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)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '2'
> par7 = '2'
> par6 = '2'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> par1 = '24'
> par10 <- 'FALSE'
> par9 <- '1'
> par8 <- '2'
> par7 <- '2'
> par6 <- '2'
> par5 <- '12'
> par4 <- '1'
> par3 <- '1'
> 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:
          ar1      ar2     ma1      ma2    sar1    sar2     sma1
      -0.9830  -0.3497  0.0184  -0.5342  0.3909  0.2356  -1.0000
s.e.   0.2231   0.1567  0.1919   0.1651  0.1947  0.2483   0.3141

sigma^2 estimated as 60955:  log likelihood = -414.29,  aic = 844.58
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 73 
End = 96 
Frequency = 1 
 [1] 10216.858  9350.151 10327.180  9907.719  9976.621 10150.781 10466.092
 [8] 10598.537 10271.910 10299.124  9651.370 10170.164 10278.641  9486.329
[15] 10467.603 10036.424 10197.586 10229.288 10549.049 10712.965 10363.580
[22] 10432.356  9750.755 10226.172

$se
Time Series:
Start = 73 
End = 96 
Frequency = 1 
 [1] 258.7033 258.8489 260.1203 277.4202 278.2201 287.0056 291.0451 295.8239
 [9] 301.0595 305.4352 310.2924 314.7351 361.6552 366.2475 372.0634 385.1807
[17] 390.3728 399.9793 407.2195 414.7974 422.3799 429.6123 436.8412 443.7404

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 73 
End = 96 
Frequency = 1 
 [1]  9709.799  8842.807  9817.344  9363.975  9431.309  9588.250  9895.644
 [8] 10018.722  9681.833  9700.471  9043.197  9553.284  9569.797  8768.484
[15]  9738.359  9281.470  9432.455  9445.329  9750.899  9899.962  9535.716
[22]  9590.316  8894.547  9356.441
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 73 
End = 96 
Frequency = 1 
 [1] 10723.916  9857.495 10837.016 10451.462 10521.932 10713.312 11036.541
 [8] 11178.351 10861.986 10897.777 10259.543 10787.045 10987.485 10204.174
[15] 11196.848 10791.378 10962.717 11013.248 11347.199 11525.968 11191.445
[22] 11274.396 10606.964 11095.903
> 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$pred))
 [1]  9769.000  9321.000  9939.000  9336.000 10195.000  9464.000 10010.000
 [8] 10213.000  9563.000  9890.000  9305.000  9391.000  9928.000  8686.000
[15]  9843.000  9627.000 10074.000  9503.000 10119.000 10000.000  9313.000
[22]  9866.000  9172.000  9241.000  9659.000  8904.000  9755.000  9080.000
[29]  9435.000  8971.000 10063.000  9793.000  9454.000  9759.000  8820.000
[36]  9403.000  9676.000  8642.000  9402.000  9610.000  9294.000  9448.000
[43] 10319.000  9548.000  9801.000  9596.000  8923.000  9746.000  9829.000
[50]  9125.000  9782.000  9441.000  9162.000  9915.000 10444.000 10209.000
[57]  9985.000  9842.000  9429.000 10132.000  9849.000  9172.000 10313.000
[64]  9819.000  9955.000 10048.000 10082.000 10541.000 10208.000 10233.000
[71]  9439.000  9963.000 10216.858  9350.151 10327.180  9907.719  9976.621
[78] 10150.781 10466.092 10598.537 10271.910 10299.124  9651.370 10170.164
[85] 10278.641  9486.329 10467.603 10036.424 10197.586 10229.288 10549.049
[92] 10712.965 10363.580 10432.356  9750.755 10226.172
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 73 
End = 96 
Frequency = 1 
 [1] 0.02532122 0.02768392 0.02518793 0.02800041 0.02788721 0.02827424
 [7] 0.02780838 0.02791177 0.02930901 0.02965642 0.03215008 0.03094691
[13] 0.03518511 0.03860793 0.03554428 0.03837828 0.03828091 0.03910139
[19] 0.03860248 0.03871920 0.04075618 0.04118076 0.04480075 0.04339262
> postscript(file="/var/wessaorg/rcomp/tmp/1bvxk1354367695.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2isth1354367695.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/3ml9z1354367695.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/45pom1354367695.tab") 
> 
> try(system("convert tmp/1bvxk1354367695.ps tmp/1bvxk1354367695.png",intern=TRUE))
character(0)
> try(system("convert tmp/2isth1354367695.ps tmp/2isth1354367695.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  3.952   0.581   4.522