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(26.663
+ ,23.598
+ ,26.931
+ ,24.740
+ ,25.806
+ ,24.364
+ ,24.477
+ ,23.901
+ ,23.175
+ ,23.227
+ ,21.672
+ ,21.870
+ ,21.439
+ ,21.089
+ ,23.709
+ ,21.669
+ ,21.752
+ ,20.761
+ ,23.479
+ ,23.824
+ ,23.105
+ ,23.110
+ ,21.759
+ ,22.073
+ ,21.937
+ ,20.035
+ ,23.590
+ ,21.672
+ ,22.222
+ ,22.123
+ ,23.950
+ ,23.504
+ ,22.238
+ ,23.142
+ ,21.059
+ ,21.573
+ ,21.548
+ ,20.000
+ ,22.424
+ ,20.615
+ ,21.761
+ ,22.874
+ ,24.104
+ ,23.748
+ ,23.262
+ ,22.907
+ ,21.519
+ ,22.025
+ ,22.604
+ ,20.894
+ ,24.677
+ ,23.673
+ ,25.320
+ ,23.583
+ ,24.671
+ ,24.454
+ ,24.122
+ ,24.252
+ ,22.084
+ ,22.991
+ ,23.287
+ ,23.049
+ ,25.076
+ ,24.037
+ ,24.430
+ ,24.667
+ ,26.451
+ ,25.618
+ ,25.014
+ ,25.110
+ ,22.964
+ ,23.981
+ ,23.798
+ ,22.270
+ ,24.775
+ ,22.646
+ ,23.988
+ ,24.737
+ ,26.276
+ ,25.816
+ ,25.210
+ ,25.199
+ ,23.162
+ ,24.707
+ ,24.364
+ ,22.644
+ ,25.565
+ ,24.062
+ ,25.431
+ ,24.635
+ ,27.009
+ ,26.606
+ ,26.268
+ ,26.462
+ ,25.246
+ ,25.180
+ ,24.657
+ ,23.304
+ ,26.982
+ ,26.199
+ ,27.210
+ ,26.122
+ ,26.706
+ ,26.878
+ ,26.152
+ ,26.379
+ ,24.712
+ ,25.688
+ ,24.990
+ ,24.239
+ ,26.721
+ ,23.475
+ ,24.767
+ ,26.219
+ ,28.361
+ ,28.599
+ ,27.914
+ ,27.784
+ ,25.693
+ ,26.881
+ ,26.217
+ ,24.218
+ ,27.914
+ ,26.975
+ ,28.527
+ ,27.139
+ ,28.982
+ ,28.169
+ ,28.056
+ ,29.136
+ ,26.291
+ ,26.987
+ ,26.589
+ ,24.848
+ ,27.543
+ ,26.896
+ ,28.878
+ ,27.390
+ ,28.065
+ ,28.141
+ ,29.048
+ ,28.484
+ ,26.634
+ ,27.735
+ ,27.132
+ ,24.924
+ ,28.963
+ ,26.589
+ ,27.931
+ ,28.009
+ ,29.229
+ ,28.759
+ ,28.405
+ ,27.945
+ ,25.912
+ ,26.619
+ ,26.076
+ ,25.286
+ ,27.660
+ ,25.951
+ ,26.398
+ ,25.565
+ ,28.865
+ ,30.000
+ ,29.261
+ ,29.012
+ ,26.992
+ ,27.897)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '2'
> par7 = '0'
> par6 = '2'
> 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:
          ar1      ar2     sar1     sar2     sma1
      -0.0488  -0.1878  -0.4801  -0.3275  -0.6203
s.e.   0.0882   0.0902   0.1352   0.1219   0.1438

sigma^2 estimated as 0.3922:  log likelihood = -133.97,  aic = 279.95
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 145 
End = 168 
Frequency = 1 
 [1] 27.31907 26.08944 29.05103 26.99032 28.11828 28.34596 30.12523 30.00413
 [9] 29.27207 29.47441 27.54754 28.43664 27.92202 26.39692 29.56049 28.07623
[17] 29.47327 28.91131 30.54296 30.22508 29.94582 30.31876 28.10290 28.96107

$se
Time Series:
Start = 145 
End = 168 
Frequency = 1 
 [1] 0.6263024 0.8643953 0.9885528 1.1037914 1.2168779 1.3190848 1.4125465
 [8] 1.5004609 1.5837199 1.6627601 1.7381751 1.8104633 1.8640325 1.9168104
[15] 1.9708501 2.0231887 2.0737382 2.1231527 2.1715238 2.2188245 2.2651239
[22] 2.3104992 2.3550027 2.3986804

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 145 
End = 168 
Frequency = 1 
 [1] 26.09152 24.39522 27.11347 24.82689 25.73320 25.76055 27.35663 27.06322
 [9] 26.16798 26.21540 24.14071 24.88813 24.26852 22.63997 25.69763 24.11078
[17] 25.40874 24.74993 26.28677 25.87618 25.50617 25.79018 23.48709 24.25966
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 145 
End = 168 
Frequency = 1 
 [1] 28.54663 27.78365 30.98860 29.15375 30.50336 30.93136 32.89382 32.94503
 [9] 32.37616 32.73342 30.95436 31.98515 31.57553 30.15387 33.42336 32.04168
[17] 33.53780 33.07269 34.79915 34.57398 34.38546 34.84734 32.71870 33.66248
> 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$pred))
  [1] 26.66300 23.59800 26.93100 24.74000 25.80600 24.36400 24.47700 23.90100
  [9] 23.17500 23.22700 21.67200 21.87000 21.43900 21.08900 23.70900 21.66900
 [17] 21.75200 20.76100 23.47900 23.82400 23.10500 23.11000 21.75900 22.07300
 [25] 21.93700 20.03500 23.59000 21.67200 22.22200 22.12300 23.95000 23.50400
 [33] 22.23800 23.14200 21.05900 21.57300 21.54800 20.00000 22.42400 20.61500
 [41] 21.76100 22.87400 24.10400 23.74800 23.26200 22.90700 21.51900 22.02500
 [49] 22.60400 20.89400 24.67700 23.67300 25.32000 23.58300 24.67100 24.45400
 [57] 24.12200 24.25200 22.08400 22.99100 23.28700 23.04900 25.07600 24.03700
 [65] 24.43000 24.66700 26.45100 25.61800 25.01400 25.11000 22.96400 23.98100
 [73] 23.79800 22.27000 24.77500 22.64600 23.98800 24.73700 26.27600 25.81600
 [81] 25.21000 25.19900 23.16200 24.70700 24.36400 22.64400 25.56500 24.06200
 [89] 25.43100 24.63500 27.00900 26.60600 26.26800 26.46200 25.24600 25.18000
 [97] 24.65700 23.30400 26.98200 26.19900 27.21000 26.12200 26.70600 26.87800
[105] 26.15200 26.37900 24.71200 25.68800 24.99000 24.23900 26.72100 23.47500
[113] 24.76700 26.21900 28.36100 28.59900 27.91400 27.78400 25.69300 26.88100
[121] 26.21700 24.21800 27.91400 26.97500 28.52700 27.13900 28.98200 28.16900
[129] 28.05600 29.13600 26.29100 26.98700 26.58900 24.84800 27.54300 26.89600
[137] 28.87800 27.39000 28.06500 28.14100 29.04800 28.48400 26.63400 27.73500
[145] 27.31907 26.08944 29.05103 26.99032 28.11828 28.34596 30.12523 30.00413
[153] 29.27207 29.47441 27.54754 28.43664 27.92202 26.39692 29.56049 28.07623
[161] 29.47327 28.91131 30.54296 30.22508 29.94582 30.31876 28.10290 28.96107
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 145 
End = 168 
Frequency = 1 
 [1] 0.02292546 0.03313200 0.03402815 0.04089582 0.04327711 0.04653520
 [7] 0.04688916 0.05000848 0.05410344 0.05641369 0.06309730 0.06366656
[13] 0.06675851 0.07261493 0.06667176 0.07206056 0.07035996 0.07343676
[19] 0.07109736 0.07341005 0.07564074 0.07620692 0.08379929 0.08282430
> postscript(file="/var/wessaorg/rcomp/tmp/1b8n61322841665.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2eizp1322841665.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/3noyl1322841665.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/4vcl51322841665.tab") 
> 
> try(system("convert tmp/1b8n61322841665.ps tmp/1b8n61322841665.png",intern=TRUE))
character(0)
> try(system("convert tmp/2eizp1322841665.ps tmp/2eizp1322841665.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.985   0.308   2.287