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(91.98,91.72,90.27,91.89,92.07,92.92,93.34,93.60,92.41,93.60,93.77,93.60,93.60,93.51,92.66,94.20,94.37,94.45,94.62,94.37,93.43,94.79,94.88,94.79,94.62,94.71,93.77,95.73,95.99,95.82,95.47,95.82,94.71,96.33,96.50,96.16,96.33,96.33,95.05,96.84,96.92,97.44,97.78,97.69,96.67,98.29,98.20,98.71,98.54,98.20,96.92,99.06,99.65,99.82,99.99,100.33,99.31,101.10,101.10,100.93,100.85,100.93,99.60,101.88,101.81,102.38,102.74,102.82,101.72,103.47,102.98,102.68,102.90,103.03,101.29,103.69,103.68,104.20,104.08,104.16,103.05,104.66,104.46,104.95,105.85,106.23,104.86,107.44,108.23,108.45,109.39,110.15,109.13,110.28,110.17,109.99,109.26,109.11,107.06,109.53,108.92,109.24,109.12,109.00,107.23,109.49,109.04,109.02)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '1'
> 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      ma1     sma1
      0.7802  -0.7207  -0.6365
s.e.  0.5291   0.5819   0.1246

sigma^2 estimated as 0.1060:  log likelihood = -27.72,  aic = 63.44
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 97 
End = 108 
Frequency = 1 
 [1] 110.3433 110.4854 109.0811 111.4015 111.7582 112.1087 112.5149 112.8624
 [9] 111.8038 113.2668 113.1159 113.1135

$se
Time Series:
Start = 97 
End = 108 
Frequency = 1 
 [1] 0.3256923 0.4744047 0.5955561 0.7020923 0.7988095 0.8881286 0.9715040
 [8] 1.0499146 1.1240733 1.1945281 1.2617167 1.3259982

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 97 
End = 108 
Frequency = 1 
 [1] 109.7050 109.5556 107.9138 110.0254 110.1925 110.3680 110.6107 110.8045
 [9] 109.6006 110.9255 110.6429 110.5145
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 97 
End = 108 
Frequency = 1 
 [1] 110.9817 111.4152 110.2484 112.7776 113.3239 113.8495 114.4190 114.9202
 [9] 114.0070 115.6081 115.5889 115.7124
> 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$pred))
  [1]  91.9800  91.7200  90.2700  91.8900  92.0700  92.9200  93.3400  93.6000
  [9]  92.4100  93.6000  93.7700  93.6000  93.6000  93.5100  92.6600  94.2000
 [17]  94.3700  94.4500  94.6200  94.3700  93.4300  94.7900  94.8800  94.7900
 [25]  94.6200  94.7100  93.7700  95.7300  95.9900  95.8200  95.4700  95.8200
 [33]  94.7100  96.3300  96.5000  96.1600  96.3300  96.3300  95.0500  96.8400
 [41]  96.9200  97.4400  97.7800  97.6900  96.6700  98.2900  98.2000  98.7100
 [49]  98.5400  98.2000  96.9200  99.0600  99.6500  99.8200  99.9900 100.3300
 [57]  99.3100 101.1000 101.1000 100.9300 100.8500 100.9300  99.6000 101.8800
 [65] 101.8100 102.3800 102.7400 102.8200 101.7200 103.4700 102.9800 102.6800
 [73] 102.9000 103.0300 101.2900 103.6900 103.6800 104.2000 104.0800 104.1600
 [81] 103.0500 104.6600 104.4600 104.9500 105.8500 106.2300 104.8600 107.4400
 [89] 108.2300 108.4500 109.3900 110.1500 109.1300 110.2800 110.1700 109.9900
 [97] 110.3433 110.4854 109.0811 111.4015 111.7582 112.1087 112.5149 112.8624
[105] 111.8038 113.2668 113.1159 113.1135
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 97 
End = 108 
Frequency = 1 
 [1] 0.002951627 0.004293822 0.005459754 0.006302357 0.007147659 0.007922030
 [7] 0.008634450 0.009302609 0.010053984 0.010546143 0.011154195 0.011722724
> postscript(file="/var/www/html/rcomp/tmp/1v0hl1260569922.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2n1fv1260569922.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/3ni661260569922.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/4ln961260569922.tab") 
> 
> system("convert tmp/1v0hl1260569922.ps tmp/1v0hl1260569922.png")
> system("convert tmp/2n1fv1260569922.ps tmp/2n1fv1260569922.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.236   0.323   1.392