R version 2.13.0 (2011-04-13)
Copyright (C) 2011 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(2851,2672,2755,2721,2946,3036,2282,2212,2922,4301,5764,7132,2541,2475,3031,3266,3776,3230,3028,1759,3595,4474,6838,8357,3113,3006,4047,3523,3937,3986,3260,1573,3528,5211,7614,9254,5375,3088,3718,4514,4520,4539,3663,1643,4739,5428,8314,10651,3633,4292,4154,4121,4647,4753,3965,1723,5048,6922,9858,11331,4016,3957,4510,4276,4968,4677,3523,1821,5222,6873,10803,13916,2639,2899,3370,3740,2927,3986,4217,1738,5221,6424,9842,13076,3934,3162,4286,4676,5010,4874,4633,1659,5951,6981,9851,12670)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '2'
> par7 = '0'
> par6 = '2'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> par2 = '-0.4'
> 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     sar1    sar2    sma1
      0.2444  0.2275  -0.5061  0.0247  0.2892
s.e.  0.1180  0.1161   0.7778  0.2524  0.7619

sigma^2 estimated as 6.187e-06:  log likelihood = 328.99,  aic = -645.99
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 85 
End = 96 
Frequency = 1 
 [1] 0.04128324 0.04050040 0.03791889 0.03674181 0.03930522 0.03584587
 [7] 0.03623503 0.05030230 0.03252801 0.02989454 0.02503993 0.02228519

$se
Time Series:
Start = 85 
End = 96 
Frequency = 1 
 [1] 0.002487447 0.002560657 0.002658484 0.002676841 0.002687495 0.002690620
 [7] 0.002691996 0.002692471 0.002692660 0.002692729 0.002692756 0.002692766

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 85 
End = 96 
Frequency = 1 
 [1] 0.03640784 0.03548152 0.03270826 0.03149520 0.03403773 0.03057226
 [7] 0.03095871 0.04502506 0.02725039 0.02461679 0.01976213 0.01700737
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 85 
End = 96 
Frequency = 1 
 [1] 0.04615864 0.04551929 0.04312952 0.04198842 0.04457271 0.04111949
 [7] 0.04151134 0.05557955 0.03780562 0.03517229 0.03031773 0.02756301
> 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$pred))
 [1]  2851.000  2672.000  2755.000  2721.000  2946.000  3036.000  2282.000
 [8]  2212.000  2922.000  4301.000  5764.000  7132.000  2541.000  2475.000
[15]  3031.000  3266.000  3776.000  3230.000  3028.000  1759.000  3595.000
[22]  4474.000  6838.000  8357.000  3113.000  3006.000  4047.000  3523.000
[29]  3937.000  3986.000  3260.000  1573.000  3528.000  5211.000  7614.000
[36]  9254.000  5375.000  3088.000  3718.000  4514.000  4520.000  4539.000
[43]  3663.000  1643.000  4739.000  5428.000  8314.000 10651.000  3633.000
[50]  4292.000  4154.000  4121.000  4647.000  4753.000  3965.000  1723.000
[57]  5048.000  6922.000  9858.000 11331.000  4016.000  3957.000  4510.000
[64]  4276.000  4968.000  4677.000  3523.000  1821.000  5222.000  6873.000
[71] 10803.000 13916.000  2639.000  2899.000  3370.000  3740.000  2927.000
[78]  3986.000  4217.000  1738.000  5221.000  6424.000  9842.000 13076.000
[85]  2887.790  3029.365  3571.584  3864.548  3264.934  4110.571  4001.092
[92]  1762.099  5240.303  6471.730 10078.992 13488.363
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 85 
End = 96 
Frequency = 1 
 [1] 0.1883354 0.2000061 0.2281069 0.2397494 0.2208812 0.2492877 0.2459462
 [8] 0.1628932 0.2840430 0.3189687 0.4118202 0.4925443
> postscript(file="/var/wessaorg/rcomp/tmp/1da931323203205.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/wessaorg/rcomp/tmp/26wq51323203205.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/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/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/wessaorg/rcomp/tmp/3llxc1323203205.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/wessaorg/rcomp/tmp/4oulp1323203205.tab") 
> 
> try(system("convert tmp/1da931323203205.ps tmp/1da931323203205.png",intern=TRUE))
character(0)
> try(system("convert tmp/26wq51323203205.ps tmp/26wq51323203205.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.814   0.310   2.302