R version 2.13.0 (2011-04-13)
Copyright (C) 2011 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(179.257
+ ,179.947
+ ,179.094
+ ,181.624
+ ,184.954
+ ,187.928
+ ,187.151
+ ,189.959
+ ,192.492
+ ,191.103
+ ,191.737
+ ,192.31
+ ,192.013
+ ,192.106
+ ,192.141
+ ,194.58
+ ,196.421
+ ,199.021
+ ,198.136
+ ,199.426
+ ,200.997
+ ,201.277
+ ,201.663
+ ,202.874
+ ,204.256
+ ,205.597
+ ,205.471
+ ,211.064
+ ,212.856
+ ,217.036
+ ,219.302
+ ,219.759
+ ,221.388
+ ,220.834
+ ,221.788
+ ,222.358
+ ,222.972
+ ,224.164
+ ,224.915
+ ,226.294
+ ,224.69
+ ,227.021
+ ,229.284
+ ,229.189
+ ,230.032
+ ,229.389
+ ,231.053
+ ,232.56
+ ,232.681
+ ,231.555
+ ,231.428
+ ,232.141
+ ,234.939
+ ,235.424
+ ,235.471
+ ,236.355
+ ,238.693
+ ,236.958
+ ,237.06
+ ,239.282
+ ,238.252
+ ,241.552
+ ,236.23
+ ,238.909
+ ,240.723
+ ,242.12
+ ,242.1
+ ,243.276
+ ,244.677
+ ,243.494
+ ,244.902
+ ,245.247
+ ,245.578
+ ,243.052
+ ,238.121
+ ,241.863
+ ,241.203
+ ,243.634
+ ,242.351
+ ,245.18
+ ,246.126
+ ,244.424
+ ,245.166
+ ,247.258
+ ,245.094
+ ,246.02
+ ,243.082
+ ,245.555
+ ,243.685
+ ,247.277
+ ,245.029
+ ,246.169
+ ,246.778
+ ,244.577
+ ,246.048
+ ,245.775
+ ,245.328
+ ,245.477
+ ,241.903
+ ,243.219
+ ,248.088
+ ,248.521
+ ,247.389
+ ,249.057
+ ,248.916
+ ,249.193
+ ,250.768
+ ,253.106
+ ,249.829
+ ,249.447
+ ,246.755
+ ,250.785
+ ,250.14
+ ,255.755
+ ,254.671
+ ,253.919
+ ,253.741
+ ,252.729
+ ,253.81
+ ,256.653
+ ,255.231
+ ,258.405
+ ,251.061
+ ,254.811
+ ,254.895
+ ,258.325
+ ,257.608
+ ,258.759
+ ,258.621
+ ,257.852
+ ,260.56
+ ,262.358
+ ,260.812
+ ,261.165
+ ,257.164
+ ,260.72
+ ,259.581
+ ,264.743
+ ,261.845
+ ,262.262
+ ,261.631
+ ,258.953
+ ,259.966
+ ,262.85
+ ,262.204
+ ,263.418
+ ,262.752
+ ,266.433
+ ,267.722
+ ,266.003
+ ,262.971
+ ,265.521
+ ,264.676
+ ,270.223
+ ,269.508
+ ,268.457
+ ,265.814
+ ,266.68
+ ,263.018
+ ,269.285
+ ,269.829
+ ,270.911
+ ,266.844
+ ,271.244
+ ,269.907
+ ,271.296
+ ,270.157
+ ,271.322
+ ,267.179
+ ,264.101
+ ,265.518
+ ,269.419
+ ,268.714
+ ,272.482
+ ,268.351
+ ,268.175
+ ,270.674
+ ,272.764
+ ,272.599
+ ,270.333
+ ,270.846
+ ,270.491
+ ,269.16
+ ,274.027
+ ,273.784
+ ,276.663
+ ,274.525
+ ,271.344
+ ,271.115
+ ,270.798
+ ,273.911
+ ,273.985
+ ,271.917
+ ,273.338
+ ,270.601
+ ,273.547
+ ,275.363
+ ,281.229
+ ,277.793
+ ,279.913
+ ,282.5
+ ,280.041
+ ,282.166
+ ,290.304
+ ,283.519
+ ,287.816
+ ,285.226
+ ,287.595
+ ,289.741
+ ,289.148
+ ,288.301
+ ,290.155
+ ,289.648
+ ,288.225
+ ,289.351
+ ,294.735
+ ,305.333
+ ,309.03
+ ,310.215
+ ,321.935
+ ,325.734
+ ,320.846
+ ,323.023
+ ,319.753
+ ,321.753
+ ,320.757
+ ,324.479
+ ,324.641
+ ,322.767
+ ,324.181
+ ,321.389
+ ,327.897
+ ,334.287
+ ,332.653
+ ,334.819
+ ,335.264
+ ,339.622
+ ,342.44
+ ,346.585
+ ,335.378
+ ,337.01
+ ,339.13
+ ,341.193
+ ,343.507
+ ,348.915
+ ,346.431
+ ,348.322
+ ,348.288
+ ,346.597
+ ,351.076
+ ,355.215
+ ,350.562
+ ,355.266)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '1'
> par7 = '0'
> par6 = '1'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '1'
> par1 = '24'
> #'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    sar1     sma1
      -0.1179  0.9762  -0.8395
s.e.   0.0660  0.0263   0.0928

sigma^2 estimated as 5.021:  log likelihood = -512.58,  aic = 1033.15
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 230 
End = 253 
Frequency = 1 
 [1] 324.1333 322.6381 326.7237 327.8156 328.8943 327.6908 327.9921 328.6049
 [9] 328.2302 329.5294 331.2544 330.8224 331.9914 330.5512 334.5373 335.6034
[17] 336.6564 335.4815 335.7756 336.3738 336.0081 337.2763 338.9602 338.5386

$se
Time Series:
Start = 230 
End = 253 
Frequency = 1 
 [1]  2.240918  2.988122  3.600029  4.120291  4.582043  5.001324  5.388078
 [8]  5.748872  6.088322  6.409821  6.715947  7.008720  7.379937  7.722623
[15]  8.051942  8.368175  8.672900  8.967274  9.252287  9.528779  9.797471
[22] 10.058989 10.313877 10.562624

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 230 
End = 253 
Frequency = 1 
 [1] 319.7412 316.7813 319.6677 319.7398 319.9135 317.8882 317.4314 317.3371
 [9] 316.2971 316.9661 318.0911 317.0853 317.5268 315.4149 318.7555 319.2018
[17] 319.6575 317.9057 317.6412 317.6974 316.8051 317.5607 318.7450 317.8358
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 230 
End = 253 
Frequency = 1 
 [1] 328.5255 328.4948 333.7798 335.8914 337.8751 337.4934 338.5527 339.8727
 [9] 340.1633 342.0926 344.4176 344.5595 346.4561 345.6875 350.3191 352.0050
[17] 353.6553 353.0574 353.9101 355.0503 355.2112 356.9919 359.1754 359.2413
> 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] 179.2570 179.9470 179.0940 181.6240 184.9540 187.9280 187.1510 189.9590
  [9] 192.4920 191.1030 191.7370 192.3100 192.0130 192.1060 192.1410 194.5800
 [17] 196.4210 199.0210 198.1360 199.4260 200.9970 201.2770 201.6630 202.8740
 [25] 204.2560 205.5970 205.4710 211.0640 212.8560 217.0360 219.3020 219.7590
 [33] 221.3880 220.8340 221.7880 222.3580 222.9720 224.1640 224.9150 226.2940
 [41] 224.6900 227.0210 229.2840 229.1890 230.0320 229.3890 231.0530 232.5600
 [49] 232.6810 231.5550 231.4280 232.1410 234.9390 235.4240 235.4710 236.3550
 [57] 238.6930 236.9580 237.0600 239.2820 238.2520 241.5520 236.2300 238.9090
 [65] 240.7230 242.1200 242.1000 243.2760 244.6770 243.4940 244.9020 245.2470
 [73] 245.5780 243.0520 238.1210 241.8630 241.2030 243.6340 242.3510 245.1800
 [81] 246.1260 244.4240 245.1660 247.2580 245.0940 246.0200 243.0820 245.5550
 [89] 243.6850 247.2770 245.0290 246.1690 246.7780 244.5770 246.0480 245.7750
 [97] 245.3280 245.4770 241.9030 243.2190 248.0880 248.5210 247.3890 249.0570
[105] 248.9160 249.1930 250.7680 253.1060 249.8290 249.4470 246.7550 250.7850
[113] 250.1400 255.7550 254.6710 253.9190 253.7410 252.7290 253.8100 256.6530
[121] 255.2310 258.4050 251.0610 254.8110 254.8950 258.3250 257.6080 258.7590
[129] 258.6210 257.8520 260.5600 262.3580 260.8120 261.1650 257.1640 260.7200
[137] 259.5810 264.7430 261.8450 262.2620 261.6310 258.9530 259.9660 262.8500
[145] 262.2040 263.4180 262.7520 266.4330 267.7220 266.0030 262.9710 265.5210
[153] 264.6760 270.2230 269.5080 268.4570 265.8140 266.6800 263.0180 269.2850
[161] 269.8290 270.9110 266.8440 271.2440 269.9070 271.2960 270.1570 271.3220
[169] 267.1790 264.1010 265.5180 269.4190 268.7140 272.4820 268.3510 268.1750
[177] 270.6740 272.7640 272.5990 270.3330 270.8460 270.4910 269.1600 274.0270
[185] 273.7840 276.6630 274.5250 271.3440 271.1150 270.7980 273.9110 273.9850
[193] 271.9170 273.3380 270.6010 273.5470 275.3630 281.2290 277.7930 279.9130
[201] 282.5000 280.0410 282.1660 290.3040 283.5190 287.8160 285.2260 287.5950
[209] 289.7410 289.1480 288.3010 290.1550 289.6480 288.2250 289.3510 294.7350
[217] 305.3330 309.0300 310.2150 321.9350 325.7340 320.8460 323.0230 319.7530
[225] 321.7530 320.7570 324.4790 324.6410 322.7670 324.1333 322.6381 326.7237
[233] 327.8156 328.8943 327.6908 327.9921 328.6049 328.2302 329.5294 331.2544
[241] 330.8224 331.9914 330.5512 334.5373 335.6034 336.6564 335.4815 335.7756
[249] 336.3738 336.0081 337.2763 338.9602 338.5386
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 230 
End = 253 
Frequency = 1 
 [1] 0.006913569 0.009261530 0.011018571 0.012568928 0.013931658 0.015262328
 [7] 0.016427464 0.017494785 0.018548939 0.019451442 0.020274289 0.021185748
[13] 0.022229298 0.023362865 0.024068893 0.024934714 0.025761874 0.026729562
[19] 0.027554968 0.028327943 0.029158437 0.029824178 0.030427984 0.031200650
> postscript(file="/var/wessaorg/rcomp/tmp/177zx1324290843.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/wessaorg/rcomp/tmp/2z6y11324290843.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/3ivjv1324290843.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/wessaorg/rcomp/tmp/4qnr71324290844.tab") 
> 
> try(system("convert tmp/177zx1324290843.ps tmp/177zx1324290843.png",intern=TRUE))
character(0)
> try(system("convert tmp/2z6y11324290843.ps tmp/2z6y11324290843.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.113   0.143   1.314