R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(3010,2910,3840,3580,3140,3550,3250,2820,2260,2060,2120,2210,2190,2180,2350,2440,2370,2440,2610,3040,3190,3120,3170,3600,3420,3650,4180,2960,2710,2950,3030,3770,4740,4450,5550,5580,5890,7480,10450,6360,6710,6200,4490,3480,2520,1920,2010,1950,2240,2370,2840,2700,2980,3290,3300,3000,2330,2190,1970,2170,2830,3190,3550,3240,3450,3570,3230,3260,2700)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '1'
> par7 = '1'
> par6 = '3'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '-1.3'
> 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      ma1    sar1
      1.3157  -0.2593  -0.1726  -1.0000  0.5108
s.e.  0.1400   0.2276   0.1364   0.0418  0.1424

sigma^2 estimated as 1.888e-11:  log likelihood = 609.48,  aic = -1206.96
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 58 
End = 69 
Frequency = 1 
 [1] 5.155081e-05 5.052290e-05 5.105549e-05 4.553953e-05 4.258045e-05
 [6] 3.675833e-05 3.653637e-05 3.324308e-05 3.042958e-05 2.967879e-05
[11] 3.100234e-05 3.671935e-05

$se
Time Series:
Start = 58 
End = 69 
Frequency = 1 
 [1] 4.370458e-06 7.262151e-06 9.777361e-06 1.168751e-05 1.303562e-05
 [6] 1.390897e-05 1.442496e-05 1.469725e-05 1.482065e-05 1.486419e-05
[11] 1.487165e-05 1.486664e-05

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 58 
End = 69 
Frequency = 1 
 [1] 4.298471e-05 3.628908e-05 3.189186e-05 2.263201e-05 1.703064e-05
 [6] 9.496739e-06 8.263442e-06 4.436481e-06 1.381107e-06 5.449779e-07
[11] 1.853905e-06 7.580743e-06
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 58 
End = 69 
Frequency = 1 
 [1] 6.011691e-05 6.475672e-05 7.021912e-05 6.844705e-05 6.813026e-05
 [6] 6.401992e-05 6.480929e-05 6.204969e-05 5.947806e-05 5.881261e-05
[11] 6.015078e-05 6.585796e-05
> 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$pred))
 [1]  3010.000  2910.000  3840.000  3580.000  3140.000  3550.000  3250.000
 [8]  2820.000  2260.000  2060.000  2120.000  2210.000  2190.000  2180.000
[15]  2350.000  2440.000  2370.000  2440.000  2610.000  3040.000  3190.000
[22]  3120.000  3170.000  3600.000  3420.000  3650.000  4180.000  2960.000
[29]  2710.000  2950.000  3030.000  3770.000  4740.000  4450.000  5550.000
[36]  5580.000  5890.000  7480.000 10450.000  6360.000  6710.000  6200.000
[43]  4490.000  3480.000  2520.000  1920.000  2010.000  1950.000  2240.000
[50]  2370.000  2840.000  2700.000  2980.000  3290.000  3300.000  3000.000
[57]  2330.000  1987.378  2018.408  2002.192  2186.257  2302.215  2577.893
[64]  2589.931  2785.128  2981.176  3039.021  2938.719  2579.997
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 58 
End = 69 
Frequency = 1 
 [1]  0.07654545  0.14789583  0.22252917  0.36343638  0.52227631  0.93484751
 [7]  1.09057682  1.89173158  4.99627108 10.53516846  3.94378760  1.20694467
> postscript(file="/var/www/html/rcomp/tmp/1xl2d1293207274.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/html/rcomp/tmp/2m4g71293207274.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/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/3bndi1293207274.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/html/rcomp/tmp/4enco1293207274.tab") 
> 
> try(system("convert tmp/1xl2d1293207274.ps tmp/1xl2d1293207274.png",intern=TRUE))
character(0)
> try(system("convert tmp/2m4g71293207274.ps tmp/2m4g71293207274.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.858   0.356   1.849