R version 2.13.0 (2011-04-13)
Copyright (C) 2011 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(90604,97527,111940,100280,100009,95558,98533,92694,97920,110933,110855,111716,96348,105425,114874,104199,101166,99010,101607,97492,106088,113536,112475,115491,97733,102591,114783,100397,97772,96128,91261,90686,97792,108848,109989,109453,93945,98750,119043,104776,103262,106735,101600,99358,105240,114079,121637,111747,99496,104992,124255,108258,106940,104939,105896,107287,110783,122139,125823,120480,103296,117121,129924,118589,118062,113597,117161,112893,119657,136562,140446,138744,120324,118113,130257,125510,117986,118316,122075,117573,122566,135934,138394,137999,118780,117907,142932,132200,125666,127958,127718,124368,135241,144734,142320,141481,120471,123422,145829,134572,132156,140265,137771,134035,144016,151905,155791,148440,129862,134264,151952,143191,137242,136993,134431,132523,133486,140120,137521,112193,94256,99047,109761,102160,104792,104341,112430,113034,114197,127876,135199,123663,112578,117104,139703,114961,134222,128390,134197,135963,135936,146803,143231,131510)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '0'
> par6 = '3'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '0.1'
> 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     sma1
      -0.1774  0.0368  0.3455  -0.6789
s.e.   0.0854  0.0880  0.0867   0.0898

sigma^2 estimated as 0.0001212:  log likelihood = 363.82,  aic = -717.65
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 133 
End = 144 
Frequency = 1 
 [1] 3.186151 3.202375 3.242948 3.221212 3.217440 3.218934 3.226119 3.221823
 [9] 3.232890 3.260477 3.267263 3.239802

$se
Time Series:
Start = 133 
End = 144 
Frequency = 1 
 [1] 0.01101014 0.01425606 0.01730398 0.02188975 0.02502140 0.02807849
 [7] 0.03129835 0.03397298 0.03658512 0.03912400 0.04142499 0.04366139

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 133 
End = 144 
Frequency = 1 
 [1] 3.164572 3.174433 3.209032 3.178308 3.168398 3.163901 3.164774 3.155236
 [9] 3.161183 3.183794 3.186070 3.154226
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 133 
End = 144 
Frequency = 1 
 [1] 3.207731 3.230317 3.276864 3.264116 3.266482 3.273968 3.287464 3.288410
 [9] 3.304596 3.337160 3.348456 3.325378
> 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$pred))
  [1]  90604.0  97527.0 111940.0 100280.0 100009.0  95558.0  98533.0  92694.0
  [9]  97920.0 110933.0 110855.0 111716.0  96348.0 105425.0 114874.0 104199.0
 [17] 101166.0  99010.0 101607.0  97492.0 106088.0 113536.0 112475.0 115491.0
 [25]  97733.0 102591.0 114783.0 100397.0  97772.0  96128.0  91261.0  90686.0
 [33]  97792.0 108848.0 109989.0 109453.0  93945.0  98750.0 119043.0 104776.0
 [41] 103262.0 106735.0 101600.0  99358.0 105240.0 114079.0 121637.0 111747.0
 [49]  99496.0 104992.0 124255.0 108258.0 106940.0 104939.0 105896.0 107287.0
 [57] 110783.0 122139.0 125823.0 120480.0 103296.0 117121.0 129924.0 118589.0
 [65] 118062.0 113597.0 117161.0 112893.0 119657.0 136562.0 140446.0 138744.0
 [73] 120324.0 118113.0 130257.0 125510.0 117986.0 118316.0 122075.0 117573.0
 [81] 122566.0 135934.0 138394.0 137999.0 118780.0 117907.0 142932.0 132200.0
 [89] 125666.0 127958.0 127718.0 124368.0 135241.0 144734.0 142320.0 141481.0
 [97] 120471.0 123422.0 145829.0 134572.0 132156.0 140265.0 137771.0 134035.0
[105] 144016.0 151905.0 155791.0 148440.0 129862.0 134264.0 151952.0 143191.0
[113] 137242.0 136993.0 134431.0 132523.0 133486.0 140120.0 137521.0 112193.0
[121]  94256.0  99047.0 109761.0 102160.0 104792.0 104341.0 112430.0 113034.0
[129] 114197.0 127876.0 135199.0 123663.0 107811.3 113428.5 128647.1 120280.0
[137] 118879.0 119432.1 122124.9 120508.3 124712.2 135772.4 138624.9 127404.5
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 133 
End = 144 
Frequency = 1 
 [1] 0.03562873 0.04630636 0.05594132 0.07217608 0.08332497 0.09425554
 [7] 0.10575214 0.11581390 0.12515537 0.13352461 0.14194804 0.15196644
> postscript(file="/var/wessaorg/rcomp/tmp/1n20o1324422909.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/wessaorg/rcomp/tmp/2c96i1324422910.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/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/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/wessaorg/rcomp/tmp/3ytzk1324422910.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/wessaorg/rcomp/tmp/4ybms1324422910.tab") 
> 
> try(system("convert tmp/1n20o1324422909.ps tmp/1n20o1324422909.png",intern=TRUE))
character(0)
> try(system("convert tmp/2c96i1324422910.ps tmp/2c96i1324422910.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.072   0.160   1.229