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(423.4,404.1,500,472.6,496.1,562,434.8,538.2,577.6,518.1,625.2,561.2,523.3,536.1,607.3,637.3,606.9,652.9,617.2,670.4,729.9,677.2,710,844.3,748.2,653.9,742.6,854.2,808.4,1819,1936.5,1966.1,2083.1,1620.1,1527.6,1795,1685.1,1851.8,2164.4,1981.8,1726.5,2144.6,1758.2,1672.9,1837.3,1596.1,1446,1898.4,1964.1,1755.9,2255.3,1881.2,2117.9,1656.5,1544.1,2098.9,2133.3,1963.5,1801.2,2365.4,1936.5,1667.6,1983.5,2058.6,2448.3,1858.1,1625.4,2130.6,2515.7,2230.2,2086.9,2235,2100.2,2288.6,2490,2573.7,2543.8,2004.7,2390,2338.4,2724.5,2292.5,2386,2477.9,2337,2605.1,2560.8,2839.3,2407.2,2085.2,2735.6,2798.7,3053.2,2405,2471.9,2727.3,2790.7,2385.4,3206.6,2705.6,3518.4,1954.9,2584.3,2535.8,2685.9,2866,2236.6,2934.9,2668.6,2371.2,3165.9,2887.2,3112.2,2671.2,2432.6,2812.3,3095.7,2862.9,2607.3,2862.5)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '2'
> par7 = '1'
> par6 = '2'
> 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: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> 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      ma1     sar1     sar2     sma1
      0.3460  0.3482  -0.9556  -0.0992  -0.3318  -0.3438
s.e.  0.1148  0.1071   0.0600   0.2055   0.1297   0.2113

sigma^2 estimated as 76322:  log likelihood = -672.69,  aic = 1359.37
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 2737.755 2623.568 3186.707 2943.090 3455.431 2365.740 2782.747 2817.457
 [9] 3063.024 3013.050 2667.805 3121.985

$se
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 276.2787 296.6007 330.5182 345.4110 358.9884 368.0273 375.4703 381.2704
 [9] 386.1364 390.2471 393.8437 397.0456

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 2196.249 2042.231 2538.892 2266.085 2751.814 1644.407 2046.825 2070.167
 [9] 2306.197 2248.166 1895.871 2343.775
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 3279.261 3204.906 3834.523 3620.095 4159.048 3087.074 3518.669 3564.747
 [9] 3819.852 3777.935 3439.739 3900.194
> 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$pred))
  [1]  423.400  404.100  500.000  472.600  496.100  562.000  434.800  538.200
  [9]  577.600  518.100  625.200  561.200  523.300  536.100  607.300  637.300
 [17]  606.900  652.900  617.200  670.400  729.900  677.200  710.000  844.300
 [25]  748.200  653.900  742.600  854.200  808.400 1819.000 1936.500 1966.100
 [33] 2083.100 1620.100 1527.600 1795.000 1685.100 1851.800 2164.400 1981.800
 [41] 1726.500 2144.600 1758.200 1672.900 1837.300 1596.100 1446.000 1898.400
 [49] 1964.100 1755.900 2255.300 1881.200 2117.900 1656.500 1544.100 2098.900
 [57] 2133.300 1963.500 1801.200 2365.400 1936.500 1667.600 1983.500 2058.600
 [65] 2448.300 1858.100 1625.400 2130.600 2515.700 2230.200 2086.900 2235.000
 [73] 2100.200 2288.600 2490.000 2573.700 2543.800 2004.700 2390.000 2338.400
 [81] 2724.500 2292.500 2386.000 2477.900 2337.000 2605.100 2560.800 2839.300
 [89] 2407.200 2085.200 2735.600 2798.700 3053.200 2405.000 2471.900 2727.300
 [97] 2790.700 2385.400 3206.600 2705.600 3518.400 1954.900 2584.300 2535.800
[105] 2685.900 2866.000 2236.600 2934.900 2737.755 2623.568 3186.707 2943.090
[113] 3455.431 2365.740 2782.747 2817.457 3063.024 3013.050 2667.805 3121.985
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 0.1009143 0.1130524 0.1037178 0.1173634 0.1038911 0.1555654 0.1349279
 [8] 0.1353243 0.1260638 0.1295189 0.1476284 0.1271773
> postscript(file="/var/www/html/rcomp/tmp/1j4b31259788892.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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.se <- array(0, dim=fx)
> perf.mse <- 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$pred[i]
+ perf.mape[i] = perf.mape[i] + abs(perf.pe[i])
+ perf.se[i] = (x[nx+i] - forecast$pred[i])^2
+ perf.mse[i] = perf.mse[i] + perf.se[i]
+ 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 = perf.mape / fx
> perf.mse = perf.mse / fx
> perf.rmse = sqrt(perf.mse)
> postscript(file="/var/www/html/rcomp/tmp/263jn1259788892.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[1:12] <- 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/3u44d1259788892.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.mape[i],4))
+ a<-table.element(a,round(perf.se[i],4))
+ a<-table.element(a,round(perf.mse[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/4i5151259788892.tab") 
> 
> system("convert tmp/1j4b31259788892.ps tmp/1j4b31259788892.png")
> system("convert tmp/263jn1259788892.ps tmp/263jn1259788892.png")
> 
> 
> proc.time()
   user  system elapsed 
  3.039   0.339   3.187