R version 2.6.1 (2007-11-26)
Copyright (C) 2007 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(92.81,59.04,72.81,91.81,68.07,49.16,124.61,109.89,110.51,114.77,92.37,103.63,90.43,65.86,83.33,94.49,68.98,55.46,132.89,121.71,127.01,134.04,106.48,117.55,101.61,82.66,89.28,109.24,88.16,59.23,164.21,125.13,152.68,132.96,112.42,136.43,107.32,87.61,97.86,106.60,92.17,65.31,161.49,162.25,175.13,147.28,144.48,122.67,102.27,88.64,89.59,112.20,91.98,57.85,160.49,128.33,140.69,126.61,129.27,124.27,112.90,92.54,85.70,116.72,92.08,58.98,154.50,145.55,146.60,143.51,113.52,104.80)
> par10 = 'TRUE'
> par9 = '0'
> par8 = '0'
> par7 = '1'
> par6 = '2'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> par2 = '-0.8'
> 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     ar2      ma1
      0.6484  0.2882  -0.5674
s.e.  0.1906  0.1705   0.1574

sigma^2 estimated as 3.074e-06:  log likelihood = 235.96,  aic = -463.93
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 61 
End = 72 
Frequency = 1 
 [1] 0.02630449 0.02865800 0.02854361 0.02391917 0.02783273 0.03984284
 [7] 0.01808512 0.02141220 0.01991232 0.02155601 0.02117602 0.02179671

$se
Time Series:
Start = 61 
End = 72 
Frequency = 1 
 [1] 0.001753262 0.001758999 0.001857628 0.001906330 0.001958655 0.002002128
 [7] 0.002041427 0.002076135 0.002107112 0.002134741 0.002159444 0.002181557

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 61 
End = 72 
Frequency = 1 
 [1] 0.02286810 0.02521036 0.02490266 0.02018276 0.02399377 0.03591867
 [7] 0.01408392 0.01734297 0.01578238 0.01737191 0.01694351 0.01752086
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 61 
End = 72 
Frequency = 1 
 [1] 0.02974089 0.03210563 0.03218457 0.02765557 0.03167170 0.04376701
 [7] 0.02208631 0.02548142 0.02404226 0.02574010 0.02540853 0.02607256
> 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$pred))
 [1]  92.81000  59.04000  72.81000  91.81000  68.07000  49.16000 124.61000
 [8] 109.89000 110.51000 114.77000  92.37000 103.63000  90.43000  65.86000
[15]  83.33000  94.49000  68.98000  55.46000 132.89000 121.71000 127.01000
[22] 134.04000 106.48000 117.55000 101.61000  82.66000  89.28000 109.24000
[29]  88.16000  59.23000 164.21000 125.13000 152.68000 132.96000 112.42000
[36] 136.43000 107.32000  87.61000  97.86000 106.60000  92.17000  65.31000
[43] 161.49000 162.25000 175.13000 147.28000 144.48000 122.67000 102.27000
[50]  88.64000  89.59000 112.20000  91.98000  57.85000 160.49000 128.33000
[57] 140.69000 126.61000 129.27000 124.27000  94.39796  84.80915  85.23418
[64] 106.30837  87.96404  56.17747 150.78158 122.08814 133.68959 121.07085
[71] 123.79254 119.40194
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 61 
End = 72 
Frequency = 1 
 [1] 0.09757221 0.08865883 0.09488999 0.12068178 0.10400414 0.07060243
 [7] 0.18721064 0.15379280 0.17202563 0.15797783 0.16400578 0.16012549
> postscript(file="/var/www/html/rcomp/tmp/1ukv51199886727.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/258pb1199886727.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 
> 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/31iie1199886727.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/4eagw1199886727.tab") 
> 
> system("convert tmp/1ukv51199886727.ps tmp/1ukv51199886727.png")
> system("convert tmp/258pb1199886727.ps tmp/258pb1199886727.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.961   0.367   1.227