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(175.348,154.439,136.186,113.662,106.157,100.546,98.314,118.179,112.295,126.938,130.92,181.279,180.389,146.917,150.597,124.222,101.554,102.138,110.315,111.015,105.017,119.888,127.623,149.415,159.755,139.737,136.283,101.952,104.044,96.712,100.665,103.699,103.765,122.732,127.297,160.278,191.784,155.375,142.616,115.331,102.136,95.205,101.566,105.273,117.394,121.148,116.666,154.841,177.74,154.427,133.159,118.102,101.361,101.345,102.233,108.522,101.939,118.405,125.06,178,167.714,143.582,139.259,104.674,103.722,106.153,106.21,113.986,96.906,107.512,112.616,148.507,130.48,137.436,128.21,97.552,91.55,83.104,84.68,85.98,84.891,89.896,94.835,115.348,131.284,134.701,127.193,87.077,72.744,77.542,78.005,85.329,86.041,96.384,116.678,160.672,152.364,144.936,122.974,94.456,82.491,84.89,85.277,81.206,71.012,87.302,97.427,133.242,137.064,119.042,116.47,96.028,79.281,73.872,80.964,86.739,89.997,96.292,101.355,136.543)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '0'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> par1 = '24'
> #'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:
          ma1     sma1
      -0.5808  -0.9223
s.e.   0.1163   0.4473

sigma^2 estimated as 80.43:  log likelihood = -309.51,  aic = 625.02
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 97 
End = 120 
Frequency = 1 
 [1] 157.79478 140.00860 130.87286 101.76604  91.87410  89.42362  91.75982
 [8]  97.94648  94.97354 106.66372 112.99801 150.05176 156.15211 138.36593
[15] 129.23019 100.12337  90.23143  87.78095  90.11715  96.30381  93.33087
[22] 105.02105 111.35534 148.40909

$se
Time Series:
Start = 97 
End = 120 
Frequency = 1 
 [1]  9.260213 10.034180 10.752582 11.425902 12.061695 12.665611 13.242014
 [8] 13.794353 14.325411 14.837474 15.332445 15.811929 16.637867 17.193835
[15] 17.732380 18.255044 18.763155 19.257864 19.740178 20.210986 20.671074
[22] 21.121142 21.561817 21.993665

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 97 
End = 120 
Frequency = 1 
 [1] 139.64477 120.34161 109.79780  79.37127  68.23318  64.59903  65.80547
 [8]  70.90955  66.89573  77.58228  82.94642 119.06038 123.54189 104.66601
[15]  94.47472  64.34348  53.45565  50.03554  51.42640  56.69028  52.81556
[22]  63.62362  69.09418 105.30151
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 97 
End = 120 
Frequency = 1 
 [1] 175.9448 159.6756 151.9479 124.1608 115.5150 114.2482 117.7142 124.9834
 [9] 123.0513 135.7452 143.0496 181.0431 188.7623 172.0658 163.9857 135.9033
[17] 127.0072 125.5264 128.8079 135.9173 133.8462 146.4185 153.6165 191.5167
> 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$pred))
  [1] 175.34800 154.43900 136.18600 113.66200 106.15700 100.54600  98.31400
  [8] 118.17900 112.29500 126.93800 130.92000 181.27900 180.38900 146.91700
 [15] 150.59700 124.22200 101.55400 102.13800 110.31500 111.01500 105.01700
 [22] 119.88800 127.62300 149.41500 159.75500 139.73700 136.28300 101.95200
 [29] 104.04400  96.71200 100.66500 103.69900 103.76500 122.73200 127.29700
 [36] 160.27800 191.78400 155.37500 142.61600 115.33100 102.13600  95.20500
 [43] 101.56600 105.27300 117.39400 121.14800 116.66600 154.84100 177.74000
 [50] 154.42700 133.15900 118.10200 101.36100 101.34500 102.23300 108.52200
 [57] 101.93900 118.40500 125.06000 178.00000 167.71400 143.58200 139.25900
 [64] 104.67400 103.72200 106.15300 106.21000 113.98600  96.90600 107.51200
 [71] 112.61600 148.50700 130.48000 137.43600 128.21000  97.55200  91.55000
 [78]  83.10400  84.68000  85.98000  84.89100  89.89600  94.83500 115.34800
 [85] 131.28400 134.70100 127.19300  87.07700  72.74400  77.54200  78.00500
 [92]  85.32900  86.04100  96.38400 116.67800 160.67200 157.79478 140.00860
 [99] 130.87286 101.76604  91.87410  89.42362  91.75982  97.94648  94.97354
[106] 106.66372 112.99801 150.05176 156.15211 138.36593 129.23019 100.12337
[113]  90.23143  87.78095  90.11715  96.30381  93.33087 105.02105 111.35534
[120] 148.40909
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 97 
End = 120 
Frequency = 1 
 [1] 0.05868516 0.07166831 0.08216052 0.11227618 0.13128503 0.14163608
 [7] 0.14431168 0.14083561 0.15083581 0.13910515 0.13568774 0.10537649
[13] 0.10654910 0.12426350 0.13721546 0.18232551 0.20794478 0.21938545
[19] 0.21905019 0.20986694 0.22148164 0.20111341 0.19363075 0.14819621
> postscript(file="/var/www/html/rcomp/tmp/16u8r1293305842.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/www/html/rcomp/tmp/224nz1293305842.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/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/3rnkb1293305842.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/4u5jz1293305842.tab") 
> 
> try(system("convert tmp/16u8r1293305842.ps tmp/16u8r1293305842.png",intern=TRUE))
character(0)
> try(system("convert tmp/224nz1293305842.ps tmp/224nz1293305842.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.743   0.325   1.563