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(276986
+ ,260633
+ ,291551
+ ,275383
+ ,275302
+ ,231693
+ ,238829
+ ,274215
+ ,277808
+ ,299060
+ ,286629
+ ,232313
+ ,294053
+ ,267510
+ ,309739
+ ,280733
+ ,287298
+ ,235672
+ ,256449
+ ,288997
+ ,290789
+ ,321898
+ ,291834
+ ,241380
+ ,295469
+ ,258200
+ ,306102
+ ,281480
+ ,283101
+ ,237414
+ ,274834
+ ,299340
+ ,300383
+ ,340862
+ ,318794
+ ,265740
+ ,322656
+ ,281563
+ ,323461
+ ,312579
+ ,310784
+ ,262785
+ ,273754
+ ,320036
+ ,310336
+ ,342206
+ ,320052
+ ,265582
+ ,326988
+ ,300713
+ ,346414
+ ,317325
+ ,326208
+ ,270657
+ ,278158
+ ,324584
+ ,321801
+ ,343542
+ ,354040
+ ,278179
+ ,330246
+ ,307344
+ ,375874
+ ,335309
+ ,339271
+ ,280264
+ ,293689
+ ,341161
+ ,345097
+ ,368712
+ ,369403
+ ,288384
+ ,340981
+ ,319072
+ ,374214
+ ,344529
+ ,337271
+ ,281016
+ ,282224
+ ,320984
+ ,325426
+ ,366276
+ ,380296
+ ,300727
+ ,359326
+ ,327610
+ ,383563
+ ,352405
+ ,329351
+ ,294486
+ ,333454
+ ,334339
+ ,358000
+ ,396057
+ ,386976
+ ,307155
+ ,363909
+ ,344700
+ ,397561
+ ,376791
+ ,337085
+ ,299252
+ ,323136
+ ,329091
+ ,346991
+ ,461999
+ ,436533
+ ,360372
+ ,415467
+ ,382110
+ ,432197
+ ,424254
+ ,386728
+ ,354508
+ ,375765
+ ,367986
+ ,402378
+ ,426516
+ ,433313
+ ,338461
+ ,416834
+ ,381099
+ ,445673
+ ,412408
+ ,393997
+ ,348241
+ ,380134
+ ,373688
+ ,393588
+ ,434192
+ ,430731
+ ,344468
+ ,411891
+ ,370497
+ ,437305
+ ,411270
+ ,385495
+ ,341273
+ ,384217
+ ,373223
+ ,415771
+ ,448634
+ ,454341
+ ,350297
+ ,419104
+ ,398027
+ ,456059
+ ,430052
+ ,399757
+ ,362731
+ ,384896
+ ,385349
+ ,432289
+ ,468891
+ ,442702
+ ,370178
+ ,439400
+ ,393900
+ ,468700
+ ,438800
+ ,430100
+ ,366300
+ ,391000
+ ,380900
+ ,431400
+ ,465400
+ ,471500
+ ,387500
+ ,446400
+ ,421500
+ ,504800
+ ,492071
+ ,421253
+ ,396682
+ ,428000
+ ,421900
+ ,465600
+ ,525793
+ ,499855
+ ,435287
+ ,479499
+ ,473027
+ ,554410
+ ,489574
+ ,462157
+ ,420331)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '2'
> par5 = '12'
> par4 = '1'
> par3 = '2'
> par2 = '0.5'
> 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:
          ar1      ar2      ma1     sma1
      -0.5191  -0.2079  -0.9998  -0.5667
s.e.   0.0777   0.0829   0.0194   0.0722

sigma^2 estimated as 115.8:  log likelihood = -616.27,  aic = 1242.53
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 175 
End = 186 
Frequency = 1 
 [1] 648.6534 641.4670 677.7499 705.0303 702.1656 636.5640 687.3622 663.0283
 [9] 718.7142 703.0918 671.8763 640.4881

$se
Time Series:
Start = 175 
End = 186 
Frequency = 1 
 [1] 10.80005 12.01995 13.42566 15.07011 16.34598 17.59052 18.78746 19.91020
 [9] 20.99247 22.03609 23.04418 24.02310

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 175 
End = 186 
Frequency = 1 
 [1] 627.4853 617.9079 651.4357 675.4929 670.1275 602.0866 650.5388 624.0043
 [9] 677.5690 659.9010 626.7097 593.4029
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 175 
End = 186 
Frequency = 1 
 [1] 669.8215 665.0261 704.0642 734.5677 734.2037 671.0414 724.1856 702.0523
 [9] 759.8595 746.2825 717.0429 687.5734
> 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$pred))
  [1] 276986.0 260633.0 291551.0 275383.0 275302.0 231693.0 238829.0 274215.0
  [9] 277808.0 299060.0 286629.0 232313.0 294053.0 267510.0 309739.0 280733.0
 [17] 287298.0 235672.0 256449.0 288997.0 290789.0 321898.0 291834.0 241380.0
 [25] 295469.0 258200.0 306102.0 281480.0 283101.0 237414.0 274834.0 299340.0
 [33] 300383.0 340862.0 318794.0 265740.0 322656.0 281563.0 323461.0 312579.0
 [41] 310784.0 262785.0 273754.0 320036.0 310336.0 342206.0 320052.0 265582.0
 [49] 326988.0 300713.0 346414.0 317325.0 326208.0 270657.0 278158.0 324584.0
 [57] 321801.0 343542.0 354040.0 278179.0 330246.0 307344.0 375874.0 335309.0
 [65] 339271.0 280264.0 293689.0 341161.0 345097.0 368712.0 369403.0 288384.0
 [73] 340981.0 319072.0 374214.0 344529.0 337271.0 281016.0 282224.0 320984.0
 [81] 325426.0 366276.0 380296.0 300727.0 359326.0 327610.0 383563.0 352405.0
 [89] 329351.0 294486.0 333454.0 334339.0 358000.0 396057.0 386976.0 307155.0
 [97] 363909.0 344700.0 397561.0 376791.0 337085.0 299252.0 323136.0 329091.0
[105] 346991.0 461999.0 436533.0 360372.0 415467.0 382110.0 432197.0 424254.0
[113] 386728.0 354508.0 375765.0 367986.0 402378.0 426516.0 433313.0 338461.0
[121] 416834.0 381099.0 445673.0 412408.0 393997.0 348241.0 380134.0 373688.0
[129] 393588.0 434192.0 430731.0 344468.0 411891.0 370497.0 437305.0 411270.0
[137] 385495.0 341273.0 384217.0 373223.0 415771.0 448634.0 454341.0 350297.0
[145] 419104.0 398027.0 456059.0 430052.0 399757.0 362731.0 384896.0 385349.0
[153] 432289.0 468891.0 442702.0 370178.0 439400.0 393900.0 468700.0 438800.0
[161] 430100.0 366300.0 391000.0 380900.0 431400.0 465400.0 471500.0 387500.0
[169] 446400.0 421500.0 504800.0 492071.0 421253.0 396682.0 420751.2 411479.9
[177] 459345.0 497067.8 493036.6 405213.7 472466.8 439606.5 516550.1 494338.0
[185] 451417.7 410225.1
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 175 
End = 186 
Frequency = 1 
 [1] 0.03384325 0.03816465 0.04038745 0.04364577 0.04762093 0.05676376
 [7] 0.05612966 0.06182582 0.06008888 0.06460870 0.07090219 0.07777231
> postscript(file="/var/wessaorg/rcomp/tmp/1cg5m1323113666.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2cttx1323113666.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/3gfxd1323113666.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/4wibr1323113666.tab") 
> 
> try(system("convert tmp/1cg5m1323113666.ps tmp/1cg5m1323113666.png",intern=TRUE))
character(0)
> try(system("convert tmp/2cttx1323113666.ps tmp/2cttx1323113666.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.428   0.119   1.550