R version 2.9.0 (2009-04-17)
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ISBN 3-900051-07-0

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> x <- c(46,62,66,59,58,61,41,27,58,70,49,59,44,36,72,45,56,54,53,35,61,52,47,51,52,63,74,45,51,64,36,30,55,64,39,40,63,45,59,55,40,64,27,28,45,57,45,69,60,56,58,50,51,53,37,22,55,70,62,58,39,49,58,47,42,62,39,40,72,70,54,65)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '0'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> par2 = '2.0'
> par1 = '12'
> #'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")


sigma^2 estimated as 1470088:  log likelihood = -408.93,  aic = 819.86
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 61 
End = 72 
Frequency = 1 
 [1] 3600 3136 3364 2500 2601 2809 1369  484 3025 4900 3844 3364

$se
Time Series:
Start = 61 
End = 72 
Frequency = 1 
 [1] 1212.472 1212.472 1212.472 1212.472 1212.472 1212.472 1212.472 1212.472
 [9] 1212.472 1212.472 1212.472 1212.472

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 61 
End = 72 
Frequency = 1 
 [1]  1223.5549   759.5549   987.5549   123.5549   224.5549   432.5549
 [7] -1007.4451 -1892.4451   648.5549  2523.5549  1467.5549   987.5549
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 61 
End = 72 
Frequency = 1 
 [1] 5976.445 5512.445 5740.445 4876.445 4977.445 5185.445 3745.445 2860.445
 [9] 5401.445 7276.445 6220.445 5740.445
> 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$pred))
 [1] 46 62 66 59 58 61 41 27 58 70 49 59 44 36 72 45 56 54 53 35 61 52 47 51 52
[26] 63 74 45 51 64 36 30 55 64 39 40 63 45 59 55 40 64 27 28 45 57 45 69 60 56
[51] 58 50 51 53 37 22 55 70 62 58 60 56 58 50 51 53 37 22 55 70 62 58
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 61 
End = 72 
Frequency = 1 
 [1] 0.1471724 0.1662340 0.1562784 0.2023627 0.1955883 0.1829999 0.3337016
 [8] 0.7301282 0.1715633 0.1115312 0.1388232 0.1562784
> postscript(file="/var/www/html/rcomp/tmp/1d7we1291379182.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))
Error in plot.window(...) : need finite 'ylim' values
Calls: plot -> plot.default -> localWindow -> plot.window
Execution halted