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(83.87
+ ,84.23
+ ,84.61
+ ,84.82
+ ,85.04
+ ,85.06
+ ,84.93
+ ,84.98
+ ,85.23
+ ,85.30
+ ,85.33
+ ,85.55
+ ,85.70
+ ,85.88
+ ,86.04
+ ,86.07
+ ,86.31
+ ,86.38
+ ,86.35
+ ,86.55
+ ,86.70
+ ,86.74
+ ,86.85
+ ,86.95
+ ,86.80
+ ,87.01
+ ,87.17
+ ,87.43
+ ,87.66
+ ,87.68
+ ,87.59
+ ,87.65
+ ,87.72
+ ,87.70
+ ,87.71
+ ,87.80
+ ,87.62
+ ,87.84
+ ,88.17
+ ,88.47
+ ,88.58
+ ,88.57
+ ,88.55
+ ,88.68
+ ,88.79
+ ,88.85
+ ,88.95
+ ,89.27
+ ,89.09
+ ,89.42
+ ,89.72
+ ,89.85
+ ,89.96
+ ,90.25
+ ,90.20
+ ,90.27
+ ,90.78
+ ,90.79
+ ,90.98
+ ,91.25
+ ,90.75
+ ,91.01
+ ,91.50
+ ,92.09
+ ,92.56
+ ,92.66
+ ,92.38
+ ,92.38
+ ,92.66
+ ,92.69
+ ,92.59
+ ,92.98
+ ,92.98
+ ,93.15
+ ,93.65
+ ,94.06
+ ,94.24
+ ,94.24
+ ,94.11
+ ,94.16
+ ,94.43
+ ,94.67
+ ,94.60
+ ,95.00
+ ,94.84
+ ,95.26
+ ,95.81
+ ,95.92
+ ,95.85
+ ,95.90
+ ,95.80
+ ,96.00
+ ,96.34
+ ,96.43
+ ,96.48
+ ,96.75
+ ,96.51
+ ,96.69
+ ,97.28
+ ,97.69
+ ,98.08
+ ,98.09
+ ,97.92
+ ,98.06
+ ,98.23
+ ,98.57
+ ,98.53
+ ,98.92
+ ,98.42
+ ,98.73
+ ,99.32
+ ,99.73
+ ,100.00
+ ,100.08
+ ,100.02
+ ,100.26
+ ,100.71
+ ,100.95
+ ,100.75
+ ,101.03
+ ,100.64
+ ,100.93
+ ,101.41
+ ,102.07
+ ,102.42
+ ,102.53
+ ,102.43
+ ,102.60
+ ,102.65
+ ,102.74
+ ,102.82
+ ,103.21
+ ,102.75
+ ,103.09
+ ,103.71
+ ,104.30
+ ,104.58
+ ,104.71
+ ,104.44
+ ,104.57
+ ,104.95
+ ,105.49
+ ,106.03
+ ,106.48
+ ,106.25
+ ,106.70
+ ,107.60
+ ,108.05
+ ,108.72
+ ,109.17
+ ,109.08
+ ,109.04
+ ,109.34
+ ,109.37
+ ,108.96
+ ,108.77
+ ,108.11
+ ,108.67
+ ,109.05
+ ,109.43
+ ,109.62
+ ,109.85
+ ,109.34
+ ,109.65
+ ,109.69
+ ,109.91
+ ,110.09)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '0'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '-2.0'
> par1 = '12'
> par1 <- as.numeric(par1) #cut off periods
> par2 <- as.numeric(-3) #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:
         ma1     sma1
      0.1956  -0.9772
s.e.  0.0937   0.4819

sigma^2 estimated as 2.427e-17:  log likelihood = 2500.99,  aic = -4995.98
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 156 
End = 167 
Frequency = 1 
 [1] 7.641141e-07 7.721580e-07 7.608622e-07 7.439469e-07 7.314326e-07
 [6] 7.219094e-07 7.185870e-07 7.228610e-07 7.187262e-07 7.092494e-07
[11] 7.049311e-07 7.037502e-07

$se
Time Series:
Start = 156 
End = 167 
Frequency = 1 
 [1] 5.074823e-09 7.909774e-09 9.958384e-09 1.165222e-08 1.312933e-08
 [6] 1.445628e-08 1.567128e-08 1.679863e-08 1.785494e-08 1.885215e-08
[11] 1.979920e-08 2.070298e-08

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 156 
End = 167 
Frequency = 1 
 [1] 7.541675e-07 7.566548e-07 7.413437e-07 7.211086e-07 7.056992e-07
 [6] 6.935751e-07 6.878713e-07 6.899357e-07 6.837305e-07 6.722992e-07
[11] 6.661246e-07 6.631723e-07
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 156 
End = 167 
Frequency = 1 
 [1] 7.740608e-07 7.876611e-07 7.803806e-07 7.667853e-07 7.571661e-07
 [6] 7.502437e-07 7.493027e-07 7.557863e-07 7.537219e-07 7.461996e-07
[11] 7.437375e-07 7.443280e-07
> 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$pred))
  [1]  83.8700  84.2300  84.6100  84.8200  85.0400  85.0600  84.9300  84.9800
  [9]  85.2300  85.3000  85.3300  85.5500  85.7000  85.8800  86.0400  86.0700
 [17]  86.3100  86.3800  86.3500  86.5500  86.7000  86.7400  86.8500  86.9500
 [25]  86.8000  87.0100  87.1700  87.4300  87.6600  87.6800  87.5900  87.6500
 [33]  87.7200  87.7000  87.7100  87.8000  87.6200  87.8400  88.1700  88.4700
 [41]  88.5800  88.5700  88.5500  88.6800  88.7900  88.8500  88.9500  89.2700
 [49]  89.0900  89.4200  89.7200  89.8500  89.9600  90.2500  90.2000  90.2700
 [57]  90.7800  90.7900  90.9800  91.2500  90.7500  91.0100  91.5000  92.0900
 [65]  92.5600  92.6600  92.3800  92.3800  92.6600  92.6900  92.5900  92.9800
 [73]  92.9800  93.1500  93.6500  94.0600  94.2400  94.2400  94.1100  94.1600
 [81]  94.4300  94.6700  94.6000  95.0000  94.8400  95.2600  95.8100  95.9200
 [89]  95.8500  95.9000  95.8000  96.0000  96.3400  96.4300  96.4800  96.7500
 [97]  96.5100  96.6900  97.2800  97.6900  98.0800  98.0900  97.9200  98.0600
[105]  98.2300  98.5700  98.5300  98.9200  98.4200  98.7300  99.3200  99.7300
[113] 100.0000 100.0800 100.0200 100.2600 100.7100 100.9500 100.7500 101.0300
[121] 100.6400 100.9300 101.4100 102.0700 102.4200 102.5300 102.4300 102.6000
[129] 102.6500 102.7400 102.8200 103.2100 102.7500 103.0900 103.7100 104.3000
[137] 104.5800 104.7100 104.4400 104.5700 104.9500 105.4900 106.0300 106.4800
[145] 106.2500 106.7000 107.6000 108.0500 108.7200 109.1700 109.0800 109.0400
[153] 109.3400 109.3700 108.9600 109.3824 109.0012 109.5380 110.3619 110.9878
[161] 111.4737 111.6452 111.4248 111.6380 112.1331 112.3616 112.4244
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 156 
End = 167 
Frequency = 1 
 [1] 0.002233224 0.003461005 0.004438896 0.005330371 0.006127679 0.006855193
 [7] 0.007483784 0.007990247 0.008560237 0.009180906 0.009721255 0.010200725
> postscript(file="/var/www/html/rcomp/tmp/1byw21262014705.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2hbp41262014705.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/3y5oi1262014705.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/4ngha1262014705.tab") 
> 
> try(system("convert tmp/1byw21262014705.ps tmp/1byw21262014705.png",intern=TRUE))
character(0)
> try(system("convert tmp/2hbp41262014705.ps tmp/2hbp41262014705.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.817   0.318   1.586