R version 2.12.0 (2010-10-15)
Copyright (C) 2010 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(1579,2146,2462,3695,4831,5134,6250,5760,6249,2917,1741,2359,1511,2059,2635,2867,4403,5720,4502,5749,5627,2846,1762,2429,1169,2154,2249,2687,4359,5382,4459,6398,4596,3024,1887,2070,1351,2218,2461,3028,4784,4975,4607,6249,4809,3157,1910,2228,1594,2467,2222,3607,4685,4962,5770,5480,5000,3228,1993,2288,1580,2111,2192,3601,4665,4876,5813,5589,5331,3075,2002,2306,1507,1992,2487,3490,4647,5594,5611,5788,6204,3013,1931,2549,1504,2090,2702,2939,4500,6208,6415,5657,5964,3163,1997,2422,1376,2202,2683,3303,5202,5231,4880,7998,4977,3531,2025,2205,1442,2238,2179,3218,5139,4990,4914,6084,5672,3548,1793,2086)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '2'
> par7 = '0'
> par6 = '3'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> 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: 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:
          ar1     ar2     ar3    sar1     sar2     sma1
      -0.1509  0.1324  0.3791  0.2344  -0.2332  -1.0000
s.e.   0.0942  0.0975  0.1163  0.1378   0.1287   0.2067

sigma^2 estimated as 4.420e-07:  log likelihood = 552.15,  aic = -1090.29
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 0.02596347 0.02129699 0.02037134 0.01709726 0.01438617 0.01401523
 [7] 0.01408414 0.01239025 0.01394953 0.01769245 0.02281828 0.02105798

$se
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 0.0007034029 0.0007112861 0.0007195043 0.0007567272 0.0007591703
 [6] 0.0007635242 0.0007665574 0.0007668351 0.0007680362 0.0007678274
[11] 0.0007677436 0.0007679027

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 0.02458480 0.01990287 0.01896112 0.01561408 0.01289819 0.01251872
 [7] 0.01258169 0.01088725 0.01244418 0.01618751 0.02131351 0.01955289
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 0.02734214 0.02269111 0.02178157 0.01858045 0.01587414 0.01551173
 [7] 0.01558659 0.01389324 0.01545488 0.01919739 0.02432306 0.02256307
> 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$pred))
  [1] 1579.000 2146.000 2462.000 3695.000 4831.000 5134.000 6250.000 5760.000
  [9] 6249.000 2917.000 1741.000 2359.000 1511.000 2059.000 2635.000 2867.000
 [17] 4403.000 5720.000 4502.000 5749.000 5627.000 2846.000 1762.000 2429.000
 [25] 1169.000 2154.000 2249.000 2687.000 4359.000 5382.000 4459.000 6398.000
 [33] 4596.000 3024.000 1887.000 2070.000 1351.000 2218.000 2461.000 3028.000
 [41] 4784.000 4975.000 4607.000 6249.000 4809.000 3157.000 1910.000 2228.000
 [49] 1594.000 2467.000 2222.000 3607.000 4685.000 4962.000 5770.000 5480.000
 [57] 5000.000 3228.000 1993.000 2288.000 1580.000 2111.000 2192.000 3601.000
 [65] 4665.000 4876.000 5813.000 5589.000 5331.000 3075.000 2002.000 2306.000
 [73] 1507.000 1992.000 2487.000 3490.000 4647.000 5594.000 5611.000 5788.000
 [81] 6204.000 3013.000 1931.000 2549.000 1504.000 2090.000 2702.000 2939.000
 [89] 4500.000 6208.000 6415.000 5657.000 5964.000 3163.000 1997.000 2422.000
 [97] 1376.000 2202.000 2683.000 3303.000 5202.000 5231.000 4880.000 7998.000
[105] 4977.000 3531.000 2025.000 2205.000 1483.456 2204.772 2409.687 3420.951
[113] 4831.809 5090.960 5041.261 6513.886 5139.025 3194.656 1920.587 2255.104
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 0.05882705 0.07397905 0.07871486 0.10153249 0.12450741 0.12927211
 [7] 0.12912844 0.15059200 0.13090298 0.09927650 0.07458611 0.08156927
> postscript(file="/var/www/rcomp/tmp/1zs121291984999.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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.mape1 <- array(0, dim=fx)
> perf.se <- array(0, dim=fx)
> perf.mse <- array(0, dim=fx)
> perf.mse1 <- 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$pred[i]
+ perf.se[i] = (x[nx+i] - forecast$pred[i])^2
+ 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[1] = abs(perf.pe[1])
> perf.mse[1] = abs(perf.se[1])
> for (i in 2:fx) {
+ perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i])
+ perf.mape1[i] = perf.mape[i] / i
+ perf.mse[i] = perf.mse[i-1] + perf.se[i]
+ perf.mse1[i] = perf.mse[i] / i
+ }
> perf.rmse = sqrt(perf.mse1)
> postscript(file="/var/www/rcomp/tmp/2vkzt1291984999.ps",horizontal=F,onefile=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:par1] <- 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/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/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/rcomp/tmp/3vcvq1291984999.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.mape1[i],4))
+ a<-table.element(a,round(perf.se[i],4))
+ a<-table.element(a,round(perf.mse1[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/rcomp/tmp/4gdtv1291984999.tab") 
> 
> try(system("convert tmp/1zs121291984999.ps tmp/1zs121291984999.png",intern=TRUE))
character(0)
> try(system("convert tmp/2vkzt1291984999.ps tmp/2vkzt1291984999.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  2.330   1.970   4.279