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(17823.2,17872,17420.4,16704.4,15991.2,15583.6,19123.5,17838.7,17209.4,18586.5,16258.1,15141.6,19202.1,17746.5,19090.1,18040.3,17515.5,17751.8,21072.4,17170,19439.5,19795.4,17574.9,16165.4,19464.6,19932.1,19961.2,17343.4,18924.2,18574.1,21350.6,18594.6,19832.1,20844.4,19640.2,17735.4,19813.6,22160,20664.3,17877.4,20906.5,21164.1,21374.4,22952.3,21343.5,23899.3,22392.9,18274.1,22786.7,22321.5,17842.2,16373.5,15933.8,16446.1,17729,16643,16196.7,18252.1,17570.4,15836.8)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '3'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> par1 = '24'
> par1 <- as.numeric(par1) #cut off periods
> par1 <- 28
> 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
> par6 <- 3
> par7 <- as.numeric(par7) #q
> par7 <- 3
> 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      ma2     ma3
      -0.401  -0.1651  0.1367  -0.7843  -0.1538  0.1583
s.e.     NaN      NaN     NaN      NaN      NaN     NaN

sigma^2 estimated as 672383:  log likelihood = -155.48,  aic = 324.97
Warning message:
In sqrt(diag(x$var.coef)) : NaNs produced
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 20145.44 20430.24 18566.01 16927.16 20249.81 20794.45 20757.41 18156.60
 [9] 19752.05 19384.23 22167.74 19413.85 20960.26 21247.45 19383.29 17743.42
[17] 21066.79 21611.32 21574.06 18973.46 20568.84 20200.98 22984.55 20230.64
[25] 21777.04 22064.24 20200.07 18560.20

$se
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1]  819.9900  833.9588  834.2942  896.1686  896.7576  903.5160  920.4413
 [8]  925.4710  934.2826  944.3249  951.6117  960.2175 1349.6945 1349.9861
[15] 1353.9510 1428.0073 1436.7456 1456.1522 1487.1512 1503.7102 1525.0850
[22] 1547.7105 1566.8010 1587.3565 1917.0170 1919.5337 1933.2498 2018.4438

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 18538.25 18795.68 16930.80 15170.67 18492.16 19023.56 18953.34 16342.68
 [9] 17920.85 17533.35 20302.58 17531.83 18314.86 18601.47 16729.54 14944.52
[17] 18250.77 18757.26 18659.24 16026.18 17579.67 17167.47 19913.62 17119.42
[25] 18019.69 18301.95 16410.90 14604.05
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 21752.62 22064.79 20201.23 18683.66 22007.45 22565.35 22561.47 19970.53
 [9] 21583.24 21235.11 24032.90 21295.88 23605.66 23893.42 22037.03 20542.31
[17] 23882.81 24465.38 24488.87 21920.73 23558.01 23234.50 26055.48 23341.86
[25] 25534.40 25826.53 23989.24 22516.35
> 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$pred))
 [1] 17823.20 17872.00 17420.40 16704.40 15991.20 15583.60 19123.50 17838.70
 [9] 17209.40 18586.50 16258.10 15141.60 19202.10 17746.50 19090.10 18040.30
[17] 17515.50 17751.80 21072.40 17170.00 19439.50 19795.40 17574.90 16165.40
[25] 19464.60 19932.10 19961.20 17343.40 18924.20 18574.10 21350.60 18594.60
[33] 20145.44 20430.24 18566.01 16927.16 20249.81 20794.45 20757.41 18156.60
[41] 19752.05 19384.23 22167.74 19413.85 20960.26 21247.45 19383.29 17743.42
[49] 21066.79 21611.32 21574.06 18973.46 20568.84 20200.98 22984.55 20230.64
[57] 21777.04 22064.24 20200.07 18560.20
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 0.04070351 0.04081983 0.04493664 0.05294263 0.04428474 0.04344986
 [7] 0.04434279 0.05097160 0.04730054 0.04871615 0.04292777 0.04946043
[13] 0.06439301 0.06353639 0.06985146 0.08048096 0.06819956 0.06737915
[19] 0.06893238 0.07925336 0.07414540 0.07661560 0.06816758 0.07846299
[25] 0.08802926 0.08699750 0.09570509 0.10875118
> postscript(file="/var/www/html/rcomp/tmp/141741260562898.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2jpzr1260562898.ps",horizontal=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/3xugl1260562898.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/43y7r1260562898.tab") 
> system("convert tmp/141741260562898.ps tmp/141741260562898.png")
> system("convert tmp/2jpzr1260562898.ps tmp/2jpzr1260562898.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.908   0.336   1.006