 16.20000 15.60000
 [57] 17.20000 14.90000 13.80000 17.50000 16.20000 17.50000 16.60000 16.20000
 [65] 16.60000 19.60000 15.90000 18.00000 18.30000 16.30000 14.90000 18.20000
 [73] 18.40000 18.50000 16.00000 17.40000 17.20000 19.60000 17.20000 18.30000
 [81] 19.30000 18.10000 16.20000 18.40000 20.50000 19.00000 16.50000 18.70000
 [89] 19.00000 19.20000 20.50000 19.30000 20.60000 20.10000 16.10000 20.40000
 [97] 19.70000 15.60000 14.40000 13.70000 14.10000 15.00000 14.20000 13.60000
[105] 15.40000 14.80000 12.50000 16.20000 16.10000 14.05248 13.13139 12.79959
[113] 12.96461 14.95086 12.96267 13.18493 14.40122 13.31059 11.65644 14.82335
[121] 15.33790
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 110 
End = 121 
Frequency = 1 
 [1] 0.05118163 0.06184713 0.07693053 0.09709369 0.09256085 0.12126610
 [7] 0.13274065 0.13047631 0.15317943 0.18656118 0.15492319 0.15836793
> postscript(file="/var/www/html/rcomp/tmp/19tkt1293191988.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/253hk1293191988.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/3mdeh1293191988.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/4qwun1293191988.tab") 
> 
> try(system("convert tmp/19tkt1293191988.ps tmp/19tkt1293191988.png",intern=TRUE))
character(0)
> try(system("convert tmp/253hk1293191988.ps tmp/253hk1293191988.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  4.330   0.571  37.063