R version 3.2.2 (2015-08-14) -- "Fire Safety"
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> x <- c(704177,310154,310302,435329,497822,265224,301331,426815,510865,300614,358423,502547,596516,342535,377994,507900,677901,351931,442446,597344,754476,426933,450376,642635,827784,469829,526038,710645,939567,462391,562784,745282,973380,513575,507811,764929,921722,493969,580275,804671,1031509,593149,638170,874457,1177875,689356,752624,934424,1191042,660037,751254,973871,1179078,675609,766401,1053303)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '1'
> par7 = '1'
> par6 = '1'
> par5 = '4'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> par1 = '24'
> par10 <- 'FALSE'
> par9 <- '1'
> par8 <- '1'
> par7 <- '1'
> par6 <- '1'
> par5 <- '4'
> par4 <- '1'
> par3 <- '1'
> par2 <- '1'
> par1 <- '24'
> #'GNU S' R Code compiled by R2WASP v. 1.2.327 ()
> #Author: root
> #To cite this work: Wessa P., (2013), ARIMA Forecasting (v1.0.9) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_arimaforecasting.wasp/
> #Source of accompanying publication: 
> #
> 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     ma1    sar1     sma1
      -0.3219  0.0059  0.1681  -0.0029
s.e.   0.6445  0.7022  1.4156   1.3740

sigma^2 estimated as 2.487e+09:  log likelihood = -330.49,  aic = 670.97
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 33 
End = 56 
Frequency = 1 
 [1]  981794.5  484798.7  592541.9  774676.3 1012467.5  512139.1  621118.1
 [8]  803191.3 1041197.5  540308.8  649495.6  831558.5 1069600.9  568618.0
[15]  677839.7  859900.9 1097949.3  596950.6  706178.2  888239.1 1126288.6
[22]  625287.2  734515.8  916576.6

$se
Time Series:
Start = 33 
End = 56 
Frequency = 1 
 [1]  49870.89  60422.28  72016.28  81219.29 125891.09 147916.70 169917.59
 [8] 188539.85 235920.50 265974.86 295577.46 321692.17 372258.03 408513.99
[15] 444178.97 476467.12 530304.83 571753.32 612571.98 650170.24 707228.82
[22] 753234.72 798608.59 840918.03

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 33 
End = 56 
Frequency = 1 
 [1]  884047.56  366371.03  451389.95  615486.50  765720.97  222222.32
 [7]  288079.61  433653.21  578793.32   18998.09   70163.78  201041.89
[13]  339975.12 -232069.41 -192751.06  -73974.63   58551.86 -523685.87
[19] -494462.87 -386094.53 -259879.93 -851052.84 -830757.06 -731622.70
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 33 
End = 56 
Frequency = 1 
 [1] 1079541.5  603226.4  733693.8  933866.1 1259214.0  802055.8  954156.6
 [8] 1172729.4 1503601.7 1061619.6 1228827.4 1462075.2 1799226.6 1369305.4
[15] 1548430.5 1793776.5 2137346.8 1717587.2 1906819.3 2162572.8 2512457.0
[22] 2101627.3 2299788.6 2564776.0
> 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$pred))
 [1]  704177.0  310154.0  310302.0  435329.0  497822.0  265224.0  301331.0
 [8]  426815.0  510865.0  300614.0  358423.0  502547.0  596516.0  342535.0
[15]  377994.0  507900.0  677901.0  351931.0  442446.0  597344.0  754476.0
[22]  426933.0  450376.0  642635.0  827784.0  469829.0  526038.0  710645.0
[29]  939567.0  462391.0  562784.0  745282.0  981794.5  484798.7  592541.9
[36]  774676.3 1012467.5  512139.1  621118.1  803191.3 1041197.5  540308.8
[43]  649495.6  831558.5 1069600.9  568618.0  677839.7  859900.9 1097949.3
[50]  596950.6  706178.2  888239.1 1126288.6  625287.2  734515.8  916576.6
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 33 
End = 56 
Frequency = 1 
 [1] 0.05079565 0.12463374 0.12153788 0.10484287 0.12434087 0.28882137
 [7] 0.27356729 0.23473841 0.22658573 0.49226452 0.45508770 0.38685450
[13] 0.34803453 0.71843308 0.65528613 0.55409537 0.48299573 0.95778995
[19] 0.86744673 0.73197657 0.62792862 1.20462199 1.08725860 0.91745522
> postscript(file="/var/wessaorg/rcomp/tmp/1gc511449167190.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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.spe <- array(0, dim=fx)
> perf.scalederr <- array(0, dim=fx)
> perf.mase <- array(0, dim=fx)
> perf.mase1 <- array(0, dim=fx)
> perf.mape <- array(0, dim=fx)
> perf.smape <- array(0, dim=fx)
> perf.mape1 <- array(0, dim=fx)
> perf.smape1 <- 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)
> perf.scaleddenom <- 0
> for (i in 2:fx) {
+ perf.scaleddenom = perf.scaleddenom + abs(x[nx+i] - x[nx+i-1])
+ }
> perf.scaleddenom = perf.scaleddenom / (fx-1)
> for (i in 1:fx) {
+ locSD <- (ub[i] - forecast$pred[i]) / 1.96
+ perf.scalederr[i] = (x[nx+i] - forecast$pred[i]) / perf.scaleddenom
+ perf.pe[i] = (x[nx+i] - forecast$pred[i]) / x[nx+i]
+ perf.spe[i] = 2*(x[nx+i] - forecast$pred[i]) / (x[nx+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.smape[1] = abs(perf.spe[1])
> perf.mape1[1] = perf.mape[1]
> perf.smape1[1] = perf.smape[1]
> perf.mse[1] = perf.se[1]
> perf.mase[1] = abs(perf.scalederr[1])
> perf.mase1[1] = perf.mase[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.smape[i] = perf.smape[i-1] + abs(perf.spe[i])
+ perf.smape1[i] = perf.smape[i] / i
+ perf.mse[i] = perf.mse[i-1] + perf.se[i]
+ perf.mse1[i] = perf.mse[i] / i
+ perf.mase[i] = perf.mase[i-1] + abs(perf.scalederr[i])
+ perf.mase1[i] = perf.mase[i] / i
+ }
> perf.rmse = sqrt(perf.mse1)
> postscript(file="/var/wessaorg/rcomp/tmp/265w81449167190.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/35qzu1449167191.tab") 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Univariate ARIMA Extrapolation Forecast Performance',10,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,'sMAPE',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.element(a,'ScaledE',1,header=TRUE)
> a<-table.element(a,'MASE',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.smape1[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.element(a,round(perf.scalederr[i],4))
+ a<-table.element(a,round(perf.mase1[i],4))
+ a<-table.row.end(a)
+ }
> a<-table.end(a)
> table.save(a,file="/var/wessaorg/rcomp/tmp/4ogva1449167191.tab") 
> 
> try(system("convert tmp/1gc511449167190.ps tmp/1gc511449167190.png",intern=TRUE))
character(0)
> try(system("convert tmp/265w81449167190.ps tmp/265w81449167190.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.019   0.182   2.801