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

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> x <- c(67.8,66.9,71.5,75.9,71.9,70.7,73.5,76.1,82.5,87.1,83.2,86.1,85.9,77.4,74.4,69.9,73.8,69.2,69.7,71,71.2,75.8,73,66.4,58.6,55.5,52.6,54.9,54.6,51.2,50.9,49.6,53.4,52,47.5,42.1,44.5,43.2,51.4,59.4,60.3,61.4,68.8,73.6,81.8,79.6,85.8,88.1,89.1,95,96.2,84.2,96.9,103.1,99.3,103.5,112.4,111.1,113.7,92,93,98.4,92.6,94.6,99.5,97.6,91.3,93.6,93.1,78.4,70.2,69.3,71.1,73.5,85.9,91.5,91.8,88.3,91.3,94,99.3,96.7,88,96.7,106.8,114.3,105.7,90.1,91.6,97.7,100.8,104.6,95.9,102.7,104,107.9,113.8,113.8,123.1,125.1,137.6,134,140.3,152.1,150.6,167.3,153.2,142,154.4,158.5,180.9,181.3,172.4,192,199.3,215.4,214.3,201.5,190.5,196,215.7,209.4,214.1,237.8,239,237.8,251.5,248.8,215.4,201.2,203.1,214.2,188.9,203,213.3,228.5,228.2,240.9,258.8,248.5,269.2,289.6,323.4,317.2,322.8,340.9,368.2,388.5,441.2,474.3,483.9,417.9,365.9,263,199.4)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> par4 = '0'
> par3 = '2'
> par2 = '-0.1'
> 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:
         ar1      ma1
      0.1442  -0.9986
s.e.  0.0847   0.1614

sigma^2 estimated as 1.939e-05:  log likelihood = 562.67,  aic = -1119.35
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 144 
End = 155 
Frequency = 1 
 [1] 0.5596047 0.5588132 0.5581205 0.5574421 0.5567657 0.5560897 0.5554136
 [8] 0.5547376 0.5540616 0.5533856 0.5527096 0.5520335

$se
Time Series:
Start = 144 
End = 155 
Frequency = 1 
 [1] 0.004415816 0.006733888 0.008514783 0.010008587 0.011324273 0.012517452
 [7] 0.013620273 0.014653142 0.015629935 0.016560581 0.017452467 0.018311261

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 144 
End = 155 
Frequency = 1 
 [1] 0.5509497 0.5456148 0.5414316 0.5378253 0.5345702 0.5315555 0.5287179
 [8] 0.5260175 0.5234269 0.5209268 0.5185027 0.5161435
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 144 
End = 155 
Frequency = 1 
 [1] 0.5682597 0.5720116 0.5748095 0.5770589 0.5789613 0.5806239 0.5821094
 [8] 0.5834578 0.5846963 0.5858443 0.5869164 0.5879236
> 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$pred))
  [1]  67.8000  66.9000  71.5000  75.9000  71.9000  70.7000  73.5000  76.1000
  [9]  82.5000  87.1000  83.2000  86.1000  85.9000  77.4000  74.4000  69.9000
 [17]  73.8000  69.2000  69.7000  71.0000  71.2000  75.8000  73.0000  66.4000
 [25]  58.6000  55.5000  52.6000  54.9000  54.6000  51.2000  50.9000  49.6000
 [33]  53.4000  52.0000  47.5000  42.1000  44.5000  43.2000  51.4000  59.4000
 [41]  60.3000  61.4000  68.8000  73.6000  81.8000  79.6000  85.8000  88.1000
 [49]  89.1000  95.0000  96.2000  84.2000  96.9000 103.1000  99.3000 103.5000
 [57] 112.4000 111.1000 113.7000  92.0000  93.0000  98.4000  92.6000  94.6000
 [65]  99.5000  97.6000  91.3000  93.6000  93.1000  78.4000  70.2000  69.3000
 [73]  71.1000  73.5000  85.9000  91.5000  91.8000  88.3000  91.3000  94.0000
 [81]  99.3000  96.7000  88.0000  96.7000 106.8000 114.3000 105.7000  90.1000
 [89]  91.6000  97.7000 100.8000 104.6000  95.9000 102.7000 104.0000 107.9000
 [97] 113.8000 113.8000 123.1000 125.1000 137.6000 134.0000 140.3000 152.1000
[105] 150.6000 167.3000 153.2000 142.0000 154.4000 158.5000 180.9000 181.3000
[113] 172.4000 192.0000 199.3000 215.4000 214.3000 201.5000 190.5000 196.0000
[121] 215.7000 209.4000 214.1000 237.8000 239.0000 237.8000 251.5000 248.8000
[129] 215.4000 201.2000 203.1000 214.2000 188.9000 203.0000 213.3000 228.5000
[137] 228.2000 240.9000 258.8000 248.5000 269.2000 289.6000 323.4000 332.0367
[145] 336.7699 340.9730 345.1455 349.3614 353.6321 357.9600 362.3463 366.7917
[153] 371.2972 375.8636 380.4919
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 144 
End = 155 
Frequency = 1 
 [1] 0.08605904 0.13775746 0.18097133 0.21980716 0.25613645 0.29093209
 [7] 0.32476262 0.35799336 0.39087694 0.42359827 0.45629906 0.48909208
> postscript(file="/var/www/html/rcomp/tmp/1ky8i1229889918.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2w8je1229889919.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/3przg1229889919.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/485iq1229889919.tab") 
> 
> system("convert tmp/1ky8i1229889918.ps tmp/1ky8i1229889918.png")
> system("convert tmp/2w8je1229889919.ps tmp/2w8je1229889919.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.618   0.338   0.726