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(9700,9081,9084,9743,8587,9731,9563,9998,9437,10038,9918,9252,9737,9035,9133,9487,8700,9627,8947,9283,8829,9947,9628,9318,9605,8640,9214,9567,8547,9185,9470,9123,9278,10170,9434,9655,9429,8739,9552,9687,9019,9672,9206,9069,9788,10312,10105,9863,9656,9295,9946,9701,9049,10190,9706,9765,9893,9994,10433,10073,10112,9266,9820,10097,9115,10411,9678,10408,10153,10368,10581,10597,10680,9738,9556)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '2'
> par7 = '2'
> par6 = '0'
> par5 = '1'
> par4 = '1'
> par3 = '0'
> par2 = '1'
> par1 = '24'
> par10 <- 'FALSE'
> par9 <- '1'
> par8 <- '2'
> par7 <- '2'
> par6 <- '0'
> par5 <- '1'
> par4 <- '1'
> par3 <- '0'
> par2 <- '1'
> par1 <- '24'
> #'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     ma2    sar1    sar2     sma1
      -1.2049  0.2049  0.4276  0.1537  -0.2044
s.e.   0.5089  0.4963  0.4259  0.1924   0.4958

sigma^2 estimated as 176645:  log likelihood = -374.63,  aic = 761.26
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 52 
End = 75 
Frequency = 1 
 [1] 9451.390 9537.882 9481.659 9470.917 9457.681 9450.369 9445.208 9441.877
 [9] 9439.660 9438.199 9437.234 9436.597 9436.176 9435.898 9435.714 9435.593
[17] 9435.513 9435.460 9435.425 9435.402 9435.387 9435.377 9435.370 9435.366

$se
Time Series:
Start = 52 
End = 75 
Frequency = 1 
 [1] 424.2012 424.4146 434.6769 437.1725 438.8587 439.7008 440.1910 440.4767
 [9] 440.6507 440.7588 440.8273 440.8712 440.8997 440.9183 440.9305 440.9384
[17] 440.9437 440.9472 440.9494 440.9509 440.9519 440.9526 440.9530 440.9533

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 52 
End = 75 
Frequency = 1 
 [1] 8619.955 8706.029 8629.693 8614.059 8597.517 8588.556 8582.434 8578.543
 [9] 8575.984 8574.312 8573.213 8572.489 8572.012 8571.698 8571.491 8571.354
[17] 8571.264 8571.204 8571.165 8571.139 8571.121 8571.110 8571.103 8571.098
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 52 
End = 75 
Frequency = 1 
 [1] 10282.82 10369.73 10333.63 10327.78 10317.84 10312.18 10307.98 10305.21
 [9] 10303.34 10302.09 10301.26 10300.70 10300.34 10300.10 10299.94 10299.83
[17] 10299.76 10299.72 10299.69 10299.67 10299.65 10299.64 10299.64 10299.63
> 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$pred))
 [1]  9700.000  9081.000  9084.000  9743.000  8587.000  9731.000  9563.000
 [8]  9998.000  9437.000 10038.000  9918.000  9252.000  9737.000  9035.000
[15]  9133.000  9487.000  8700.000  9627.000  8947.000  9283.000  8829.000
[22]  9947.000  9628.000  9318.000  9605.000  8640.000  9214.000  9567.000
[29]  8547.000  9185.000  9470.000  9123.000  9278.000 10170.000  9434.000
[36]  9655.000  9429.000  8739.000  9552.000  9687.000  9019.000  9672.000
[43]  9206.000  9069.000  9788.000 10312.000 10105.000  9863.000  9656.000
[50]  9295.000  9946.000  9451.390  9537.882  9481.659  9470.917  9457.681
[57]  9450.369  9445.208  9441.877  9439.660  9438.199  9437.234  9436.597
[64]  9436.176  9435.898  9435.714  9435.593  9435.513  9435.460  9435.425
[71]  9435.402  9435.387  9435.377  9435.370  9435.366
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 52 
End = 75 
Frequency = 1 
 [1] 0.04488242 0.04449779 0.04584397 0.04615947 0.04640236 0.04652737
 [7] 0.04660469 0.04665139 0.04668078 0.04669945 0.04671149 0.04671930
[13] 0.04672441 0.04672775 0.04672995 0.04673140 0.04673235 0.04673298
[19] 0.04673339 0.04673367 0.04673385 0.04673397 0.04673404 0.04673410
> postscript(file="/var/fisher/rcomp/tmp/1xict1355481646.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/fisher/rcomp/tmp/256nq1355481646.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/fisher/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/fisher/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/fisher/rcomp/tmp/3giz71355481646.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/fisher/rcomp/tmp/45qla1355481646.tab") 
> 
> try(system("convert tmp/1xict1355481646.ps tmp/1xict1355481646.png",intern=TRUE))
character(0)
> try(system("convert tmp/256nq1355481646.ps tmp/256nq1355481646.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.589   0.431   2.004