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(1149822
+ ,1086979
+ ,1276674
+ ,1522522
+ ,1742117
+ ,1737275
+ ,1979900
+ ,2061036
+ ,1867943
+ ,1707752
+ ,1298756
+ ,1281814
+ ,1281151
+ ,1164976
+ ,1454329
+ ,1645288
+ ,1817743
+ ,1895785
+ ,2236311
+ ,2295951
+ ,2087315
+ ,1980891
+ ,1465446
+ ,1445026
+ ,1488120
+ ,1338333
+ ,1715789
+ ,1806090
+ ,2083316
+ ,2092278
+ ,2430800
+ ,2424894
+ ,2299016
+ ,2130688
+ ,1652221
+ ,1608162
+ ,1647074
+ ,1479691
+ ,1884978
+ ,2007898
+ ,2208954
+ ,2217164
+ ,2534291
+ ,2560312
+ ,2429069
+ ,2315077
+ ,1799608
+ ,1772590
+ ,1744799
+ ,1659093
+ ,2099821
+ ,2135736
+ ,2427894
+ ,2468882
+ ,2703217
+ ,2766841
+ ,2655236
+ ,2550373
+ ,2052097
+ ,1998055
+ ,1920748
+ ,1876694
+ ,2380930
+ ,2467402
+ ,2770771
+ ,2781340
+ ,3143926
+ ,3172235
+ ,2952540
+ ,2920877
+ ,2384552
+ ,2248987
+ ,2208616
+ ,2178756
+ ,2632870
+ ,2706905
+ ,3029745
+ ,3015402
+ ,3391414
+ ,3507805
+ ,3177852
+ ,3142961
+ ,2545815
+ ,2414007
+ ,2372578
+ ,2332664
+ ,2825328
+ ,2901478
+ ,3263955
+ ,3226738
+ ,3610786
+ ,3709274
+ ,3467185
+ ,3449646
+ ,2802951
+ ,2462530
+ ,2490645
+ ,2561520
+ ,3067554
+ ,3226951
+ ,3546493
+ ,3492787
+ ,3952263
+ ,3932072
+ ,3720284
+ ,3651555
+ ,2914972
+ ,2713514
+ ,2703997
+ ,2591373
+ ,3163748
+ ,3355137
+ ,3613702
+ ,3686773
+ ,4098716
+ ,4063517
+ ,3551489
+ ,3226663
+ ,2656842
+ ,2597484
+ ,2572399
+ ,2596631
+ ,3165225
+ ,3303145
+ ,3698247
+ ,3668631
+ ,4130433
+ ,4131400
+ ,3864358
+ ,3721110
+ ,2892532
+ ,2843451
+ ,2747502
+ ,2668775
+ ,3018602
+ ,3013392
+ ,3393657
+ ,3544233
+ ,4075832
+ ,4032923
+ ,3734509
+ ,3761285
+ ,2970090
+ ,2847849
+ ,2741680
+ ,2830639
+ ,3257673
+ ,3480085
+ ,3843271
+ ,3796961
+ ,4337767
+ ,4243630
+ ,3927202
+ ,3915296
+ ,3087396
+ ,2963792
+ ,2955792
+ ,2829925
+ ,3281195
+ ,3548011
+ ,4059648
+ ,3941175
+ ,4528594
+ ,4433151
+ ,4145737
+ ,4077132
+ ,3198519
+ ,3078660
+ ,3028202
+ ,2858642
+ ,3398954
+ ,3808883
+ ,4175961
+ ,4227542
+ ,4744616
+ ,4608012
+ ,4295049
+ ,4201144
+ ,3353276
+ ,3286851
+ ,3169889
+ ,3051720
+ ,3695426
+ ,3905501
+ ,4296458
+ ,4246247
+ ,4921849
+ ,4821446
+ ,4425064
+ ,4379099
+ ,3472889
+ ,3359160
+ ,3200944
+ ,3153170
+ ,3741498
+ ,3918719
+ ,4403449
+ ,4400407
+ ,4847473
+ ,4716136
+ ,4297440
+ ,4272253
+ ,3271834
+ ,3168388
+ ,2911748
+ ,2720999
+ ,3199918
+ ,3672623
+ ,3892013
+ ,3850845
+ ,4532467
+ ,4484739
+ ,4014972
+ ,3983758
+ ,3158459
+ ,3100569
+ ,2935404
+ ,2855719
+ ,3465611
+ ,3006985
+ ,4095110
+ ,4104793
+ ,4730788
+ ,4642726
+ ,4246919
+ ,4308117)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '0'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '0.3'
> 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:
          ma1     sma1
      -0.2639  -0.5706
s.e.   0.0795   0.0778

sigma^2 estimated as 0.4956:  log likelihood = -217.05,  aic = 440.1
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 215 
End = 226 
Frequency = 1 
 [1] 88.59279 87.73071 86.23689 85.08061 89.57032 92.15053 94.62506 94.44014
 [9] 98.48098 97.93521 95.11893 94.84017

$se
Time Series:
Start = 215 
End = 226 
Frequency = 1 
 [1] 0.7039733 0.8741455 1.0162098 1.1407166 1.2529111 1.3558533 1.4515130
 [8] 1.5412469 1.6260363 1.7066183 1.7835632 1.8573233

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 215 
End = 226 
Frequency = 1 
 [1] 87.21300 86.01738 84.24512 82.84481 87.11462 89.49306 91.78009 91.41930
 [9] 95.29395 94.59024 91.62315 91.19981
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 215 
End = 226 
Frequency = 1 
 [1]  89.97258  89.44403  88.22866  87.31642  92.02603  94.80800  97.47002
 [8]  97.46099 101.66801 101.28018  98.61472  98.48052
> 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$pred))
  [1] 1149822 1086979 1276674 1522522 1742117 1737275 1979900 2061036 1867943
 [10] 1707752 1298756 1281814 1281151 1164976 1454329 1645288 1817743 1895785
 [19] 2236311 2295951 2087315 1980891 1465446 1445026 1488120 1338333 1715789
 [28] 1806090 2083316 2092278 2430800 2424894 2299016 2130688 1652221 1608162
 [37] 1647074 1479691 1884978 2007898 2208954 2217164 2534291 2560312 2429069
 [46] 2315077 1799608 1772590 1744799 1659093 2099821 2135736 2427894 2468882
 [55] 2703217 2766841 2655236 2550373 2052097 1998055 1920748 1876694 2380930
 [64] 2467402 2770771 2781340 3143926 3172235 2952540 2920877 2384552 2248987
 [73] 2208616 2178756 2632870 2706905 3029745 3015402 3391414 3507805 3177852
 [82] 3142961 2545815 2414007 2372578 2332664 2825328 2901478 3263955 3226738
 [91] 3610786 3709274 3467185 3449646 2802951 2462530 2490645 2561520 3067554
[100] 3226951 3546493 3492787 3952263 3932072 3720284 3651555 2914972 2713514
[109] 2703997 2591373 3163748 3355137 3613702 3686773 4098716 4063517 3551489
[118] 3226663 2656842 2597484 2572399 2596631 3165225 3303145 3698247 3668631
[127] 4130433 4131400 3864358 3721110 2892532 2843451 2747502 2668775 3018602
[136] 3013392 3393657 3544233 4075832 4032923 3734509 3761285 2970090 2847849
[145] 2741680 2830639 3257673 3480085 3843271 3796961 4337767 4243630 3927202
[154] 3915296 3087396 2963792 2955792 2829925 3281195 3548011 4059648 3941175
[163] 4528594 4433151 4145737 4077132 3198519 3078660 3028202 2858642 3398954
[172] 3808883 4175961 4227542 4744616 4608012 4295049 4201144 3353276 3286851
[181] 3169889 3051720 3695426 3905501 4296458 4246247 4921849 4821446 4425064
[190] 4379099 3472889 3359160 3200944 3153170 3741498 3918719 4403449 4400407
[199] 4847473 4716136 4297440 4272253 3271834 3168388 2911748 2720999 3199918
[208] 3672623 3892013 3850845 4532467 4484739 4014972 3983758 3099759 3000351
[217] 2833416 2708749 3215243 3534485 3860888 3835796 4410704 4329750 3928468
[226] 3890222
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 215 
End = 226 
Frequency = 1 
 [1] 0.02697185 0.03397653 0.04034909 0.04607781 0.04813633 0.05071618
 [7] 0.05294965 0.05645844 0.05714516 0.06043648 0.06522676 0.06825239
> postscript(file="/var/www/rcomp/tmp/1k24r1292185916.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/29ljk1292185916.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/3ymgw1292185916.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/4cvvn1292185916.tab") 
> 
> try(system("convert tmp/1k24r1292185916.ps tmp/1k24r1292185916.png",intern=TRUE))
character(0)
> try(system("convert tmp/29ljk1292185916.ps tmp/29ljk1292185916.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.810   0.440   1.223