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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Type 'demo()' for some demos, 'help()' for on-line help, or
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Type 'q()' to quit R.

> x <- c(87.28
+ ,87.28
+ ,87.09
+ ,86.92
+ ,87.59
+ ,90.72
+ ,90.69
+ ,90.3
+ ,89.55
+ ,88.94
+ ,88.41
+ ,87.82
+ ,87.07
+ ,86.82
+ ,86.4
+ ,86.02
+ ,85.66
+ ,85.32
+ ,85
+ ,84.67
+ ,83.94
+ ,82.83
+ ,81.95
+ ,81.19
+ ,80.48
+ ,78.86
+ ,69.47
+ ,68.77
+ ,70.06
+ ,73.95
+ ,75.8
+ ,77.79
+ ,81.57
+ ,83.07
+ ,84.34
+ ,85.1
+ ,85.25
+ ,84.26
+ ,83.63
+ ,86.44
+ ,85.3
+ ,84.1
+ ,83.36
+ ,82.48
+ ,81.58
+ ,80.47
+ ,79.34
+ ,82.13
+ ,81.69
+ ,80.7
+ ,79.88
+ ,79.16
+ ,78.38
+ ,77.42
+ ,76.47
+ ,75.46
+ ,74.48
+ ,78.27
+ ,80.7
+ ,79.91
+ ,78.75
+ ,77.78
+ ,81.14
+ ,81.08
+ ,80.03
+ ,78.91
+ ,78.01
+ ,76.9
+ ,75.97
+ ,81.93
+ ,80.27
+ ,78.67
+ ,77.42
+ ,76.16
+ ,74.7
+ ,76.39
+ ,76.04
+ ,74.65
+ ,73.29
+ ,71.79
+ ,74.39
+ ,74.91
+ ,74.54
+ ,73.08
+ ,72.75
+ ,71.32
+ ,70.38
+ ,70.35
+ ,70.01
+ ,69.36
+ ,67.77
+ ,69.26
+ ,69.8
+ ,68.38
+ ,67.62
+ ,68.39
+ ,66.95
+ ,65.21
+ ,66.64
+ ,63.45
+ ,60.66
+ ,62.34
+ ,60.32
+ ,58.64
+ ,60.46
+ ,58.59
+ ,61.87
+ ,61.85
+ ,67.44
+ ,77.06
+ ,91.74
+ ,93.15
+ ,94.15
+ ,93.11
+ ,91.51
+ ,89.96
+ ,88.16
+ ,86.98
+ ,88.03
+ ,86.24
+ ,84.65
+ ,83.23
+ ,81.7
+ ,80.25
+ ,78.8
+ ,77.51
+ ,76.2
+ ,75.04
+ ,74
+ ,75.49
+ ,77.14
+ ,76.15
+ ,76.27
+ ,78.19
+ ,76.49
+ ,77.31
+ ,76.65
+ ,74.99
+ ,73.51
+ ,72.07
+ ,70.59
+ ,71.96
+ ,76.29
+ ,74.86
+ ,74.93
+ ,71.9
+ ,71.01
+ ,77.47
+ ,75.78
+ ,76.6
+ ,76.07
+ ,74.57
+ ,73.02
+ ,72.65
+ ,73.16
+ ,71.53
+ ,69.78
+ ,67.98
+ ,69.96
+ ,72.16
+ ,70.47
+ ,68.86
+ ,67.37
+ ,65.87
+ ,72.16
+ ,71.34
+ ,69.93
+ ,68.44
+ ,67.16
+ ,66.01
+ ,67.25
+ ,70.91
+ ,69.75
+ ,68.59
+ ,67.48
+ ,66.31
+ ,64.81
+ ,66.58
+ ,65.97
+ ,64.7
+ ,64.7
+ ,60.94
+ ,59.08
+ ,58.42
+ ,57.77
+ ,57.11
+ ,53.31
+ ,49.96
+ ,49.4
+ ,48.84
+ ,48.3
+ ,47.74
+ ,47.24
+ ,46.76
+ ,46.29
+ ,48.9
+ ,49.23
+ ,48.53
+ ,48.03
+ ,54.34
+ ,53.79
+ ,53.24
+ ,52.96
+ ,52.17
+ ,51.7
+ ,58.55
+ ,78.2
+ ,77.03
+ ,76.19
+ ,77.15
+ ,75.87
+ ,95.47
+ ,109.67
+ ,112.28
+ ,112.01
+ ,107.93
+ ,105.96
+ ,105.06
+ ,102.98
+ ,102.2
+ ,105.23
+ ,101.85
+ ,99.89
+ ,96.23
+ ,94.76
+ ,91.51
+ ,91.63
+ ,91.54
+ ,85.23
+ ,87.83
+ ,87.38
+ ,84.44
+ ,85.19
+ ,84.03
+ ,86.73
+ ,102.52
+ ,104.45
+ ,106.98
+ ,107.02
+ ,99.26
+ ,94.45
+ ,113.44
+ ,157.33
+ ,147.38
+ ,171.89
+ ,171.95
+ ,132.71
+ ,126.02
+ ,121.18
+ ,115.45
+ ,110.48
+ ,117.85
+ ,117.63
+ ,124.65
+ ,109.59
+ ,111.27
+ ,99.78
+ ,98.21
+ ,99.2
+ ,97.97
+ ,89.55
+ ,87.91
+ ,93.34
+ ,94.42
+ ,93.2
+ ,90.29
+ ,91.46
+ ,89.98
+ ,88.35
+ ,88.41
+ ,82.44
+ ,79.89
+ ,75.69
+ ,75.66
+ ,84.5
+ ,96.73
+ ,87.48
+ ,82.39
+ ,83.48
+ ,79.31
+ ,78.16
+ ,72.77
+ ,72.45
+ ,68.46
+ ,67.62
+ ,68.76
+ ,70.07
+ ,68.55
+ ,65.3
+ ,58.96
+ ,59.17
+ ,62.37
+ ,66.28
+ ,55.62
+ ,55.23
+ ,55.85
+ ,56.75
+ ,50.89
+ ,53.88
+ ,52.95
+ ,55.08
+ ,53.61
+ ,58.78
+ ,61.85
+ ,55.91
+ ,53.32
+ ,46.41
+ ,44.57
+ ,50
+ ,50
+ ,53.36
+ ,46.23
+ ,50.45
+ ,49.07
+ ,45.85
+ ,48.45
+ ,49.96
+ ,46.53
+ ,50.51
+ ,47.58
+ ,48.05
+ ,46.84
+ ,47.67
+ ,49.16
+ ,55.54
+ ,55.82
+ ,58.22
+ ,56.19
+ ,57.77
+ ,63.19
+ ,54.76
+ ,55.74
+ ,62.54
+ ,61.39
+ ,69.6
+ ,79.23
+ ,80
+ ,93.68
+ ,107.63
+ ,100.18
+ ,97.3
+ ,90.45
+ ,80.64
+ ,80.58
+ ,75.82
+ ,85.59
+ ,89.35
+ ,89.42
+ ,104.73
+ ,95.32
+ ,89.27
+ ,90.44
+ ,86.97
+ ,79.98
+ ,81.22
+ ,87.35
+ ,83.64
+ ,82.22)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '0'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '1'
> par1 = '24'
> par1 <- as.numeric(par1) #cut off periods
> par1 <- 28
> 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
> par6 <- 3
> par7 <- as.numeric(par7) #q
> par7 <- 3
> 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     ma2     ma3
      -0.1056  -0.4009  -0.6392  0.2425  0.4914  0.8027
s.e.   0.1484   0.1044   0.1388  0.1254  0.0768  0.1219

sigma^2 estimated as 24.51:  log likelihood = -993.95,  aic = 2001.9
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 331 
End = 358 
Frequency = 1 
 [1] 63.82758 65.27299 65.19499 64.21627 63.42702 63.95259 64.83905 65.03921
 [9] 64.32678 63.75517 63.97320 64.63469 64.84279 64.41627 63.95508 64.04176
[17] 64.49011 64.70279 64.44519 64.10056 64.10429 64.40670 64.59355 64.45020
[25] 64.19714 64.16190 64.35870 64.51379

$se
Time Series:
Start = 331 
End = 358 
Frequency = 1 
 [1]  4.950619  7.495610  9.604162 11.598525 12.997599 14.110672 15.133533
 [8] 16.289984 17.436100 18.435791 19.261599 20.057364 20.907781 21.786601
[15] 22.589505 23.297264 23.971990 24.678114 25.404590 26.094582 26.723492
[22] 27.325378 27.941311 28.572160 29.183545 29.755683 30.305310 30.859958

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 331 
End = 358 
Frequency = 1 
 [1] 54.124363 50.581592 46.370837 41.483163 37.951729 36.295669 35.177326
 [8] 33.110843 30.152021 27.621019 26.220466 25.322260 23.863537 21.714532
[15] 19.679650 18.379126 17.505011 16.333688 14.652195 12.955180 11.726240
[22] 10.848959  9.828580  8.448769  6.997392  5.840764  4.960288  4.028273
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 331 
End = 358 
Frequency = 1 
 [1]  73.53079  79.96439  84.01915  86.94938  88.90232  91.60950  94.50077
 [8]  96.96758  98.50153  99.88932 101.72593 103.94713 105.82204 107.11801
[15] 108.23051 109.70440 111.47521 113.07190 114.23819 115.24594 116.48233
[22] 117.96444 119.35852 120.45164 121.39689 122.48304 123.75710 124.99931
> 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]  87.28000  87.28000  87.09000  86.92000  87.59000  90.72000  90.69000
  [8]  90.30000  89.55000  88.94000  88.41000  87.82000  87.07000  86.82000
 [15]  86.40000  86.02000  85.66000  85.32000  85.00000  84.67000  83.94000
 [22]  82.83000  81.95000  81.19000  80.48000  78.86000  69.47000  68.77000
 [29]  70.06000  73.95000  75.80000  77.79000  81.57000  83.07000  84.34000
 [36]  85.10000  85.25000  84.26000  83.63000  86.44000  85.30000  84.10000
 [43]  83.36000  82.48000  81.58000  80.47000  79.34000  82.13000  81.69000
 [50]  80.70000  79.88000  79.16000  78.38000  77.42000  76.47000  75.46000
 [57]  74.48000  78.27000  80.70000  79.91000  78.75000  77.78000  81.14000
 [64]  81.08000  80.03000  78.91000  78.01000  76.90000  75.97000  81.93000
 [71]  80.27000  78.67000  77.42000  76.16000  74.70000  76.39000  76.04000
 [78]  74.65000  73.29000  71.79000  74.39000  74.91000  74.54000  73.08000
 [85]  72.75000  71.32000  70.38000  70.35000  70.01000  69.36000  67.77000
 [92]  69.26000  69.80000  68.38000  67.62000  68.39000  66.95000  65.21000
 [99]  66.64000  63.45000  60.66000  62.34000  60.32000  58.64000  60.46000
[106]  58.59000  61.87000  61.85000  67.44000  77.06000  91.74000  93.15000
[113]  94.15000  93.11000  91.51000  89.96000  88.16000  86.98000  88.03000
[120]  86.24000  84.65000  83.23000  81.70000  80.25000  78.80000  77.51000
[127]  76.20000  75.04000  74.00000  75.49000  77.14000  76.15000  76.27000
[134]  78.19000  76.49000  77.31000  76.65000  74.99000  73.51000  72.07000
[141]  70.59000  71.96000  76.29000  74.86000  74.93000  71.90000  71.01000
[148]  77.47000  75.78000  76.60000  76.07000  74.57000  73.02000  72.65000
[155]  73.16000  71.53000  69.78000  67.98000  69.96000  72.16000  70.47000
[162]  68.86000  67.37000  65.87000  72.16000  71.34000  69.93000  68.44000
[169]  67.16000  66.01000  67.25000  70.91000  69.75000  68.59000  67.48000
[176]  66.31000  64.81000  66.58000  65.97000  64.70000  64.70000  60.94000
[183]  59.08000  58.42000  57.77000  57.11000  53.31000  49.96000  49.40000
[190]  48.84000  48.30000  47.74000  47.24000  46.76000  46.29000  48.90000
[197]  49.23000  48.53000  48.03000  54.34000  53.79000  53.24000  52.96000
[204]  52.17000  51.70000  58.55000  78.20000  77.03000  76.19000  77.15000
[211]  75.87000  95.47000 109.67000 112.28000 112.01000 107.93000 105.96000
[218] 105.06000 102.98000 102.20000 105.23000 101.85000  99.89000  96.23000
[225]  94.76000  91.51000  91.63000  91.54000  85.23000  87.83000  87.38000
[232]  84.44000  85.19000  84.03000  86.73000 102.52000 104.45000 106.98000
[239] 107.02000  99.26000  94.45000 113.44000 157.33000 147.38000 171.89000
[246] 171.95000 132.71000 126.02000 121.18000 115.45000 110.48000 117.85000
[253] 117.63000 124.65000 109.59000 111.27000  99.78000  98.21000  99.20000
[260]  97.97000  89.55000  87.91000  93.34000  94.42000  93.20000  90.29000
[267]  91.46000  89.98000  88.35000  88.41000  82.44000  79.89000  75.69000
[274]  75.66000  84.50000  96.73000  87.48000  82.39000  83.48000  79.31000
[281]  78.16000  72.77000  72.45000  68.46000  67.62000  68.76000  70.07000
[288]  68.55000  65.30000  58.96000  59.17000  62.37000  66.28000  55.62000
[295]  55.23000  55.85000  56.75000  50.89000  53.88000  52.95000  55.08000
[302]  53.61000  58.78000  61.85000  55.91000  53.32000  46.41000  44.57000
[309]  50.00000  50.00000  53.36000  46.23000  50.45000  49.07000  45.85000
[316]  48.45000  49.96000  46.53000  50.51000  47.58000  48.05000  46.84000
[323]  47.67000  49.16000  55.54000  55.82000  58.22000  56.19000  57.77000
[330]  63.19000  63.82758  65.27299  65.19499  64.21627  63.42702  63.95259
[337]  64.83905  65.03921  64.32678  63.75517  63.97320  64.63469  64.84279
[344]  64.41627  63.95508  64.04176  64.49011  64.70279  64.44519  64.10056
[351]  64.10429  64.40670  64.59355  64.45020  64.19714  64.16190  64.35870
[358]  64.51379
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 331 
End = 358 
Frequency = 1 
 [1] 0.07756239 0.11483480 0.14731440 0.18061660 0.20492211 0.22064271
 [7] 0.23340152 0.25046405 0.27105509 0.28916543 0.30108856 0.31031885
[13] 0.32243803 0.33821581 0.35320893 0.36378236 0.37171574 0.38140726
[19] 0.39420459 0.40708820 0.41687529 0.42426297 0.43257123 0.44332149
[25] 0.45459260 0.46375936 0.47088136 0.47834669
> postscript(file="/var/www/html/rcomp/tmp/1lmfk1260395143.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/29zel1260395143.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/3jfqu1260395143.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/4fuhb1260395143.tab") 
> 
> system("convert tmp/1lmfk1260395143.ps tmp/1lmfk1260395143.png")
> system("convert tmp/29zel1260395143.ps tmp/29zel1260395143.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.048   0.357   1.178