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(216234,213587,209465,204045,200237,203666,241476,260307,243324,244460,233575,237217,235243,230354,227184,221678,217142,219452,256446,265845,248624,241114,229245,231805,219277,219313,212610,214771,211142,211457,240048,240636,230580,208795,197922,194596,194581,185686,178106,172608,167302,168053,202300,202388,182516,173476,166444,171297,169701,164182,161914,159612,151001,158114,186530,187069,174330,169362,166827,178037,186412,189226,191563,188906,186005,195309,223532,226899,214126)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '0'
> par6 = '2'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> par1 = '12'
> par1 <- as.numeric(par1) #cut off periods
> par1 <- 28
> 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
> par6 <- 3
> par7 <- as.numeric(par7) #q
> par7 <- 3
> 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      ma2      ma3    sma1
      -0.8354  0.8496  0.9844  0.8028  -0.7735  -0.9844  0.0061
s.e.   0.0630  0.0358  0.0348  0.2857   0.1513   0.2995  0.2815

sigma^2 estimated as 21540385:  log likelihood = -279.1,  aic = 574.2
Warning message:
In arima(x[1:nx], order = c(par6, par3, par7), seasonal = list(order = c(par8,  :
  possible convergence problem: optim gave code=1
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 42 
End = 69 
Frequency = 1 
 [1] 168638.124 190807.248 194677.221 177483.073 158172.666 142348.239
 [7] 138233.699 137232.986 123650.762 118292.290 105905.947 103635.958
[13]  98813.118 121946.672 122759.817 102875.464  84164.699  62544.509
[19]  61132.620  53540.484  42055.043  32005.560  18830.453  15298.061
[25]   6241.634  31062.729  25626.578   8228.646

$se
Time Series:
Start = 42 
End = 69 
Frequency = 1 
 [1]  4819.989  6601.010  8437.874  9664.778 11115.991 12225.722 13426.237
 [8] 14538.042 15558.887 16690.531 17608.279 18721.469 21598.346 24286.155
[15] 26918.104 29184.849 31672.464 33741.473 36064.480 38082.672 40214.844
[22] 42261.009 44218.829 46300.115 49758.794 53265.436 56583.369 59826.088

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 42 
End = 69 
Frequency = 1 
 [1]  159190.946  177869.270  178138.987  158540.108  136385.322  118385.823
 [7]  111918.273  108738.424   93155.343   85578.850   71393.720   66941.880
[13]   56480.361   74345.809   70000.333   45673.160   22086.670   -3588.779
[19]   -9553.762  -21101.554  -36766.052  -50826.018  -67838.451  -75450.165
[25]  -91285.601  -73337.525  -85276.826 -109030.487
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 42 
End = 69 
Frequency = 1 
 [1] 178085.3 203745.2 211215.5 196426.0 179960.0 166310.7 164549.1 165727.5
 [9] 154146.2 151005.7 140418.2 140330.0 141145.9 169547.5 175519.3 160077.8
[17] 146242.7 128677.8 131819.0 128182.5 120876.1 114837.1 105499.4 106046.3
[25] 103768.9 135463.0 136530.0 125487.8
> 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$pred))
 [1] 216234.000 213587.000 209465.000 204045.000 200237.000 203666.000
 [7] 241476.000 260307.000 243324.000 244460.000 233575.000 237217.000
[13] 235243.000 230354.000 227184.000 221678.000 217142.000 219452.000
[19] 256446.000 265845.000 248624.000 241114.000 229245.000 231805.000
[25] 219277.000 219313.000 212610.000 214771.000 211142.000 211457.000
[31] 240048.000 240636.000 230580.000 208795.000 197922.000 194596.000
[37] 194581.000 185686.000 178106.000 172608.000 167302.000 168638.124
[43] 190807.248 194677.221 177483.073 158172.666 142348.239 138233.699
[49] 137232.986 123650.762 118292.290 105905.947 103635.958  98813.118
[55] 121946.672 122759.817 102875.464  84164.699  62544.509  61132.620
[61]  53540.484  42055.043  32005.560  18830.453  15298.061   6241.634
[67]  31062.729  25626.578   8228.646
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 42 
End = 69 
Frequency = 1 
 [1] 0.02858185 0.03459517 0.04334289 0.05445465 0.07027758 0.08588601
 [7] 0.09712709 0.10593693 0.12582929 0.14109568 0.16626337 0.18064646
[13] 0.21857772 0.19915389 0.21927455 0.28369105 0.37631530 0.53947939
[19] 0.58993841 0.71128741 0.95624309 1.32042712 2.34826153 3.02653497
[25] 7.97207752 1.71476999 2.20799551 7.27046555
> postscript(file="/var/www/html/rcomp/tmp/17o7f1260310895.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2o3781260310895.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/3jvht1260310895.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/49xt41260310895.tab") 
> 
> system("convert tmp/17o7f1260310895.ps tmp/17o7f1260310895.png")
> system("convert tmp/2o3781260310895.ps tmp/2o3781260310895.png")
> 
> 
> proc.time()
   user  system elapsed 
  2.493   0.473   2.705