R version 2.7.0 (2008-04-22)
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.

R is a collaborative project with many contributors.
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(267.850
+ ,255.468
+ ,246.717
+ ,238.276
+ ,229.336
+ ,231.047
+ ,264.440
+ ,261.308
+ ,257.844
+ ,253.687
+ ,248.286
+ ,248.641
+ ,243.753
+ ,233.495
+ ,222.356
+ ,211.333
+ ,202.478
+ ,202.746
+ ,238.802
+ ,235.385
+ ,224.820
+ ,219.386
+ ,213.106
+ ,213.166
+ ,208.201
+ ,197.775
+ ,189.191
+ ,178.543
+ ,171.809
+ ,172.365
+ ,204.140
+ ,205.467
+ ,193.079
+ ,190.224
+ ,185.553
+ ,185.184
+ ,183.059
+ ,175.496
+ ,168.120
+ ,160.374
+ ,155.290
+ ,156.152
+ ,189.784
+ ,192.250
+ ,184.896
+ ,184.835
+ ,180.172
+ ,181.875
+ ,182.412
+ ,180.627
+ ,174.303
+ ,169.431
+ ,163.902
+ ,166.114
+ ,198.414
+ ,205.626
+ ,199.333
+ ,199.588
+ ,196.569
+ ,200.880
+ ,201.579
+ ,195.483
+ ,190.617
+ ,187.576
+ ,183.968
+ ,186.998
+ ,216.617
+ ,224.692
+ ,222.476
+ ,223.247
+ ,225.618
+ ,232.758
+ ,235.868
+ ,232.863
+ ,227.564
+ ,226.822
+ ,223.864
+ ,227.155
+ ,260.300
+ ,273.944
+ ,270.779
+ ,268.104
+ ,268.703
+ ,273.413
+ ,275.597
+ ,270.111
+ ,262.272
+ ,255.823
+ ,250.753
+ ,250.512
+ ,277.888
+ ,289.694
+ ,281.310
+ ,275.425
+ ,271.287
+ ,274.059
+ ,274.113
+ ,267.546
+ ,257.622
+ ,250.612
+ ,243.829
+ ,243.180
+ ,275.362
+ ,287.027
+ ,279.175
+ ,282.416
+ ,275.424
+ ,277.862
+ ,284.998
+ ,272.182
+ ,258.613
+ ,253.046
+ ,243.315
+ ,234.312
+ ,265.912
+ ,279.384
+ ,262.547
+ ,256.102
+ ,251.133
+ ,249.598
+ ,251.592
+ ,244.976
+ ,237.527
+ ,232.790
+ ,224.726
+ ,223.918
+ ,252.637
+ ,263.736
+ ,251.143
+ ,239.530
+ ,232.401
+ ,233.749
+ ,232.055
+ ,224.473
+ ,215.866
+ ,207.808
+ ,199.440
+ ,193.330
+ ,222.787
+ ,241.434
+ ,221.263
+ ,207.448
+ ,200.241
+ ,205.009
+ ,206.230
+ ,198.253
+ ,194.660
+ ,185.847
+ ,180.314
+ ,176.282
+ ,203.541
+ ,222.042
+ ,197.519
+ ,185.142
+ ,176.355
+ ,180.448
+ ,180.143
+ ,173.666
+ ,165.687
+ ,162.719
+ ,157.079
+ ,153.730
+ ,182.698
+ ,200.765
+ ,176.512
+ ,166.618
+ ,158.644
+ ,159.585
+ ,163.095
+ ,159.044
+ ,155.511
+ ,153.745
+ ,150.569
+ ,150.605
+ ,179.612
+ ,194.690
+ ,189.917
+ ,184.128
+ ,175.335
+ ,179.566
+ ,181.140
+ ,177.876
+ ,175.041
+ ,169.292
+ ,166.070
+ ,166.972
+ ,206.348
+ ,215.706
+ ,202.108
+ ,195.411
+ ,193.111
+ ,195.198
+ ,198.770
+ ,194.163
+ ,190.420
+ ,189.733
+ ,186.029
+ ,191.531
+ ,232.571
+ ,243.477
+ ,227.247
+ ,217.859
+ ,208.679
+ ,213.188
+ ,216.234
+ ,213.587
+ ,209.465
+ ,204.045
+ ,200.237
+ ,203.666
+ ,241.476
+ ,260.307
+ ,243.324
+ ,244.460
+ ,233.575
+ ,237.217
+ ,235.243
+ ,230.354
+ ,227.184
+ ,221.678
+ ,217.142
+ ,219.452
+ ,256.446
+ ,265.845
+ ,248.624
+ ,241.114
+ ,229.245
+ ,231.805
+ ,219.277
+ ,219.313
+ ,212.610
+ ,214.771
+ ,211.142
+ ,211.457
+ ,240.048
+ ,240.636
+ ,230.580
+ ,208.795
+ ,197.922
+ ,194.596
+ ,194.581
+ ,185.686
+ ,178.106
+ ,172.608
+ ,167.302
+ ,168.053
+ ,202.300
+ ,202.388
+ ,182.516
+ ,173.476
+ ,166.444
+ ,171.297)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '2'
> 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:
         ar1     ar2      ma1     sma1
      0.7751  0.1694  -0.8123  -0.4240
s.e.  0.0936  0.0728   0.0726   0.0809

sigma^2 estimated as 14.03:  log likelihood = -623.09,  aic = 1256.19
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 241 
End = 252 
Frequency = 1 
 [1] 184.8127 179.9258 171.7290 168.1534 161.6763 160.5340 190.5196 193.7268
 [9] 178.6876 161.7325 148.9339 146.4460

$se
Time Series:
Start = 241 
End = 252 
Frequency = 1 
 [1]  3.746102  5.200350  6.643154  8.034193  9.413643 10.789120 12.165296
 [8] 13.543665 14.924450 16.307170 17.691006 19.074983

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 241 
End = 252 
Frequency = 1 
 [1] 177.4703 169.7331 158.7084 152.4064 143.2256 139.3873 166.6757 167.1812
 [9] 149.4356 129.7704 114.2595 109.0591
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 241 
End = 252 
Frequency = 1 
 [1] 192.1551 190.1185 184.7496 183.9005 180.1271 181.6806 214.3636 220.2724
 [9] 207.9395 193.6945 183.6082 183.8330
> 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] 267.8500 255.4680 246.7170 238.2760 229.3360 231.0470 264.4400 261.3080
  [9] 257.8440 253.6870 248.2860 248.6410 243.7530 233.4950 222.3560 211.3330
 [17] 202.4780 202.7460 238.8020 235.3850 224.8200 219.3860 213.1060 213.1660
 [25] 208.2010 197.7750 189.1910 178.5430 171.8090 172.3650 204.1400 205.4670
 [33] 193.0790 190.2240 185.5530 185.1840 183.0590 175.4960 168.1200 160.3740
 [41] 155.2900 156.1520 189.7840 192.2500 184.8960 184.8350 180.1720 181.8750
 [49] 182.4120 180.6270 174.3030 169.4310 163.9020 166.1140 198.4140 205.6260
 [57] 199.3330 199.5880 196.5690 200.8800 201.5790 195.4830 190.6170 187.5760
 [65] 183.9680 186.9980 216.6170 224.6920 222.4760 223.2470 225.6180 232.7580
 [73] 235.8680 232.8630 227.5640 226.8220 223.8640 227.1550 260.3000 273.9440
 [81] 270.7790 268.1040 268.7030 273.4130 275.5970 270.1110 262.2720 255.8230
 [89] 250.7530 250.5120 277.8880 289.6940 281.3100 275.4250 271.2870 274.0590
 [97] 274.1130 267.5460 257.6220 250.6120 243.8290 243.1800 275.3620 287.0270
[105] 279.1750 282.4160 275.4240 277.8620 284.9980 272.1820 258.6130 253.0460
[113] 243.3150 234.3120 265.9120 279.3840 262.5470 256.1020 251.1330 249.5980
[121] 251.5920 244.9760 237.5270 232.7900 224.7260 223.9180 252.6370 263.7360
[129] 251.1430 239.5300 232.4010 233.7490 232.0550 224.4730 215.8660 207.8080
[137] 199.4400 193.3300 222.7870 241.4340 221.2630 207.4480 200.2410 205.0090
[145] 206.2300 198.2530 194.6600 185.8470 180.3140 176.2820 203.5410 222.0420
[153] 197.5190 185.1420 176.3550 180.4480 180.1430 173.6660 165.6870 162.7190
[161] 157.0790 153.7300 182.6980 200.7650 176.5120 166.6180 158.6440 159.5850
[169] 163.0950 159.0440 155.5110 153.7450 150.5690 150.6050 179.6120 194.6900
[177] 189.9170 184.1280 175.3350 179.5660 181.1400 177.8760 175.0410 169.2920
[185] 166.0700 166.9720 206.3480 215.7060 202.1080 195.4110 193.1110 195.1980
[193] 198.7700 194.1630 190.4200 189.7330 186.0290 191.5310 232.5710 243.4770
[201] 227.2470 217.8590 208.6790 213.1880 216.2340 213.5870 209.4650 204.0450
[209] 200.2370 203.6660 241.4760 260.3070 243.3240 244.4600 233.5750 237.2170
[217] 235.2430 230.3540 227.1840 221.6780 217.1420 219.4520 256.4460 265.8450
[225] 248.6240 241.1140 229.2450 231.8050 219.2770 219.3130 212.6100 214.7710
[233] 211.1420 211.4570 240.0480 240.6360 230.5800 208.7950 197.9220 194.5960
[241] 184.8127 179.9258 171.7290 168.1534 161.6763 160.5340 190.5196 193.7268
[249] 178.6876 161.7325 148.9339 146.4460
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 241 
End = 252 
Frequency = 1 
 [1] 0.02026972 0.02890275 0.03868394 0.04777894 0.05822524 0.06720771
 [7] 0.06385324 0.06991117 0.08352260 0.10082804 0.11878432 0.13025265
> postscript(file="/var/www/html/rcomp/tmp/14rg71228849995.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/25ag11228849995.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/3dq8w1228849995.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/4k6d61228849995.tab") 
> 
> system("convert tmp/14rg71228849995.ps tmp/14rg71228849995.png")
> system("convert tmp/25ag11228849995.ps tmp/25ag11228849995.png")
> 
> 
> proc.time()
   user  system elapsed 
  4.174   0.555   4.304