R version 2.8.0 (2008-10-20)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

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Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> x <- c(46402
+ ,45329
+ ,42185
+ ,49341
+ ,50472
+ ,33020
+ ,29567
+ ,22870
+ ,25730
+ ,32609
+ ,23536
+ ,15135
+ ,36776
+ ,29982
+ ,38062
+ ,34226
+ ,24906
+ ,30233
+ ,27405
+ ,20784
+ ,22886
+ ,25425
+ ,20838
+ ,15655
+ ,37158
+ ,36364
+ ,43213
+ ,31635
+ ,30113
+ ,29985
+ ,20919
+ ,19429
+ ,21427
+ ,26064
+ ,20109
+ ,15369
+ ,35466
+ ,25954
+ ,33504
+ ,28115
+ ,28501
+ ,28618
+ ,21434
+ ,20177
+ ,21484
+ ,25642
+ ,23515
+ ,12941
+ ,36190
+ ,37785
+ ,38407
+ ,33326
+ ,30304
+ ,27576
+ ,27048
+ ,17291
+ ,21018
+ ,26792
+ ,19426
+ ,13927
+ ,35647
+ ,31746
+ ,31277
+ ,31583
+ ,25607
+ ,28151
+ ,24947
+ ,18077
+ ,23429
+ ,26313
+ ,18862
+ ,14753
+ ,36409
+ ,33163
+ ,34122
+ ,35225
+ ,28249
+ ,30374
+ ,26311
+ ,22069
+ ,23651
+ ,28628
+ ,23187
+ ,14727
+ ,43080
+ ,32519
+ ,39657
+ ,33614
+ ,28671
+ ,34243
+ ,27336
+ ,22916
+ ,24537
+ ,26128
+ ,22602
+ ,15744
+ ,41086
+ ,39690
+ ,43129
+ ,37863
+ ,35953
+ ,29133
+ ,24693
+ ,22205
+ ,21725
+ ,27192
+ ,21790
+ ,13253
+ ,37702
+ ,30364
+ ,32609
+ ,30212
+ ,29965
+ ,28352
+ ,25814
+ ,22414
+ ,20506
+ ,28806
+ ,22228
+ ,13971
+ ,36845
+ ,35338
+ ,35022
+ ,34777
+ ,26887
+ ,23970
+ ,22780
+ ,17351
+ ,21382
+ ,24561
+ ,17409
+ ,11514
+ ,31514
+ ,27071
+ ,29462
+ ,26105
+ ,22397
+ ,23843
+ ,21705
+ ,18089
+ ,20764
+ ,25316
+ ,17704
+ ,15548
+ ,28029
+ ,29383
+ ,36438
+ ,32034
+ ,22679
+ ,24319
+ ,18004
+ ,17537
+ ,20366
+ ,22782
+ ,19169
+ ,13807
+ ,29743
+ ,25591
+ ,29096
+ ,26482
+ ,22405
+ ,27044
+ ,17970
+ ,18730
+ ,19684
+ ,19785
+ ,18479
+ ,10698
+ ,31956
+ ,29506
+ ,34506
+ ,27165
+ ,26736
+ ,23691
+ ,18157
+ ,17328
+ ,18205
+ ,20995
+ ,17382
+ ,9367
+ ,31124
+ ,26551
+ ,30651
+ ,25859
+ ,25100
+ ,25778
+ ,20418
+ ,18688
+ ,20424
+ ,24776
+ ,19814
+ ,12738)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '3'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '-0.6'
> par1 = '12'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> 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     ar3      ma1     sma1
      0.0568  0.1684  0.2633  -0.8929  -0.8995
s.e.  0.1161  0.1083  0.0973   0.0821   0.1018

sigma^2 estimated as 1.900e-08:  log likelihood = 1237.16,  aic = -2462.31
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 181 
End = 192 
Frequency = 1 
 [1] 0.002240001 0.002429107 0.002378425 0.002390483 0.002592948 0.002593225
 [7] 0.002845522 0.003068878 0.002919013 0.002687525 0.003020015 0.003768099

$se
Time Series:
Start = 181 
End = 192 
Frequency = 1 
 [1] 0.0001385106 0.0001403572 0.0001457963 0.0001566691 0.0001596518
 [6] 0.0001637992 0.0001679704 0.0001708461 0.0001739123 0.0001767914
[11] 0.0001793784 0.0001819431

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 181 
End = 192 
Frequency = 1 
 [1] 0.001968520 0.002154007 0.002092665 0.002083412 0.002280030 0.002272178
 [7] 0.002516300 0.002734020 0.002578145 0.002341014 0.002668433 0.003411490
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 181 
End = 192 
Frequency = 1 
 [1] 0.002511481 0.002704207 0.002664186 0.002697555 0.002905865 0.002914271
 [7] 0.003174744 0.003403737 0.003259881 0.003034036 0.003371596 0.004124707
> 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$pred))
  [1] 46402.00 45329.00 42185.00 49341.00 50472.00 33020.00 29567.00 22870.00
  [9] 25730.00 32609.00 23536.00 15135.00 36776.00 29982.00 38062.00 34226.00
 [17] 24906.00 30233.00 27405.00 20784.00 22886.00 25425.00 20838.00 15655.00
 [25] 37158.00 36364.00 43213.00 31635.00 30113.00 29985.00 20919.00 19429.00
 [33] 21427.00 26064.00 20109.00 15369.00 35466.00 25954.00 33504.00 28115.00
 [41] 28501.00 28618.00 21434.00 20177.00 21484.00 25642.00 23515.00 12941.00
 [49] 36190.00 37785.00 38407.00 33326.00 30304.00 27576.00 27048.00 17291.00
 [57] 21018.00 26792.00 19426.00 13927.00 35647.00 31746.00 31277.00 31583.00
 [65] 25607.00 28151.00 24947.00 18077.00 23429.00 26313.00 18862.00 14753.00
 [73] 36409.00 33163.00 34122.00 35225.00 28249.00 30374.00 26311.00 22069.00
 [81] 23651.00 28628.00 23187.00 14727.00 43080.00 32519.00 39657.00 33614.00
 [89] 28671.00 34243.00 27336.00 22916.00 24537.00 26128.00 22602.00 15744.00
 [97] 41086.00 39690.00 43129.00 37863.00 35953.00 29133.00 24693.00 22205.00
[105] 21725.00 27192.00 21790.00 13253.00 37702.00 30364.00 32609.00 30212.00
[113] 29965.00 28352.00 25814.00 22414.00 20506.00 28806.00 22228.00 13971.00
[121] 36845.00 35338.00 35022.00 34777.00 26887.00 23970.00 22780.00 17351.00
[129] 21382.00 24561.00 17409.00 11514.00 31514.00 27071.00 29462.00 26105.00
[137] 22397.00 23843.00 21705.00 18089.00 20764.00 25316.00 17704.00 15548.00
[145] 28029.00 29383.00 36438.00 32034.00 22679.00 24319.00 18004.00 17537.00
[153] 20366.00 22782.00 19169.00 13807.00 29743.00 25591.00 29096.00 26482.00
[161] 22405.00 27044.00 17970.00 18730.00 19684.00 19785.00 18479.00 10698.00
[169] 31956.00 29506.00 34506.00 27165.00 26736.00 23691.00 18157.00 17328.00
[177] 18205.00 20995.00 17382.00  9367.00 26076.73 22781.85 23596.68 23398.63
[185] 20433.55 20429.91 17501.02 15430.05 16772.84 19249.19 15848.38 10959.64
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 181 
End = 192 
Frequency = 1 
 [1] 0.1225833 0.1131621 0.1213256 0.1313918 0.1219639 0.1257223 0.1160393
 [8] 0.1083447 0.1173123 0.1319779 0.1168888 0.0919498
> postscript(file="/var/www/html/rcomp/tmp/1eaxh1230112458.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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.se <- array(0, dim=fx)
> perf.mse <- 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$pred[i]
+ perf.mape[i] = perf.mape[i] + abs(perf.pe[i])
+ perf.se[i] = (x[nx+i] - forecast$pred[i])^2
+ perf.mse[i] = perf.mse[i] + perf.se[i]
+ 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 = perf.mape / fx
> perf.mse = perf.mse / fx
> perf.rmse = sqrt(perf.mse)
> postscript(file="/var/www/html/rcomp/tmp/2xedg1230112459.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[1:12] <- 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/3x3rb1230112459.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.mape[i],4))
+ a<-table.element(a,round(perf.se[i],4))
+ a<-table.element(a,round(perf.mse[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/4jks71230112459.tab") 
> 
> system("convert tmp/1eaxh1230112458.ps tmp/1eaxh1230112458.png")
> system("convert tmp/2xedg1230112459.ps tmp/2xedg1230112459.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.926   0.359   4.782