R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(90.2
+ ,90
+ ,88.8
+ ,85.8
+ ,84.2
+ ,80
+ ,77.8
+ ,76.8
+ ,86.4
+ ,89.2
+ ,86.2
+ ,84.6
+ ,83.2
+ ,83.2
+ ,82.6
+ ,79.8
+ ,77.2
+ ,74.8
+ ,73
+ ,73
+ ,83.6
+ ,85.6
+ ,84.8
+ ,84.2
+ ,83.4
+ ,84.6
+ ,84.6
+ ,83.8
+ ,81.2
+ ,79.6
+ ,78
+ ,78.2
+ ,88.8
+ ,92
+ ,91
+ ,91.2
+ ,90.4
+ ,91.8
+ ,92.2
+ ,90.2
+ ,88.6
+ ,87.8
+ ,86
+ ,87.2
+ ,97.6
+ ,101.2
+ ,100.4
+ ,100.2
+ ,100.2
+ ,103
+ ,104.2
+ ,104
+ ,102.4
+ ,101.8
+ ,101
+ ,102.2
+ ,114
+ ,118.4
+ ,118.8
+ ,117.2
+ ,117.2
+ ,118.4
+ ,118.8
+ ,117.2
+ ,114.4
+ ,112.6
+ ,111
+ ,110.8
+ ,120.2
+ ,124.4
+ ,123.4
+ ,121.2
+ ,119
+ ,119.8
+ ,120
+ ,118.4
+ ,115
+ ,113.4
+ ,111
+ ,111
+ ,121.6
+ ,126.2
+ ,125.8
+ ,124.8
+ ,122
+ ,123.2
+ ,124.2
+ ,120.8
+ ,116.8
+ ,114.8
+ ,111
+ ,109
+ ,119.8
+ ,124
+ ,121.6
+ ,118
+ ,115.8
+ ,116
+ ,115.8
+ ,114.4
+ ,112
+ ,110.2
+ ,107.4
+ ,108.2
+ ,117.6
+ ,121.4
+ ,119.8
+ ,115.6
+ ,112.6
+ ,113.2
+ ,112.2
+ ,110.8
+ ,108
+ ,105.2
+ ,102.4
+ ,101
+ ,110.8
+ ,116.8
+ ,113.8
+ ,108
+ ,104.4
+ ,105.2
+ ,105.4
+ ,103.2
+ ,100.6
+ ,97.8
+ ,95.8
+ ,95
+ ,104.8
+ ,110.4
+ ,106.4
+ ,102.2
+ ,98.4
+ ,98.4
+ ,98.6
+ ,96.2
+ ,92.4
+ ,91.4
+ ,88.4
+ ,87.8
+ ,97.6
+ ,104.2
+ ,100.2
+ ,97
+ ,92.8
+ ,92
+ ,93.4
+ ,92
+ ,89.6
+ ,88.6
+ ,87.2
+ ,86.2
+ ,96.8
+ ,102
+ ,102.6
+ ,100.6
+ ,94.2
+ ,94.2
+ ,95.2
+ ,95
+ ,94
+ ,92.2
+ ,91
+ ,91.2
+ ,103.4
+ ,105
+ ,104.6
+ ,103.8
+ ,101.8
+ ,102.4
+ ,103.8
+ ,103.4
+ ,102
+ ,101.8
+ ,100.2
+ ,101.4
+ ,113.8
+ ,116
+ ,115.6
+ ,113
+ ,109.4
+ ,111
+ ,112.4
+ ,112.2
+ ,111
+ ,108.8
+ ,107.4
+ ,108.6
+ ,118.8
+ ,122.2
+ ,122.6
+ ,122.2
+ ,118.8
+ ,119
+ ,118.2
+ ,117.8
+ ,116.8
+ ,114.6
+ ,113.4
+ ,113.8
+ ,124.2
+ ,125.8
+ ,125.6
+ ,122.4
+ ,119
+ ,119.4
+ ,118.6
+ ,118
+ ,116
+ ,114.8
+ ,114.6
+ ,114.6
+ ,124
+ ,125.2
+ ,124
+ ,117.6
+ ,113.2
+ ,111.4
+ ,112.2
+ ,109.8
+ ,106.4
+ ,105.2
+ ,102.2
+ ,99.8
+ ,111
+ ,113
+ ,108.4
+ ,105.4
+ ,102
+ ,102.8
+ ,103.4
+ ,101.6
+ ,98.6
+ ,98
+ ,93.8
+ ,95.6
+ ,105.6
+ ,106.8
+ ,103.6
+ ,101.2
+ ,100.4
+ ,103.2
+ ,105.6
+ ,106.6
+ ,107.2
+ ,107.4
+ ,104.8
+ ,107.2
+ ,117.4
+ ,119.4
+ ,116.2
+ ,112.8
+ ,111.6)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '1'
> par7 = '1'
> par6 = '1'
> par5 = '6'
> par4 = '1'
> 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      ma1     sar1    sma1
      0.8683  -0.7995  -0.9774  0.1497
s.e.  0.1390   0.1642   0.0120  0.1404

sigma^2 estimated as 1.504:  log likelihood = -368.69,  aic = 747.38
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 230 
End = 253 
Frequency = 1 
 [1]  99.96206 101.33319  99.26586  95.41941  94.70196  91.93441  89.58953
 [8] 100.60808 102.55152  97.99929  95.07757  91.71504  89.69028  91.29699
[15]  89.33551  85.48628  84.73042  81.95935  79.63034  90.44359  92.30525
[22]  87.77456  84.90671  81.56181

$se
Time Series:
Start = 230 
End = 253 
Frequency = 1 
 [1]  1.226459  1.795187  2.266899  2.689852  3.081388  3.449817  3.893128
 [8]  4.312465  4.712079  5.094783  5.462579  5.816980  6.652578  7.440613
[15]  8.190386  8.907774  9.596820 10.260495 10.982261 11.680038 12.355573
[22] 13.010360 13.645714 14.262815

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 230 
End = 253 
Frequency = 1 
 [1] 97.55820 97.81463 94.82274 90.14730 88.66244 85.17277 81.95900 92.15565
 [9] 93.31585 88.01351 84.37092 80.31376 76.65123 76.71339 73.28235 68.02704
[17] 65.92066 61.84878 58.10511 67.55072 68.08833 62.27425 58.16111 53.60669
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 230 
End = 253 
Frequency = 1 
 [1] 102.36592 104.85176 103.70899 100.69153 100.74148  98.69605  97.22007
 [8] 109.06051 111.78720 107.98506 105.78423 103.11632 102.72933 105.88060
[15] 105.38867 102.94551 103.54019 102.06992 101.15557 113.33647 116.52217
[22] 113.27486 111.65231 109.51693
> 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]  90.20000  90.00000  88.80000  85.80000  84.20000  80.00000  77.80000
  [8]  76.80000  86.40000  89.20000  86.20000  84.60000  83.20000  83.20000
 [15]  82.60000  79.80000  77.20000  74.80000  73.00000  73.00000  83.60000
 [22]  85.60000  84.80000  84.20000  83.40000  84.60000  84.60000  83.80000
 [29]  81.20000  79.60000  78.00000  78.20000  88.80000  92.00000  91.00000
 [36]  91.20000  90.40000  91.80000  92.20000  90.20000  88.60000  87.80000
 [43]  86.00000  87.20000  97.60000 101.20000 100.40000 100.20000 100.20000
 [50] 103.00000 104.20000 104.00000 102.40000 101.80000 101.00000 102.20000
 [57] 114.00000 118.40000 118.80000 117.20000 117.20000 118.40000 118.80000
 [64] 117.20000 114.40000 112.60000 111.00000 110.80000 120.20000 124.40000
 [71] 123.40000 121.20000 119.00000 119.80000 120.00000 118.40000 115.00000
 [78] 113.40000 111.00000 111.00000 121.60000 126.20000 125.80000 124.80000
 [85] 122.00000 123.20000 124.20000 120.80000 116.80000 114.80000 111.00000
 [92] 109.00000 119.80000 124.00000 121.60000 118.00000 115.80000 116.00000
 [99] 115.80000 114.40000 112.00000 110.20000 107.40000 108.20000 117.60000
[106] 121.40000 119.80000 115.60000 112.60000 113.20000 112.20000 110.80000
[113] 108.00000 105.20000 102.40000 101.00000 110.80000 116.80000 113.80000
[120] 108.00000 104.40000 105.20000 105.40000 103.20000 100.60000  97.80000
[127]  95.80000  95.00000 104.80000 110.40000 106.40000 102.20000  98.40000
[134]  98.40000  98.60000  96.20000  92.40000  91.40000  88.40000  87.80000
[141]  97.60000 104.20000 100.20000  97.00000  92.80000  92.00000  93.40000
[148]  92.00000  89.60000  88.60000  87.20000  86.20000  96.80000 102.00000
[155] 102.60000 100.60000  94.20000  94.20000  95.20000  95.00000  94.00000
[162]  92.20000  91.00000  91.20000 103.40000 105.00000 104.60000 103.80000
[169] 101.80000 102.40000 103.80000 103.40000 102.00000 101.80000 100.20000
[176] 101.40000 113.80000 116.00000 115.60000 113.00000 109.40000 111.00000
[183] 112.40000 112.20000 111.00000 108.80000 107.40000 108.60000 118.80000
[190] 122.20000 122.60000 122.20000 118.80000 119.00000 118.20000 117.80000
[197] 116.80000 114.60000 113.40000 113.80000 124.20000 125.80000 125.60000
[204] 122.40000 119.00000 119.40000 118.60000 118.00000 116.00000 114.80000
[211] 114.60000 114.60000 124.00000 125.20000 124.00000 117.60000 113.20000
[218] 111.40000 112.20000 109.80000 106.40000 105.20000 102.20000  99.80000
[225] 111.00000 113.00000 108.40000 105.40000 102.00000  99.96206 101.33319
[232]  99.26586  95.41941  94.70196  91.93441  89.58953 100.60808 102.55152
[239]  97.99929  95.07757  91.71504  89.69028  91.29699  89.33551  85.48628
[246]  84.73042  81.95935  79.63034  90.44359  92.30525  87.77456  84.90671
[253]  81.56181
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 230 
End = 253 
Frequency = 1 
 [1] 0.01226925 0.01771568 0.02283664 0.02818978 0.03253774 0.03752477
 [7] 0.04345517 0.04286400 0.04594841 0.05198796 0.05745392 0.06342449
[13] 0.07417279 0.08149900 0.09168119 0.10420122 0.11326297 0.12519004
[19] 0.13791553 0.12914169 0.13385558 0.14822473 0.16071420 0.17487125
> postscript(file="/var/www/html/rcomp/tmp/1yrxu1263295849.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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.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/html/rcomp/tmp/2ekry1263295849.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: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/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/3jike1263295849.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/html/rcomp/tmp/4qjob1263295849.tab") 
> 
> try(system("convert tmp/1yrxu1263295849.ps tmp/1yrxu1263295849.png",intern=TRUE))
character(0)
> try(system("convert tmp/2ekry1263295849.ps tmp/2ekry1263295849.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.388   0.330   1.532