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

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> x <- c(1038,934,988,870,854,834,872,954,870,1238,1082,1053,934,787,1081,908,995,825,822,856,887,1094,990,936,1097,918,926,907,899,971,1087,1000,1071,1190,1116,1070,1314,1068,1185,1215,1145,1251,1363,1368,1535,1853,1866,2023,1373,1968,1424,1160,1243,1375,1539,1773,1906,2076,2004)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '1'
> par7 = '1'
> par6 = '0'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '-1.7'
> 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")

Coefficients:
          ma1     sar1
      -0.6051  -0.4308
s.e.   0.1601   0.1576

sigma^2 estimated as 2.100e-12:  log likelihood = 407.41,  aic = -808.82
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 48 
End = 59 
Frequency = 1 
 [1] 3.760363e-06 1.666938e-06 3.901707e-06 3.188819e-06 3.187714e-06
 [6] 3.593672e-06 2.588368e-06 1.541289e-06 1.977133e-06 1.128515e-06
[11] 3.143365e-08 3.062954e-07

$se
Time Series:
Start = 48 
End = 59 
Frequency = 1 
 [1] 1.449046e-06 1.557953e-06 1.659730e-06 1.755616e-06 1.846529e-06
 [6] 1.933172e-06 2.016095e-06 2.095739e-06 2.172465e-06 2.246573e-06
[11] 2.318313e-06 2.387898e-06

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 48 
End = 59 
Frequency = 1 
 [1]  9.202330e-07 -1.386651e-06  6.486366e-07 -2.521874e-07 -4.314829e-07
 [6] -1.953455e-07 -1.363178e-06 -2.566360e-06 -2.280899e-06 -3.274768e-06
[11] -4.512459e-06 -4.373985e-06
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 48 
End = 59 
Frequency = 1 
 [1] 6.600494e-06 4.720526e-06 7.154777e-06 6.629826e-06 6.806912e-06
 [6] 7.382689e-06 6.539914e-06 5.648937e-06 6.235165e-06 5.531798e-06
[11] 4.575326e-06 4.986576e-06
> 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$pred))
 [1]  1038.000   934.000   988.000   870.000   854.000   834.000   872.000
 [8]   954.000   870.000  1238.000  1082.000  1053.000   934.000   787.000
[15]  1081.000   908.000   995.000   825.000   822.000   856.000   887.000
[22]  1094.000   990.000   936.000  1097.000   918.000   926.000   907.000
[29]   899.000   971.000  1087.000  1000.000  1071.000  1190.000  1116.000
[36]  1070.000  1314.000  1068.000  1185.000  1215.000  1145.000  1251.000
[43]  1363.000  1368.000  1535.000  1853.000  1866.000  1552.535  2505.365
[50]  1519.200  1710.641  1710.990  1594.500  1933.995  2623.565  2266.069
[57]  3151.556 25899.846  6787.066
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 48 
End = 59 
Frequency = 1 
 [1] 0.6575489       NaN 0.9557762       NaN       NaN       NaN       NaN
 [8]       NaN       NaN       NaN       NaN       NaN
> postscript(file="/var/www/html/rcomp/tmp/1at711292235574.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