R version 2.13.0 (2011-04-13)
Copyright (C) 2011 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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.

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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(24.90
+ ,25.06
+ ,25.10
+ ,24.92
+ ,25.46
+ ,25.89
+ ,25.39
+ ,25.38
+ ,25.25
+ ,24.88
+ ,25.00
+ ,25.00
+ ,24.07
+ ,23.60
+ ,23.18
+ ,23.25
+ ,23.04
+ ,22.77
+ ,22.25
+ ,22.41
+ ,22.50
+ ,22.91
+ ,22.88
+ ,21.69
+ ,21.19
+ ,21.56
+ ,22.00
+ ,22.13
+ ,22.27
+ ,22.30
+ ,21.94
+ ,22.40
+ ,22.77
+ ,22.90
+ ,23.03
+ ,23.05
+ ,22.41
+ ,22.26
+ ,21.90
+ ,22.01
+ ,22.62
+ ,22.76
+ ,23.40
+ ,23.63
+ ,24.05
+ ,23.82
+ ,23.71
+ ,23.95
+ ,23.61
+ ,23.98
+ ,23.56
+ ,23.99
+ ,24.33
+ ,24.48
+ ,24.31
+ ,24.38
+ ,24.63
+ ,25.54
+ ,25.75
+ ,25.73
+ ,25.85
+ ,25.78
+ ,25.86
+ ,26.86
+ ,27.36
+ ,27.38
+ ,26.58
+ ,27.65
+ ,27.73
+ ,27.18
+ ,27.32
+ ,27.30
+ ,26.90
+ ,26.70
+ ,26.75
+ ,26.41
+ ,26.29
+ ,27.51
+ ,27.91
+ ,27.70
+ ,27.28
+ ,28.25
+ ,27.62
+ ,27.30
+ ,25.94
+ ,24.99
+ ,25.50
+ ,24.42
+ ,26.58
+ ,25.84
+ ,26.76
+ ,26.74
+ ,26.68
+ ,25.55
+ ,26.40
+ ,25.19
+ ,23.94
+ ,24.20
+ ,24.20
+ ,23.07
+ ,24.07
+ ,25.02
+ ,24.65
+ ,24.68
+ ,24.63
+ ,24.49
+ ,25.05
+ ,24.31
+ ,23.90
+ ,23.68
+ ,24.50
+ ,25.22
+ ,25.48
+ ,26.00
+ ,26.07
+ ,26.06
+ ,26.22
+ ,26.70
+ ,27.20
+ ,26.77
+ ,26.11
+ ,25.43
+ ,24.99
+ ,25.51
+ ,24.00
+ ,23.86
+ ,22.96
+ ,23.41
+ ,23.17
+ ,24.12
+ ,23.87
+ ,24.27
+ ,24.40
+ ,24.16
+ ,25.15
+ ,25.09
+ ,24.60
+ ,24.33
+ ,24.14
+ ,24.36
+ ,25.40
+ ,26.15
+ ,26.77
+ ,26.94
+ ,26.33
+ ,26.24
+ ,26.23
+ ,25.88
+ ,27.00
+ ,26.91
+ ,27.15
+ ,27.78
+ ,28.73
+ ,28.83
+ ,28.68
+ ,27.56
+ ,27.15
+ ,27.41
+ ,27.47
+ ,28.76
+ ,28.47
+ ,27.94
+ ,27.23
+ ,27.01
+ ,26.15
+ ,26.11
+ ,27.20
+ ,27.36
+ ,27.33
+ ,27.43
+ ,28.92
+ ,29.45
+ ,29.01
+ ,29.25
+ ,29.14
+ ,29.64
+ ,30.40
+ ,30.62
+ ,31.25
+ ,31.75
+ ,31.30
+ ,30.70
+ ,31.03
+ ,31.46
+ ,31.28
+ ,31.03
+ ,30.95
+ ,31.17
+ ,31.29
+ ,31.91
+ ,32.10
+ ,31.71
+ ,31.90
+ ,32.02
+ ,32.65
+ ,33.77
+ ,33.51
+ ,34.26
+ ,34.21
+ ,34.13
+ ,34.73
+ ,34.73
+ ,34.57
+ ,34.80
+ ,33.98
+ ,34.40
+ ,34.21
+ ,34.61
+ ,35.25
+ ,35.23
+ ,35.00
+ ,34.52
+ ,33.82
+ ,34.35
+ ,34.81
+ ,34.96
+ ,36.69
+ ,36.42
+ ,36.44
+ ,37.41
+ ,36.40
+ ,36.15
+ ,35.78
+ ,36.95
+ ,36.14
+ ,36.36
+ ,37.31
+ ,37.58
+ ,38.00
+ ,37.23
+ ,37.00
+ ,37.87
+ ,37.70
+ ,36.17
+ ,36.56
+ ,37.70
+ ,38.77
+ ,39.02
+ ,39.88
+ ,39.56
+ ,38.52
+ ,37.20
+ ,38.58
+ ,39.41
+ ,39.08
+ ,38.81
+ ,38.73
+ ,38.70
+ ,39.23
+ ,39.82
+ ,39.97
+ ,40.37
+ ,39.54
+ ,39.21
+ ,39.07
+ ,39.78
+ ,39.40
+ ,38.92)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '1'
> par7 = '0'
> par6 = '2'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '0.0'
> par1 = '12'
> 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    sar1
      -0.0150  0.0217  0.1194
s.e.   0.0646  0.0638  0.0654

sigma^2 estimated as 0.0004615:  log likelihood = 593.2,  aic = -1178.41
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 247 
End = 258 
Frequency = 1 
 [1] 3.659817 3.663441 3.666780 3.667546 3.670148 3.669187 3.666006 3.661844
 [9] 3.666192 3.668733 3.667729 3.666902

$se
Time Series:
Start = 247 
End = 258 
Frequency = 1 
 [1] 0.02148209 0.03015381 0.03711068 0.04294818 0.04808681 0.05272681
 [7] 0.05699037 0.06095644 0.06467977 0.06820013 0.07154748 0.07474509

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 247 
End = 258 
Frequency = 1 
 [1] 3.617712 3.604340 3.594043 3.583368 3.575898 3.565842 3.554305 3.542369
 [9] 3.539420 3.535061 3.527496 3.520401
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 247 
End = 258 
Frequency = 1 
 [1] 3.701922 3.722543 3.739517 3.751725 3.764399 3.772531 3.777708 3.781319
 [9] 3.792965 3.802405 3.807963 3.813402
> 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] 24.90000 25.06000 25.10000 24.92000 25.46000 25.89000 25.39000 25.38000
  [9] 25.25000 24.88000 25.00000 25.00000 24.07000 23.60000 23.18000 23.25000
 [17] 23.04000 22.77000 22.25000 22.41000 22.50000 22.91000 22.88000 21.69000
 [25] 21.19000 21.56000 22.00000 22.13000 22.27000 22.30000 21.94000 22.40000
 [33] 22.77000 22.90000 23.03000 23.05000 22.41000 22.26000 21.90000 22.01000
 [41] 22.62000 22.76000 23.40000 23.63000 24.05000 23.82000 23.71000 23.95000
 [49] 23.61000 23.98000 23.56000 23.99000 24.33000 24.48000 24.31000 24.38000
 [57] 24.63000 25.54000 25.75000 25.73000 25.85000 25.78000 25.86000 26.86000
 [65] 27.36000 27.38000 26.58000 27.65000 27.73000 27.18000 27.32000 27.30000
 [73] 26.90000 26.70000 26.75000 26.41000 26.29000 27.51000 27.91000 27.70000
 [81] 27.28000 28.25000 27.62000 27.30000 25.94000 24.99000 25.50000 24.42000
 [89] 26.58000 25.84000 26.76000 26.74000 26.68000 25.55000 26.40000 25.19000
 [97] 23.94000 24.20000 24.20000 23.07000 24.07000 25.02000 24.65000 24.68000
[105] 24.63000 24.49000 25.05000 24.31000 23.90000 23.68000 24.50000 25.22000
[113] 25.48000 26.00000 26.07000 26.06000 26.22000 26.70000 27.20000 26.77000
[121] 26.11000 25.43000 24.99000 25.51000 24.00000 23.86000 22.96000 23.41000
[129] 23.17000 24.12000 23.87000 24.27000 24.40000 24.16000 25.15000 25.09000
[137] 24.60000 24.33000 24.14000 24.36000 25.40000 26.15000 26.77000 26.94000
[145] 26.33000 26.24000 26.23000 25.88000 27.00000 26.91000 27.15000 27.78000
[153] 28.73000 28.83000 28.68000 27.56000 27.15000 27.41000 27.47000 28.76000
[161] 28.47000 27.94000 27.23000 27.01000 26.15000 26.11000 27.20000 27.36000
[169] 27.33000 27.43000 28.92000 29.45000 29.01000 29.25000 29.14000 29.64000
[177] 30.40000 30.62000 31.25000 31.75000 31.30000 30.70000 31.03000 31.46000
[185] 31.28000 31.03000 30.95000 31.17000 31.29000 31.91000 32.10000 31.71000
[193] 31.90000 32.02000 32.65000 33.77000 33.51000 34.26000 34.21000 34.13000
[201] 34.73000 34.73000 34.57000 34.80000 33.98000 34.40000 34.21000 34.61000
[209] 35.25000 35.23000 35.00000 34.52000 33.82000 34.35000 34.81000 34.96000
[217] 36.69000 36.42000 36.44000 37.41000 36.40000 36.15000 35.78000 36.95000
[225] 36.14000 36.36000 37.31000 37.58000 38.00000 37.23000 37.00000 37.87000
[233] 37.70000 36.17000 36.56000 37.70000 38.77000 39.02000 39.88000 39.56000
[241] 38.52000 37.20000 38.58000 39.41000 39.08000 38.81000 38.85423 38.99530
[249] 39.12570 39.15570 39.25773 39.22000 39.09547 38.93307 39.10273 39.20221
[257] 39.16288 39.13049
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 247 
End = 258 
Frequency = 1 
 [1] 0.02194075 0.03106269 0.03849367 0.04480764 0.05042581 0.05554766
 [7] 0.06029521 0.06474726 0.06895845 0.07296844 0.07680710 0.08049763
> postscript(file="/var/wessaorg/rcomp/tmp/1df8k1324649394.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/wessaorg/rcomp/tmp/2zseh1324649394.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/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/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/wessaorg/rcomp/tmp/33n591324649395.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/wessaorg/rcomp/tmp/4oe6i1324649395.tab") 
> 
> try(system("convert tmp/1df8k1324649394.ps tmp/1df8k1324649394.png",intern=TRUE))
character(0)
> try(system("convert tmp/2zseh1324649394.ps tmp/2zseh1324649394.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.774   0.142   0.912