R version 2.8.0 (2008-10-20)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(13363,12530,11420,10948,10173,10602,16094,19631,17140,14345,12632,12894,11808,10673,9939,9890,9283,10131,15864,19283,16203,13919,11937,11795,11268,10522,9929,9725,9372,10068,16230,19115,18351,16265,14103,14115,13327,12618,12129,11775,11493,12470,20792,22337,21325,18581,16475,16581,15745,14453,13712,13766,13336,15346,24446,26178,24628,21282,18850,18822,18060,17536,16417,15842,15188,16905,25430,27962,26607,23364,20827,20506,19181,18016,17354,16256,15770,17538,26899,28915,25247,22856,19980,19856,16994,16839,15618,15883,15513,17106,25272,26731,22891,19583,16939,16757,15435,14786,13680,13208,12707,14277,22436,23229,18241,16145,13994,14780,13100,12329,12463,11532,10784,13106,19491,20418,16094,14491)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '0'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '0.5'
> par1 = '12'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> 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
      -0.1463  -0.2353
s.e.   0.0994   0.1031

sigma^2 estimated as 5.363:  log likelihood = -210.42,  aic = 426.83
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 107 
End = 118 
Frequency = 1 
 [1] 117.07875 116.41625 110.29581 107.95465 103.38967 101.82070  99.75923
 [8] 106.43240 136.40268 139.57370 123.58295 114.96308

$se
Time Series:
Start = 107 
End = 118 
Frequency = 1 
 [1] 2.315912 3.045075 3.630636 4.134072 4.582530 4.990853 5.368207 5.720724
 [9] 6.052745 6.367476 6.667367 6.954338

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 107 
End = 118 
Frequency = 1 
 [1] 112.53956 110.44790 103.17976  99.85187  94.40791  92.03863  89.23754
 [8]  95.21978 124.53930 127.09345 110.51491 101.33257
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 107 
End = 118 
Frequency = 1 
 [1] 121.6179 122.3846 117.4119 116.0574 112.3714 111.6028 110.2809 117.6450
 [9] 148.2661 152.0540 136.6510 128.5936
> 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$pred))
  [1] 13363.000 12530.000 11420.000 10948.000 10173.000 10602.000 16094.000
  [8] 19631.000 17140.000 14345.000 12632.000 12894.000 11808.000 10673.000
 [15]  9939.000  9890.000  9283.000 10131.000 15864.000 19283.000 16203.000
 [22] 13919.000 11937.000 11795.000 11268.000 10522.000  9929.000  9725.000
 [29]  9372.000 10068.000 16230.000 19115.000 18351.000 16265.000 14103.000
 [36] 14115.000 13327.000 12618.000 12129.000 11775.000 11493.000 12470.000
 [43] 20792.000 22337.000 21325.000 18581.000 16475.000 16581.000 15745.000
 [50] 14453.000 13712.000 13766.000 13336.000 15346.000 24446.000 26178.000
 [57] 24628.000 21282.000 18850.000 18822.000 18060.000 17536.000 16417.000
 [64] 15842.000 15188.000 16905.000 25430.000 27962.000 26607.000 23364.000
 [71] 20827.000 20506.000 19181.000 18016.000 17354.000 16256.000 15770.000
 [78] 17538.000 26899.000 28915.000 25247.000 22856.000 19980.000 19856.000
 [85] 16994.000 16839.000 15618.000 15883.000 15513.000 17106.000 25272.000
 [92] 26731.000 22891.000 19583.000 16939.000 16757.000 15435.000 14786.000
 [99] 13680.000 13208.000 12707.000 14277.000 22436.000 23229.000 18241.000
[106] 16145.000 13707.434 13552.743 12165.165 11654.208 10689.424 10367.454
[113]  9951.903 11327.855 18605.691 19480.817 15272.745 13216.509
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 107 
End = 118 
Frequency = 1 
 [1] 0.04032852 0.05365456 0.06795827 0.07946332 0.09249626 0.10274125
 [7] 0.11329883 0.11316220 0.09260753 0.09532106 0.11360598 0.12815603
> postscript(file="/var/www/html/rcomp/tmp/1c49e1229171589.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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.se <- array(0, dim=fx)
> perf.mse <- 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$pred[i]
+ perf.mape[i] = perf.mape[i] + abs(perf.pe[i])
+ perf.se[i] = (x[nx+i] - forecast$pred[i])^2
+ perf.mse[i] = perf.mse[i] + perf.se[i]
+ 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 = perf.mape / fx
> perf.mse = perf.mse / fx
> perf.rmse = sqrt(perf.mse)
> postscript(file="/var/www/html/rcomp/tmp/2hewl1229171589.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[1:12] <- 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/3f6b21229171589.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.mape[i],4))
+ a<-table.element(a,round(perf.se[i],4))
+ a<-table.element(a,round(perf.mse[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/4d8lt1229171589.tab") 
> 
> system("convert tmp/1c49e1229171589.ps tmp/1c49e1229171589.png")
> system("convert tmp/2hewl1229171589.ps tmp/2hewl1229171589.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.654   0.334   0.791