R version 2.12.0 (2010-10-15)
Copyright (C) 2010 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(547612,563280,581302,572273,518654,520579,530577,540324,547970,555654,551174,548604,563668,586111,604378,600991,544686,537034,551531,563250,574761,580112,575093,557560,564478,580523,596594,586570,536214,523597,536535,536322,532638,528222,516141,501866,506174,517945,533590,528379,477580,469357,490243,492622,507561,516922,514258,509846,527070,541657,564591,555362,498662,511038,525919,531673,548854,560576,557274,565742,587625,619916,625809,619567,572942,572775,574205,579799,590072,593408,597141,595404,612117,628232,628884,620735,569028,567456,573100,584428,589379,590865,595454,594167,611324,612613,610763,593530,542722,536662,543599,555332,560854,562325,554788,547344,565464,577992,579714,569323,506971,500857,509127,509933,517009,519164,512238,509239,518585,522975,525192,516847,455626,454724,461251,470439,474605,476049,471067,470984,502831,512927,509673,484015,431328,436087,442867,447988,460070,467037,460170,464196,485025)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> 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      ma1     sma1
      0.893  -0.7210  -0.6398
s.e.  0.081   0.1176   0.0993

sigma^2 estimated as 41672107:  log likelihood = -1103.82,  aic = 2215.64
Warning message:
In log(s2) : NaNs produced
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 122 
End = 133 
Frequency = 1 
 [1] 515696.7 521823.5 514390.2 459225.5 458388.6 467698.2 476451.6 484124.4
 [9] 487733.9 484491.0 483164.1 504634.1

$se
Time Series:
Start = 122 
End = 133 
Frequency = 1 
 [1]  6455.666  9945.866 13120.645 16165.379 19132.274 22038.969 24891.339
 [8] 27690.876 30437.495 33130.688 35770.005 38355.245

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 122 
End = 133 
Frequency = 1 
 [1] 503043.5 502329.6 488673.8 427541.4 420889.4 424501.8 427664.6 429850.3
 [9] 428076.4 419554.9 413054.9 429457.9
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 122 
End = 133 
Frequency = 1 
 [1] 528349.8 541317.4 540106.7 490909.7 495887.9 510894.6 525238.6 538398.5
 [9] 547391.4 549427.2 553273.4 579810.4
> 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$pred))
  [1] 547612.0 563280.0 581302.0 572273.0 518654.0 520579.0 530577.0 540324.0
  [9] 547970.0 555654.0 551174.0 548604.0 563668.0 586111.0 604378.0 600991.0
 [17] 544686.0 537034.0 551531.0 563250.0 574761.0 580112.0 575093.0 557560.0
 [25] 564478.0 580523.0 596594.0 586570.0 536214.0 523597.0 536535.0 536322.0
 [33] 532638.0 528222.0 516141.0 501866.0 506174.0 517945.0 533590.0 528379.0
 [41] 477580.0 469357.0 490243.0 492622.0 507561.0 516922.0 514258.0 509846.0
 [49] 527070.0 541657.0 564591.0 555362.0 498662.0 511038.0 525919.0 531673.0
 [57] 548854.0 560576.0 557274.0 565742.0 587625.0 619916.0 625809.0 619567.0
 [65] 572942.0 572775.0 574205.0 579799.0 590072.0 593408.0 597141.0 595404.0
 [73] 612117.0 628232.0 628884.0 620735.0 569028.0 567456.0 573100.0 584428.0
 [81] 589379.0 590865.0 595454.0 594167.0 611324.0 612613.0 610763.0 593530.0
 [89] 542722.0 536662.0 543599.0 555332.0 560854.0 562325.0 554788.0 547344.0
 [97] 565464.0 577992.0 579714.0 569323.0 506971.0 500857.0 509127.0 509933.0
[105] 517009.0 519164.0 512238.0 509239.0 518585.0 522975.0 525192.0 516847.0
[113] 455626.0 454724.0 461251.0 470439.0 474605.0 476049.0 471067.0 470984.0
[121] 502831.0 515696.7 521823.5 514390.2 459225.5 458388.6 467698.2 476451.6
[129] 484124.4 487733.9 484491.0 483164.1 504634.1
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 122 
End = 133 
Frequency = 1 
 [1] 0.01251834 0.01905983 0.02550718 0.03520139 0.04173811 0.04712220
 [7] 0.05224316 0.05719785 0.06240594 0.06838246 0.07403282 0.07600604
> postscript(file="/var/www/rcomp/tmp/1oexo1323888213.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/www/rcomp/tmp/2f7m61323888213.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/www/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/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/rcomp/tmp/33m1z1323888213.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/rcomp/tmp/4iihb1323888213.tab") 
> 
> try(system("convert tmp/1oexo1323888213.ps tmp/1oexo1323888213.png",intern=TRUE))
character(0)
> try(system("convert tmp/2f7m61323888213.ps tmp/2f7m61323888213.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.270   0.040   1.296