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

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> x <- c(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
+ ,94.4
+ ,102.18)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '0'
> par6 = '2'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> par1 = '12'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> 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      ar2     sma1
      0.1251  -0.0020  -1.0000
s.e.  0.0547   0.0547   0.1932

sigma^2 estimated as 27.64:  log likelihood = -1045.29,  aic = 2098.58
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 347 
End = 358 
Frequency = 1 
 [1] 88.73784 89.52345 91.99854 91.82200 91.84064 90.70996 87.79550 87.97690
 [9] 88.23417 88.37144 89.61285 89.59600

$se
Time Series:
Start = 347 
End = 358 
Frequency = 1 
 [1]  5.349903  8.053104 10.097854 11.795430 13.278093 14.611106 15.832283
 [8] 16.965788 18.028165 19.031330 19.984201 20.893660

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 347 
End = 358 
Frequency = 1 
 [1] 78.25203 73.73937 72.20675 68.70296 65.81557 62.07220 56.76422 54.72396
 [9] 52.89897 51.07003 50.44382 48.64442
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 347 
End = 358 
Frequency = 1 
 [1]  99.22365 105.30753 111.79034 114.94105 117.86570 119.34773 118.82677
 [8] 121.22984 123.56937 125.67285 128.78189 130.54757
> 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]  87.09000  86.92000  87.59000  90.72000  90.69000  90.30000  89.55000
  [8]  88.94000  88.41000  87.82000  87.07000  86.82000  86.40000  86.02000
 [15]  85.66000  85.32000  85.00000  84.67000  83.94000  82.83000  81.95000
 [22]  81.19000  80.48000  78.86000  69.47000  68.77000  70.06000  73.95000
 [29]  75.80000  77.79000  81.57000  83.07000  84.34000  85.10000  85.25000
 [36]  84.26000  83.63000  86.44000  85.30000  84.10000  83.36000  82.48000
 [43]  81.58000  80.47000  79.34000  82.13000  81.69000  80.70000  79.88000
 [50]  79.16000  78.38000  77.42000  76.47000  75.46000  74.48000  78.27000
 [57]  80.70000  79.91000  78.75000  77.78000  81.14000  81.08000  80.03000
 [64]  78.91000  78.01000  76.90000  75.97000  81.93000  80.27000  78.67000
 [71]  77.42000  76.16000  74.70000  76.39000  76.04000  74.65000  73.29000
 [78]  71.79000  74.39000  74.91000  74.54000  73.08000  72.75000  71.32000
 [85]  70.38000  70.35000  70.01000  69.36000  67.77000  69.26000  69.80000
 [92]  68.38000  67.62000  68.39000  66.95000  65.21000  66.64000  63.45000
 [99]  60.66000  62.34000  60.32000  58.64000  60.46000  58.59000  61.87000
[106]  61.85000  67.44000  77.06000  91.74000  93.15000  94.15000  93.11000
[113]  91.51000  89.96000  88.16000  86.98000  88.03000  86.24000  84.65000
[120]  83.23000  81.70000  80.25000  78.80000  77.51000  76.20000  75.04000
[127]  74.00000  75.49000  77.14000  76.15000  76.27000  78.19000  76.49000
[134]  77.31000  76.65000  74.99000  73.51000  72.07000  70.59000  71.96000
[141]  76.29000  74.86000  74.93000  71.90000  71.01000  77.47000  75.78000
[148]  76.60000  76.07000  74.57000  73.02000  72.65000  73.16000  71.53000
[155]  69.78000  67.98000  69.96000  72.16000  70.47000  68.86000  67.37000
[162]  65.87000  72.16000  71.34000  69.93000  68.44000  67.16000  66.01000
[169]  67.25000  70.91000  69.75000  68.59000  67.48000  66.31000  64.81000
[176]  66.58000  65.97000  64.70000  64.70000  60.94000  59.08000  58.42000
[183]  57.77000  57.11000  53.31000  49.96000  49.40000  48.84000  48.30000
[190]  47.74000  47.24000  46.76000  46.29000  48.90000  49.23000  48.53000
[197]  48.03000  54.34000  53.79000  53.24000  52.96000  52.17000  51.70000
[204]  58.55000  78.20000  77.03000  76.19000  77.15000  75.87000  95.47000
[211] 109.67000 112.28000 112.01000 107.93000 105.96000 105.06000 102.98000
[218] 102.20000 105.23000 101.85000  99.89000  96.23000  94.76000  91.51000
[225]  91.63000  91.54000  85.23000  87.83000  87.38000  84.44000  85.19000
[232]  84.03000  86.73000 102.52000 104.45000 106.98000 107.02000  99.26000
[239]  94.45000 113.44000 157.33000 147.38000 171.89000 171.95000 132.71000
[246] 126.02000 121.18000 115.45000 110.48000 117.85000 117.63000 124.65000
[253] 109.59000 111.27000  99.78000  98.21000  99.20000  97.97000  89.55000
[260]  87.91000  93.34000  94.42000  93.20000  90.29000  91.46000  89.98000
[267]  88.35000  88.41000  82.44000  79.89000  75.69000  75.66000  84.50000
[274]  96.73000  87.48000  82.39000  83.48000  79.31000  78.16000  72.77000
[281]  72.45000  68.46000  67.62000  68.76000  70.07000  68.55000  65.30000
[288]  58.96000  59.17000  62.37000  66.28000  55.62000  55.23000  55.85000
[295]  56.75000  50.89000  53.88000  52.95000  55.08000  53.61000  58.78000
[302]  61.85000  55.91000  53.32000  46.41000  44.57000  50.00000  50.00000
[309]  53.36000  46.23000  50.45000  49.07000  45.85000  48.45000  49.96000
[316]  46.53000  50.51000  47.58000  48.05000  46.84000  47.67000  49.16000
[323]  55.54000  55.82000  58.22000  56.19000  57.77000  63.19000  54.76000
[330]  55.74000  62.54000  61.39000  69.60000  79.23000  80.00000  93.68000
[337] 107.63000 100.18000  97.30000  90.45000  80.64000  80.58000  75.82000
[344]  85.59000  89.35000  89.42000  88.73784  89.52345  91.99854  91.82200
[351]  91.84064  90.70996  87.79550  87.97690  88.23417  88.37144  89.61285
[358]  89.59600
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 347 
End = 358 
Frequency = 1 
 [1] 0.06028886 0.08995524 0.10976103 0.12845973 0.14457754 0.16107498
 [7] 0.18033137 0.19284366 0.20432181 0.21535611 0.22300596 0.23319859
> postscript(file="/var/www/html/rcomp/tmp/16aav1260631290.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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.se <- array(0, dim=fx)
> perf.mse <- 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$pred[i]
+ perf.mape[i] = perf.mape[i] + abs(perf.pe[i])
+ perf.se[i] = (x[nx+i] - forecast$pred[i])^2
+ perf.mse[i] = perf.mse[i] + perf.se[i]
+ 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 = perf.mape / fx
> perf.mse = perf.mse / fx
> perf.rmse = sqrt(perf.mse)
> postscript(file="/var/www/html/rcomp/tmp/22i1p1260631290.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[1:12] <- 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/37rhj1260631290.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.mape[i],4))
+ a<-table.element(a,round(perf.se[i],4))
+ a<-table.element(a,round(perf.mse[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/4oli91260631290.tab") 
> try(system("convert tmp/16aav1260631290.ps tmp/16aav1260631290.png",intern=TRUE))
character(0)
> try(system("convert tmp/22i1p1260631290.ps tmp/22i1p1260631290.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.377   0.342   1.521