R version 2.15.2 (2012-10-26) -- "Trick or Treat"
Copyright (C) 2012 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i686-pc-linux-gnu (32-bit)

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> x <- c(9769,9321,9939,9336,10195,9464,10010,10213,9563,9890,9305,9391,9928,8686,9843,9627,10074,9503,10119,10000,9313,9866,9172,9241,9659,8904,9755,9080,9435,8971,10063,9793,9454,9759,8820,9403,9676,8642,9402,9610,9294,9448,10319,9548,9801,9596,8923,9746,9829,9125,9782,9441,9162,9915,10444,10209,9985,9842,9429,10132,9849,9172,10313,9819,9955,10048,10082,10541,10208,10233,9439,9963,10158,9225,10474,9757,10490,10281,10444,10640,10695,10786,9832,9747,10411,9511,10402,9701,10540,10112,10915,11183,10384,10834,9886,10216,10943,9867,10203,10837,10573,10647,11502,10656,10866,10835,9945,10331,10718,9462,10579,10633,10346,10757,11207,11013,11015,10765,10042,10661)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '1'
> par7 = '1'
> par6 = '2'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> par2 = '-0.6'
> par1 = '12'
> par10 <- 'FALSE'
> par9 <- '1'
> par8 <- '1'
> par7 <- '1'
> par6 <- '2'
> par5 <- '12'
> par4 <- '1'
> par3 <- '0'
> par2 <- '-0.6'
> 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      ma1    sar1     sma1
      0.7793  0.2202  -0.7725  0.2575  -0.9795
s.e.  0.1154  0.1152   0.0677  0.1289   0.1188

sigma^2 estimated as 3.826e-09:  log likelihood = 785.02,  aic = -1558.04
Warning messages:
1: In log(s2) : NaNs produced
2: In log(s2) : NaNs produced
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 0.003787742 0.004017034 0.003839407 0.003860486 0.003825386 0.003850715
 [7] 0.003698996 0.003767016 0.003804835 0.003780065 0.003971952 0.003878353

$se
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 6.423803e-05 6.423416e-05 6.575967e-05 6.666025e-05 6.765116e-05
 [6] 6.859169e-05 6.951401e-05 7.041235e-05 7.128907e-05 7.214444e-05
[11] 7.297951e-05 7.378687e-05

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 0.003661835 0.003891135 0.003710518 0.003729832 0.003692789 0.003716276
 [7] 0.003562749 0.003629008 0.003665108 0.003638662 0.003828912 0.003733731
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 0.003913648 0.004142933 0.003968296 0.003991140 0.003957982 0.003985155
 [7] 0.003835244 0.003905024 0.003944561 0.003921468 0.004114991 0.004022975
> 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$pred))
  [1]  9769.000  9321.000  9939.000  9336.000 10195.000  9464.000 10010.000
  [8] 10213.000  9563.000  9890.000  9305.000  9391.000  9928.000  8686.000
 [15]  9843.000  9627.000 10074.000  9503.000 10119.000 10000.000  9313.000
 [22]  9866.000  9172.000  9241.000  9659.000  8904.000  9755.000  9080.000
 [29]  9435.000  8971.000 10063.000  9793.000  9454.000  9759.000  8820.000
 [36]  9403.000  9676.000  8642.000  9402.000  9610.000  9294.000  9448.000
 [43] 10319.000  9548.000  9801.000  9596.000  8923.000  9746.000  9829.000
 [50]  9125.000  9782.000  9441.000  9162.000  9915.000 10444.000 10209.000
 [57]  9985.000  9842.000  9429.000 10132.000  9849.000  9172.000 10313.000
 [64]  9819.000  9955.000 10048.000 10082.000 10541.000 10208.000 10233.000
 [71]  9439.000  9963.000 10158.000  9225.000 10474.000  9757.000 10490.000
 [78] 10281.000 10444.000 10640.000 10695.000 10786.000  9832.000  9747.000
 [85] 10411.000  9511.000 10402.000  9701.000 10540.000 10112.000 10915.000
 [92] 11183.000 10384.000 10834.000  9886.000 10216.000 10943.000  9867.000
 [99] 10203.000 10837.000 10573.000 10647.000 11502.000 10656.000 10866.000
[106] 10835.000  9945.000 10331.000 10865.076  9851.237 10622.491 10526.002
[113] 10687.463 10570.552 11302.995 10964.888 10783.847 10901.876 10038.298
[120] 10445.304
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 0.02957146 0.02780871 0.02987820 0.03013345 0.03089701 0.03113131
 [7] 0.03293170 0.03274595 0.03282814 0.03347155 0.03216082 0.03336051
> postscript(file="/var/wessaorg/rcomp/tmp/1ydqi1355859260.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2wauh1355859260.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/3is1a1355859260.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/4qsye1355859260.tab") 
> 
> try(system("convert tmp/1ydqi1355859260.ps tmp/1ydqi1355859260.png",intern=TRUE))
character(0)
> try(system("convert tmp/2wauh1355859260.ps tmp/2wauh1355859260.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  2.938   0.294   3.211