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(14.458,13.594,17.814,20.235,21.811,21.439,21.393,19.831,20.468,21.080,21.600,17.390,17.848,19.592,21.092,20.899,25.890,24.965,22.225,20.977,22.897,22.785,22.769,19.637,20.203,20.450,23.083,21.738,26.766,25.280,22.574,22.729,21.378,22.902,24.989,21.116,15.169,15.846,20.927,18.273,22.538,15.596,14.034,11.366,14.861,15.149,13.577,13.026,13.190,13.196,15.826,14.733,16.307,15.703,14.589,12.043,15.057,14.053,12.698,10.888,10.045,11.549,13.767,12.434,13.116,14.211,12.266,12.602,15.714,13.742,12.745,10.491,10.057,10.900,11.771,11.992,11.933,14.504,11.727,11.477,13.578,11.555,11.846,11.397,10.066,10.269,14.279,13.870,13.695,14.420,11.424,9.704,12.464,14.301,13.464,9.893,11.572,12.380,16.692,16.052,16.459,14.761,13.654,13.480,18.068,16.560,14.530,10.650,11.651,13.735,13.360,17.818,20.613,16.231,13.862,12.004,17.734,15.034,12.609,12.320,10.833,11.350,13.648,14.890,16.325,18.045,15.616,11.926,16.855,15.083,12.520,12.355)
> par20 = ''
> par19 = ''
> par18 = ''
> par17 = ''
> par16 = ''
> par15 = ''
> par14 = ''
> par13 = ''
> par12 = ''
> par11 = ''
> par10 = 'FALSE'
> par9 = '1'
> par8 = '1'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> par1 = '24'
> ylab = ''
> xlab = ''
> main = ''
> #'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      ma1    sar1     sma1
      0.3003  -0.6242  0.2556  -1.0000
s.e.  0.1999   0.1561  0.1211   0.3581

sigma^2 estimated as 2.436:  log likelihood = -187.61,  aic = 385.22
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 109 
End = 132 
Frequency = 1 
 [1] 11.31128 12.11105 15.60909 15.12416 16.69126 15.61739 13.99867 13.16491
 [9] 16.03371 15.44317 14.58332 11.55218 11.35684 11.97542 15.21161 14.75018
[17] 16.60900 15.69323 13.94326 12.94070 15.36996 15.01396 14.45323 11.63909

$se
Time Series:
Start = 109 
End = 132 
Frequency = 1 
 [1] 1.646895 1.985101 2.200240 2.377571 2.537499 2.686507 2.827270 2.961237
 [9] 3.089381 3.212450 3.331105 3.446060 3.749615 3.957398 4.138011 4.306351
[17] 4.467001 4.621679 4.771235 4.916216 5.057055 5.194145 5.327935 5.459146

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 109 
End = 132 
Frequency = 1 
 [1]  8.0833610  8.2202499 11.2966205 10.4641247 11.7177581 10.3518392
 [7]  8.4572242  7.3608813  9.9785224  9.1467727  8.0543526  4.7978989
[13]  4.0075922  4.2189206  7.1011112  6.3097362  7.8536743  6.6347384
[19]  4.5916373  3.3049137  5.4581372  4.8334356  4.0104812  0.9391672
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 109 
End = 132 
Frequency = 1 
 [1] 14.53919 16.00185 19.92156 19.78420 21.66476 20.88295 19.54012 18.96893
 [9] 22.08890 21.73958 21.11228 18.30645 18.70608 19.73192 23.32212 23.19063
[17] 25.36432 24.75172 23.29488 22.57648 25.28179 25.19448 24.89599 22.33902
> 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$pred))
  [1] 14.45800 13.59400 17.81400 20.23500 21.81100 21.43900 21.39300 19.83100
  [9] 20.46800 21.08000 21.60000 17.39000 17.84800 19.59200 21.09200 20.89900
 [17] 25.89000 24.96500 22.22500 20.97700 22.89700 22.78500 22.76900 19.63700
 [25] 20.20300 20.45000 23.08300 21.73800 26.76600 25.28000 22.57400 22.72900
 [33] 21.37800 22.90200 24.98900 21.11600 15.16900 15.84600 20.92700 18.27300
 [41] 22.53800 15.59600 14.03400 11.36600 14.86100 15.14900 13.57700 13.02600
 [49] 13.19000 13.19600 15.82600 14.73300 16.30700 15.70300 14.58900 12.04300
 [57] 15.05700 14.05300 12.69800 10.88800 10.04500 11.54900 13.76700 12.43400
 [65] 13.11600 14.21100 12.26600 12.60200 15.71400 13.74200 12.74500 10.49100
 [73] 10.05700 10.90000 11.77100 11.99200 11.93300 14.50400 11.72700 11.47700
 [81] 13.57800 11.55500 11.84600 11.39700 10.06600 10.26900 14.27900 13.87000
 [89] 13.69500 14.42000 11.42400  9.70400 12.46400 14.30100 13.46400  9.89300
 [97] 11.57200 12.38000 16.69200 16.05200 16.45900 14.76100 13.65400 13.48000
[105] 18.06800 16.56000 14.53000 10.65000 11.31128 12.11105 15.60909 15.12416
[113] 16.69126 15.61739 13.99867 13.16491 16.03371 15.44317 14.58332 11.55218
[121] 11.35684 11.97542 15.21161 14.75018 16.60900 15.69323 13.94326 12.94070
[129] 15.36996 15.01396 14.45323 11.63909
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 109 
End = 132 
Frequency = 1 
 [1] 0.1455976 0.1639083 0.1409589 0.1572035 0.1520257 0.1720202 0.2019670
 [8] 0.2249342 0.1926804 0.2080175 0.2284189 0.2983040 0.3301636 0.3304600
[15] 0.2720297 0.2919524 0.2689507 0.2945015 0.3421894 0.3799035 0.3290219
[22] 0.3459544 0.3686327 0.4690353
> postscript(file="/var/www/html/rcomp/tmp/1j1g81293206931.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2qkd21293206931.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/3pdd91293206932.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/4tete1293206932.tab") 
> 
> try(system("convert tmp/1j1g81293206931.ps tmp/1j1g81293206931.png",intern=TRUE))
character(0)
> try(system("convert tmp/2qkd21293206931.ps tmp/2qkd21293206931.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.083   0.392   2.666