R version 2.8.0 (2008-10-20)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(1721,1476,1842,2171,1670,1540,1266,897,1266,1519,1074,1435,1385,1440,1883,1822,1661,1774,1133,1361,1688,2216,2896,1382,1330,1419,1662,2040,2126,1649,1610,1952,2102,1749,2091,3036,2414,2097,2705,2431,4192,3990,2854,1966,2431,2763,2831,2023,2934,2489,3252,3018,3193,3976,2584,2512,2169,2504,1843,1408,2179,3690,2372,2494,3872,2786,2312,1599,3167,3433,2648,1978,1947,3113,2856,3174,3507,4174,2978,4428,2832,2930,3681,3253,1660,2208,3139,3409,3445,2410,3262,2897,2526,3982,4097,3403,3362,2708,3129,3550,2696,2885,2945,3600,3808,3671,4005)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '0.0'
> 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      ma1
      0.3552  -0.8667
s.e.  0.1188   0.0562

sigma^2 estimated as 0.06058:  log likelihood = -2,  aic = 10
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 96 
End = 107 
Frequency = 1 
 [1] 8.157942 8.101085 8.080890 8.073717 8.071169 8.070264 8.069942 8.069828
 [9] 8.069788 8.069773 8.069768 8.069766

$se
Time Series:
Start = 96 
End = 107 
Frequency = 1 
 [1] 0.2461392 0.2739338 0.2841496 0.2903373 0.2953125 0.2998514 0.3042018
 [8] 0.3084489 0.3126237 0.3167384 0.3207985 0.3248072

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 96 
End = 107 
Frequency = 1 
 [1] 7.675509 7.564175 7.523957 7.504656 7.492356 7.482555 7.473707 7.465268
 [9] 7.457045 7.448966 7.441003 7.433144
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 96 
End = 107 
Frequency = 1 
 [1] 8.640374 8.637996 8.637823 8.642778 8.649981 8.657973 8.666178 8.674388
 [9] 8.682530 8.690581 8.698533 8.706389
> 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$pred))
  [1] 1721.000 1476.000 1842.000 2171.000 1670.000 1540.000 1266.000  897.000
  [9] 1266.000 1519.000 1074.000 1435.000 1385.000 1440.000 1883.000 1822.000
 [17] 1661.000 1774.000 1133.000 1361.000 1688.000 2216.000 2896.000 1382.000
 [25] 1330.000 1419.000 1662.000 2040.000 2126.000 1649.000 1610.000 1952.000
 [33] 2102.000 1749.000 2091.000 3036.000 2414.000 2097.000 2705.000 2431.000
 [41] 4192.000 3990.000 2854.000 1966.000 2431.000 2763.000 2831.000 2023.000
 [49] 2934.000 2489.000 3252.000 3018.000 3193.000 3976.000 2584.000 2512.000
 [57] 2169.000 2504.000 1843.000 1408.000 2179.000 3690.000 2372.000 2494.000
 [65] 3872.000 2786.000 2312.000 1599.000 3167.000 3433.000 2648.000 1978.000
 [73] 1947.000 3113.000 2856.000 3174.000 3507.000 4174.000 2978.000 4428.000
 [81] 2832.000 2930.000 3681.000 3253.000 1660.000 2208.000 3139.000 3409.000
 [89] 3445.000 2410.000 3262.000 2897.000 2526.000 3982.000 4097.000 3490.993
 [97] 3298.046 3232.109 3209.007 3200.841 3197.946 3196.918 3196.553 3196.423
[105] 3196.377 3196.361 3196.355
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 96 
End = 107 
Frequency = 1 
 [1] 0.3163321 0.3626086 0.3802612 0.3911263 0.3999585 0.4080916 0.4159552
 [8] 0.4236972 0.4313703 0.4389946 0.4465782 0.4541254
> postscript(file="/var/www/html/rcomp/tmp/1qipo1229548319.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/20mqw1229548319.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/3ft211229548319.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/4m5y61229548319.tab") 
> 
> system("convert tmp/1qipo1229548319.ps tmp/1qipo1229548319.png")
> system("convert tmp/20mqw1229548319.ps tmp/20mqw1229548319.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.594   0.345   0.715