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(115.65
+ ,116.00
+ ,115.92
+ ,116.10
+ ,116.44
+ ,116.65
+ ,117.45
+ ,117.58
+ ,117.43
+ ,117.24
+ ,117.25
+ ,117.29
+ ,117.83
+ ,118.22
+ ,118.11
+ ,118.23
+ ,118.15
+ ,118.23
+ ,119.03
+ ,119.38
+ ,118.97
+ ,118.78
+ ,118.97
+ ,118.94
+ ,119.86
+ ,120.09
+ ,120.13
+ ,120.15
+ ,119.90
+ ,120.00
+ ,120.84
+ ,121.17
+ ,120.81
+ ,121.00
+ ,121.12
+ ,121.29
+ ,122.09
+ ,121.88
+ ,121.31
+ ,121.33
+ ,121.45
+ ,121.67
+ ,122.78
+ ,122.84
+ ,122.34
+ ,122.37
+ ,122.72
+ ,122.68
+ ,122.78
+ ,123.08
+ ,122.92
+ ,123.51
+ ,124.18
+ ,124.05
+ ,124.36
+ ,123.87
+ ,123.84
+ ,123.85
+ ,123.83
+ ,123.84
+ ,124.27
+ ,124.56
+ ,124.57
+ ,124.87
+ ,125.08
+ ,124.86
+ ,124.89
+ ,124.58
+ ,124.83
+ ,124.97
+ ,125.19
+ ,125.42
+ ,125.74
+ ,126.07
+ ,126.35
+ ,126.69
+ ,126.85
+ ,127.12
+ ,127.43
+ ,127.49
+ ,128.05
+ ,127.85
+ ,128.35
+ ,128.29
+ ,128.38
+ ,128.80
+ ,129.18
+ ,130.14
+ ,130.77
+ ,131.19
+ ,131.32
+ ,131.41
+ ,131.61
+ ,131.69
+ ,131.94
+ ,131.70
+ ,132.54
+ ,132.74
+ ,133.02
+ ,132.76
+ ,133.05
+ ,132.74
+ ,133.16
+ ,133.10
+ ,133.37
+ ,133.15
+ ,133.18
+ ,133.29
+ ,133.76
+ ,134.51
+ ,134.82
+ ,134.71
+ ,134.52
+ ,134.86
+ ,135.11
+ ,135.28
+ ,135.61
+ ,135.22
+ ,135.47
+ ,135.42
+ ,135.85
+ ,136.27
+ ,136.30
+ ,136.85
+ ,137.05
+ ,137.03
+ ,137.45
+ ,137.49
+ ,137.55
+ ,138.04
+ ,138.03
+ ,137.75
+ ,138.27
+ ,138.99
+ ,139.74
+ ,139.70
+ ,139.97
+ ,140.21
+ ,140.78
+ ,140.80
+ ,140.64
+ ,140.42
+ ,140.85
+ ,140.96
+ ,141.04
+ ,141.71
+ ,141.60
+ ,142.11
+ ,142.59
+ ,142.56
+ ,143.00
+ ,143.18
+ ,143.15
+ ,143.10
+ ,143.45
+ ,143.59
+ ,143.92
+ ,144.66
+ ,144.34
+ ,144.82
+ ,144.49
+ ,144.41
+ ,144.99
+ ,144.95
+ ,145.00
+ ,145.66
+ ,146.68
+ ,147.38
+ ,147.94
+ ,149.12
+ ,149.95
+ ,150.19
+ ,151.16
+ ,151.74
+ ,152.56
+ ,152.09
+ ,152.46
+ ,152.66
+ ,152.38
+ ,152.59
+ ,152.88
+ ,153.29
+ ,152.35
+ ,152.49
+ ,152.20
+ ,151.57
+ ,151.55
+ ,151.79
+ ,151.52
+ ,151.76
+ ,151.92
+ ,152.20
+ ,152.75
+ ,153.49
+ ,153.78
+ ,154.10
+ ,154.62
+ ,154.65
+ ,154.81
+ ,154.92
+ ,155.40
+ ,155.63
+ ,155.76)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '1'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '0.0'
> 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      ma1     sar1     sma1
      0.3015  -0.1485  -0.0150  -0.8081
s.e.  0.5321   0.5524   0.1294   0.1237

sigma^2 estimated as 5.773e-06:  log likelihood = 814.48,  aic = -1618.95
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 192 
End = 203 
Frequency = 1 
 [1] 5.024267 5.027128 5.031431 5.031588 5.033484 5.034899 5.035046 5.038162
 [9] 5.038136 5.038430 5.039330 5.041066

$se
Time Series:
Start = 192 
End = 203 
Frequency = 1 
 [1] 0.002403334 0.003668127 0.004664714 0.005500706 0.006230157 0.006884020
 [7] 0.007481308 0.008034415 0.008551852 0.009039727 0.009502589 0.009943928

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 192 
End = 203 
Frequency = 1 
 [1] 5.019556 5.019938 5.022288 5.020807 5.021273 5.021406 5.020383 5.022414
 [9] 5.021375 5.020713 5.020705 5.021576
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 192 
End = 203 
Frequency = 1 
 [1] 5.028977 5.034318 5.040574 5.042369 5.045695 5.048391 5.049709 5.053909
 [9] 5.054898 5.056148 5.057955 5.060556
> 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] 115.6500 116.0000 115.9200 116.1000 116.4400 116.6500 117.4500 117.5800
  [9] 117.4300 117.2400 117.2500 117.2900 117.8300 118.2200 118.1100 118.2300
 [17] 118.1500 118.2300 119.0300 119.3800 118.9700 118.7800 118.9700 118.9400
 [25] 119.8600 120.0900 120.1300 120.1500 119.9000 120.0000 120.8400 121.1700
 [33] 120.8100 121.0000 121.1200 121.2900 122.0900 121.8800 121.3100 121.3300
 [41] 121.4500 121.6700 122.7800 122.8400 122.3400 122.3700 122.7200 122.6800
 [49] 122.7800 123.0800 122.9200 123.5100 124.1800 124.0500 124.3600 123.8700
 [57] 123.8400 123.8500 123.8300 123.8400 124.2700 124.5600 124.5700 124.8700
 [65] 125.0800 124.8600 124.8900 124.5800 124.8300 124.9700 125.1900 125.4200
 [73] 125.7400 126.0700 126.3500 126.6900 126.8500 127.1200 127.4300 127.4900
 [81] 128.0500 127.8500 128.3500 128.2900 128.3800 128.8000 129.1800 130.1400
 [89] 130.7700 131.1900 131.3200 131.4100 131.6100 131.6900 131.9400 131.7000
 [97] 132.5400 132.7400 133.0200 132.7600 133.0500 132.7400 133.1600 133.1000
[105] 133.3700 133.1500 133.1800 133.2900 133.7600 134.5100 134.8200 134.7100
[113] 134.5200 134.8600 135.1100 135.2800 135.6100 135.2200 135.4700 135.4200
[121] 135.8500 136.2700 136.3000 136.8500 137.0500 137.0300 137.4500 137.4900
[129] 137.5500 138.0400 138.0300 137.7500 138.2700 138.9900 139.7400 139.7000
[137] 139.9700 140.2100 140.7800 140.8000 140.6400 140.4200 140.8500 140.9600
[145] 141.0400 141.7100 141.6000 142.1100 142.5900 142.5600 143.0000 143.1800
[153] 143.1500 143.1000 143.4500 143.5900 143.9200 144.6600 144.3400 144.8200
[161] 144.4900 144.4100 144.9900 144.9500 145.0000 145.6600 146.6800 147.3800
[169] 147.9400 149.1200 149.9500 150.1900 151.1600 151.7400 152.5600 152.0900
[177] 152.4600 152.6600 152.3800 152.5900 152.8800 153.2900 152.3500 152.4900
[185] 152.2000 151.5700 151.5500 151.7900 151.5200 151.7600 151.9200 152.0587
[193] 152.4944 153.1521 153.1761 153.4667 153.6840 153.7067 154.1863 154.1824
[201] 154.2278 154.3666 154.6348
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 192 
End = 203 
Frequency = 1 
 [1] 0.002409003 0.003681345 0.004686104 0.005530466 0.006268350 0.006930671
 [7] 0.007536428 0.008098009 0.008623926 0.009120285 0.009591634 0.010041465
> postscript(file="/var/www/html/rcomp/tmp/12cxk1291468788.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/html/rcomp/tmp/2y4vb1291468788.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/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/3yea81291468788.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/41fqw1291468788.tab") 
> 
> try(system("convert tmp/12cxk1291468788.ps tmp/12cxk1291468788.png",intern=TRUE))
character(0)
> try(system("convert tmp/2y4vb1291468788.ps tmp/2y4vb1291468788.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.429   0.315   2.925