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

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Type 'demo()' for some demos, 'help()' for on-line help, or
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> x <- c(205597
+ ,205471
+ ,211064
+ ,212856
+ ,217036
+ ,219302
+ ,219759
+ ,221388
+ ,220834
+ ,221788
+ ,222358
+ ,222972
+ ,224164
+ ,224915
+ ,226294
+ ,224690
+ ,227021
+ ,229284
+ ,229189
+ ,230032
+ ,229389
+ ,231053
+ ,232560
+ ,232681
+ ,231555
+ ,231428
+ ,232141
+ ,234939
+ ,235424
+ ,235471
+ ,236355
+ ,238693
+ ,236958
+ ,237060
+ ,239282
+ ,238252
+ ,241552
+ ,236230
+ ,238909
+ ,240723
+ ,242120
+ ,242100
+ ,243276
+ ,244677
+ ,243494
+ ,244902
+ ,245247
+ ,245578
+ ,243052
+ ,238121
+ ,241863
+ ,241203
+ ,243634
+ ,242351
+ ,245180
+ ,246126
+ ,244424
+ ,245166
+ ,247258
+ ,245094
+ ,246020
+ ,243082
+ ,245555
+ ,243685
+ ,247277
+ ,245029
+ ,246169
+ ,246778
+ ,244577
+ ,246048
+ ,245775
+ ,245328
+ ,245477
+ ,241903
+ ,243219
+ ,248088
+ ,248521
+ ,247389
+ ,249057
+ ,248916
+ ,249193
+ ,250768
+ ,253106
+ ,249829
+ ,249447
+ ,246755
+ ,250785
+ ,250140
+ ,255755
+ ,254671
+ ,253919
+ ,253741
+ ,252729
+ ,253810
+ ,256653
+ ,255231
+ ,258405
+ ,251061
+ ,254811
+ ,254895
+ ,258325
+ ,257608
+ ,258759
+ ,258621
+ ,257852
+ ,260560
+ ,262358
+ ,260812
+ ,261165
+ ,257164
+ ,260720
+ ,259581
+ ,264743
+ ,261845
+ ,262262
+ ,261631
+ ,258953
+ ,259966
+ ,262850
+ ,262204
+ ,263418
+ ,262752
+ ,266433
+ ,267722
+ ,266003
+ ,262971
+ ,265521
+ ,264676
+ ,270223
+ ,269508
+ ,268457
+ ,265814
+ ,266680
+ ,263018
+ ,269285
+ ,269829
+ ,270911
+ ,266844
+ ,271244
+ ,269907
+ ,271296
+ ,270157
+ ,271322
+ ,267179
+ ,264101
+ ,265518
+ ,269419
+ ,268714
+ ,272482
+ ,268351
+ ,268175
+ ,270674
+ ,272764
+ ,272599
+ ,270333
+ ,270846
+ ,270491
+ ,269160
+ ,274027
+ ,273784
+ ,276663
+ ,274525
+ ,271344
+ ,271115
+ ,270798
+ ,273911
+ ,273985
+ ,271917
+ ,273338
+ ,270601
+ ,273547
+ ,275363
+ ,281229
+ ,277793
+ ,279913
+ ,282500
+ ,280041
+ ,282166
+ ,290304
+ ,283519
+ ,287816
+ ,285226
+ ,287595
+ ,289741
+ ,289148
+ ,288301
+ ,290155
+ ,289648
+ ,288225
+ ,289351
+ ,294735
+ ,305333)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '0'
> 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: 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:
          ma1     sma1
      -0.3185  -0.7804
s.e.   0.0822   0.0792

sigma^2 estimated as 3741605:  log likelihood = -1506.42,  aic = 3018.84
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 181 
End = 192 
Frequency = 1 
 [1] 284578.9 282396.4 286259.3 286755.4 290009.0 287331.7 288128.9 288848.0
 [9] 288741.0 289946.9 292043.2 289280.0

$se
Time Series:
Start = 181 
End = 192 
Frequency = 1 
 [1] 1934.674 2341.141 2686.805 2992.807 3270.302 3526.025 3764.416 3988.584
 [9] 4200.807 4402.813 4595.948 4781.288

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 181 
End = 192 
Frequency = 1 
 [1] 280786.9 277807.7 280993.2 280889.5 283599.2 280420.7 280750.6 281030.3
 [9] 280507.4 281317.4 283035.1 279908.7
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 181 
End = 192 
Frequency = 1 
 [1] 288370.8 286985.0 291525.5 292621.3 296418.8 294242.8 295507.1 296665.6
 [9] 296974.6 298576.4 301051.2 298651.3
> 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$pred))
  [1] 205597.0 205471.0 211064.0 212856.0 217036.0 219302.0 219759.0 221388.0
  [9] 220834.0 221788.0 222358.0 222972.0 224164.0 224915.0 226294.0 224690.0
 [17] 227021.0 229284.0 229189.0 230032.0 229389.0 231053.0 232560.0 232681.0
 [25] 231555.0 231428.0 232141.0 234939.0 235424.0 235471.0 236355.0 238693.0
 [33] 236958.0 237060.0 239282.0 238252.0 241552.0 236230.0 238909.0 240723.0
 [41] 242120.0 242100.0 243276.0 244677.0 243494.0 244902.0 245247.0 245578.0
 [49] 243052.0 238121.0 241863.0 241203.0 243634.0 242351.0 245180.0 246126.0
 [57] 244424.0 245166.0 247258.0 245094.0 246020.0 243082.0 245555.0 243685.0
 [65] 247277.0 245029.0 246169.0 246778.0 244577.0 246048.0 245775.0 245328.0
 [73] 245477.0 241903.0 243219.0 248088.0 248521.0 247389.0 249057.0 248916.0
 [81] 249193.0 250768.0 253106.0 249829.0 249447.0 246755.0 250785.0 250140.0
 [89] 255755.0 254671.0 253919.0 253741.0 252729.0 253810.0 256653.0 255231.0
 [97] 258405.0 251061.0 254811.0 254895.0 258325.0 257608.0 258759.0 258621.0
[105] 257852.0 260560.0 262358.0 260812.0 261165.0 257164.0 260720.0 259581.0
[113] 264743.0 261845.0 262262.0 261631.0 258953.0 259966.0 262850.0 262204.0
[121] 263418.0 262752.0 266433.0 267722.0 266003.0 262971.0 265521.0 264676.0
[129] 270223.0 269508.0 268457.0 265814.0 266680.0 263018.0 269285.0 269829.0
[137] 270911.0 266844.0 271244.0 269907.0 271296.0 270157.0 271322.0 267179.0
[145] 264101.0 265518.0 269419.0 268714.0 272482.0 268351.0 268175.0 270674.0
[153] 272764.0 272599.0 270333.0 270846.0 270491.0 269160.0 274027.0 273784.0
[161] 276663.0 274525.0 271344.0 271115.0 270798.0 273911.0 273985.0 271917.0
[169] 273338.0 270601.0 273547.0 275363.0 281229.0 277793.0 279913.0 282500.0
[177] 280041.0 282166.0 290304.0 283519.0 284578.9 282396.4 286259.3 286755.4
[185] 290009.0 287331.7 288128.9 288848.0 288741.0 289946.9 292043.2 289280.0
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 181 
End = 192 
Frequency = 1 
 [1] 0.006798376 0.008290266 0.009385911 0.010436797 0.011276551 0.012271616
 [7] 0.013065044 0.013808595 0.014548704 0.015184893 0.015737222 0.016528236
> postscript(file="/var/www/html/rcomp/tmp/1cma21229420939.ps",horizontal=F,pagecentre=F,paper="special",width=13.888888888889,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2fmjl1229420939.ps",horizontal=F,pagecentre=F,paper="special",width=13.888888888889,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/386vg1229420939.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/4741j1229420939.tab") 
> 
> system("convert tmp/1cma21229420939.ps tmp/1cma21229420939.png")
> system("convert tmp/2fmjl1229420939.ps tmp/2fmjl1229420939.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.744   0.345   0.935