R version 2.12.0 (2010-10-15)
Copyright (C) 2010 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(100.21
+ ,100.36
+ ,100.62
+ ,100.78
+ ,100.93
+ ,100.70
+ ,100.00
+ ,100.20
+ ,99.68
+ ,99.56
+ ,100.06
+ ,100.50
+ ,99.30
+ ,99.37
+ ,99.20
+ ,98.11
+ ,97.60
+ ,97.76
+ ,98.06
+ ,98.25
+ ,98.50
+ ,97.39
+ ,98.09
+ ,97.78
+ ,98.12
+ ,97.50
+ ,97.30
+ ,97.64
+ ,96.88
+ ,97.40
+ ,98.27
+ ,97.94
+ ,98.61
+ ,98.72
+ ,98.62
+ ,98.56
+ ,98.06
+ ,97.40
+ ,97.76
+ ,97.05
+ ,97.85
+ ,97.40
+ ,97.27
+ ,97.93
+ ,98.60
+ ,98.70
+ ,98.88
+ ,98.27
+ ,97.85
+ ,97.70
+ ,96.97
+ ,97.72
+ ,97.66
+ ,99.00
+ ,98.86
+ ,99.56
+ ,100.19
+ ,100.37
+ ,100.01
+ ,99.68
+ ,99.78
+ ,99.36
+ ,99.21
+ ,99.26
+ ,99.26
+ ,100.43
+ ,101.50
+ ,102.27
+ ,102.69
+ ,103.47
+ ,104.02
+ ,103.55
+ ,103.77
+ ,104.19
+ ,103.64
+ ,103.68
+ ,105.39
+ ,106.61
+ ,108.12
+ ,109.22
+ ,110.17
+ ,110.31
+ ,111.06
+ ,111.14
+ ,111.39
+ ,112.51
+ ,111.28
+ ,112.22
+ ,113.19
+ ,114.32
+ ,115.34
+ ,116.61
+ ,117.83
+ ,117.70
+ ,118.51
+ ,118.82
+ ,119.49
+ ,119.57
+ ,120.00
+ ,121.96
+ ,121.45
+ ,123.41
+ ,124.44
+ ,126.25
+ ,127.41
+ ,127.63
+ ,129.19
+ ,129.82
+ ,130.45
+ ,132.02
+ ,132.72
+ ,132.96
+ ,135.06
+ ,137.04
+ ,137.83
+ ,139.17
+ ,140.35
+ ,141.01
+ ,141.89
+ ,143.28
+ ,142.90
+ ,143.37
+ ,145.03
+ ,146.05
+ ,147.39
+ ,149.58
+ ,151.02
+ ,153.57
+ ,155.60
+ ,157.18
+ ,158.77
+ ,159.95
+ ,161.34
+ ,161.95
+ ,163.36
+ ,165.00
+ ,166.65
+ ,168.65
+ ,170.29
+ ,172.70
+ ,173.79
+ ,176.45
+ ,177.58
+ ,179.19
+ ,181.01
+ ,184.08
+ ,185.63
+ ,188.51
+ ,190.18
+ ,192.19
+ ,193.47
+ ,196.73
+ ,200.39
+ ,203.24
+ ,205.53
+ ,208.21
+ ,208.88
+ ,212.85
+ ,216.41
+ ,216.23
+ ,219.27
+ ,222.02
+ ,224.89
+ ,230.37
+ ,232.29
+ ,235.53
+ ,236.92
+ ,242.37
+ ,242.75
+ ,244.19
+ ,247.94
+ ,248.80
+ ,250.18
+ ,251.55
+ ,254.40
+ ,255.72
+ ,257.69
+ ,258.37
+ ,258.22
+ ,258.59
+ ,257.45
+ ,257.45
+ ,256.73
+ ,258.82
+ ,257.99
+ ,262.85
+ ,262.58
+ ,261.55
+ ,261.25
+ ,259.78
+ ,256.26
+ ,254.29
+ ,248.50
+ ,241.88
+ ,238.53
+ ,232.24
+ ,232.46
+ ,225.79
+ ,221.63
+ ,219.62
+ ,215.94
+ ,211.81
+ ,205.57
+ ,201.25
+ ,194.70
+ ,187.94
+ ,185.61
+ ,181.15
+ ,186.50
+ ,183.21
+ ,182.61
+ ,187.09
+ ,189.10
+ ,191.25
+ ,190.74
+ ,190.79)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '1'
> par7 = '1'
> par6 = '3'
> par5 = '12'
> par4 = '0'
> par3 = '2'
> par2 = '-1.0'
> par1 = '0'
> par1 <- 26
> 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    sar1     sma1
      -0.1945  0.0539  0.1112  -0.9157  0.7935  -0.5786
s.e.   0.0881  0.0876  0.0791   0.0328  0.1076   0.1538

sigma^2 estimated as 1.953e-09:  log likelihood = 1616.38,  aic = -3218.77
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 191 
End = 216 
Frequency = 1 
 [1] 0.003849351 0.003843343 0.003856192 0.003853079 0.003850872 0.003848734
 [7] 0.003850967 0.003833894 0.003832661 0.003829516 0.003829418 0.003834708
[13] 0.003840515 0.003838976 0.003852942 0.003855970 0.003859118 0.003862591
[19] 0.003869639 0.003861294 0.003865569 0.003868325 0.003873494 0.003882945
[25] 0.003892804 0.003896834

$se
Time Series:
Start = 191 
End = 216 
Frequency = 1 
 [1] 4.419072e-05 5.915016e-05 7.516052e-05 9.218530e-05 1.076423e-04
 [6] 1.232519e-04 1.387808e-04 1.542244e-04 1.697886e-04 1.854604e-04
[11] 2.012838e-04 2.172929e-04 2.371412e-04 2.564192e-04 2.762134e-04
[16] 2.965050e-04 3.169154e-04 3.376397e-04 3.586310e-04 3.798769e-04
[21] 4.014030e-04 4.232029e-04 4.452806e-04 4.676392e-04 4.925952e-04
[26] 5.174264e-04

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 191 
End = 216 
Frequency = 1 
 [1] 0.003762737 0.003727409 0.003708877 0.003672395 0.003639893 0.003607161
 [7] 0.003578956 0.003531614 0.003499875 0.003466013 0.003434902 0.003408814
[13] 0.003375719 0.003336394 0.003311564 0.003274820 0.003237964 0.003200817
[19] 0.003166722 0.003116735 0.003078819 0.003038847 0.003000744 0.002966372
[25] 0.002927318 0.002882678
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 191 
End = 216 
Frequency = 1 
 [1] 0.003935965 0.003959278 0.004003506 0.004033762 0.004061851 0.004090308
 [7] 0.004122977 0.004136174 0.004165446 0.004193018 0.004223935 0.004260602
[13] 0.004305312 0.004341557 0.004394321 0.004437120 0.004480272 0.004524364
[19] 0.004572555 0.004605853 0.004652319 0.004697802 0.004746244 0.004799517
[25] 0.004858291 0.004910990
> 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] 100.2100 100.3600 100.6200 100.7800 100.9300 100.7000 100.0000 100.2000
  [9]  99.6800  99.5600 100.0600 100.5000  99.3000  99.3700  99.2000  98.1100
 [17]  97.6000  97.7600  98.0600  98.2500  98.5000  97.3900  98.0900  97.7800
 [25]  98.1200  97.5000  97.3000  97.6400  96.8800  97.4000  98.2700  97.9400
 [33]  98.6100  98.7200  98.6200  98.5600  98.0600  97.4000  97.7600  97.0500
 [41]  97.8500  97.4000  97.2700  97.9300  98.6000  98.7000  98.8800  98.2700
 [49]  97.8500  97.7000  96.9700  97.7200  97.6600  99.0000  98.8600  99.5600
 [57] 100.1900 100.3700 100.0100  99.6800  99.7800  99.3600  99.2100  99.2600
 [65]  99.2600 100.4300 101.5000 102.2700 102.6900 103.4700 104.0200 103.5500
 [73] 103.7700 104.1900 103.6400 103.6800 105.3900 106.6100 108.1200 109.2200
 [81] 110.1700 110.3100 111.0600 111.1400 111.3900 112.5100 111.2800 112.2200
 [89] 113.1900 114.3200 115.3400 116.6100 117.8300 117.7000 118.5100 118.8200
 [97] 119.4900 119.5700 120.0000 121.9600 121.4500 123.4100 124.4400 126.2500
[105] 127.4100 127.6300 129.1900 129.8200 130.4500 132.0200 132.7200 132.9600
[113] 135.0600 137.0400 137.8300 139.1700 140.3500 141.0100 141.8900 143.2800
[121] 142.9000 143.3700 145.0300 146.0500 147.3900 149.5800 151.0200 153.5700
[129] 155.6000 157.1800 158.7700 159.9500 161.3400 161.9500 163.3600 165.0000
[137] 166.6500 168.6500 170.2900 172.7000 173.7900 176.4500 177.5800 179.1900
[145] 181.0100 184.0800 185.6300 188.5100 190.1800 192.1900 193.4700 196.7300
[153] 200.3900 203.2400 205.5300 208.2100 208.8800 212.8500 216.4100 216.2300
[161] 219.2700 222.0200 224.8900 230.3700 232.2900 235.5300 236.9200 242.3700
[169] 242.7500 244.1900 247.9400 248.8000 250.1800 251.5500 254.4000 255.7200
[177] 257.6900 258.3700 258.2200 258.5900 257.4500 257.4500 256.7300 258.8200
[185] 257.9900 262.8500 262.5800 261.5500 261.2500 259.7800 259.7840 260.1901
[193] 259.3232 259.5327 259.6814 259.8257 259.6751 260.8314 260.9153 261.1296
[201] 261.1363 260.7761 260.3817 260.4862 259.5419 259.3381 259.1266 258.8936
[209] 258.4221 258.9805 258.6941 258.5098 258.1648 257.5365 256.8842 256.6186
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 191 
End = 216 
Frequency = 1 
 [1] 0.01174430 0.01586898 0.02026503 0.02510223 0.02957292 0.03416868
 [7] 0.03877690 0.04366965 0.04851276 0.05350829 0.05859957 0.06374445
[13] 0.07024911 0.07685519 0.08340876 0.09054084 0.09787489 0.10548550
[19] 0.11324991 0.12188294 0.13037564 0.13926430 0.14839004 0.15764685
[25] 0.16827528 0.17949502
> postscript(file="/var/www/rcomp/tmp/1iyaq1292683237.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/www/rcomp/tmp/2wqpz1292683237.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/www/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/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/rcomp/tmp/3lr5a1292683237.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/www/rcomp/tmp/469lg1292683237.tab") 
> 
> try(system("convert tmp/1iyaq1292683237.ps tmp/1iyaq1292683237.png",intern=TRUE))
character(0)
> try(system("convert tmp/2wqpz1292683237.ps tmp/2wqpz1292683237.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.250   0.420   1.675