R version 2.12.0 (2010-10-15)
Copyright (C) 2010 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: x86_64-redhat-linux-gnu (64-bit)

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> x <- c(315.42
+ ,316.32
+ ,316.49
+ ,317.56
+ ,318.13
+ ,318.00
+ ,316.39
+ ,314.66
+ ,313.68
+ ,313.18
+ ,314.66
+ ,315.43
+ ,316.27
+ ,316.81
+ ,317.42
+ ,318.87
+ ,319.87
+ ,319.43
+ ,318.01
+ ,315.75
+ ,314.00
+ ,313.68
+ ,314.84
+ ,316.03
+ ,316.73
+ ,317.54
+ ,318.38
+ ,319.31
+ ,320.42
+ ,319.61
+ ,318.42
+ ,316.64
+ ,314.83
+ ,315.15
+ ,315.95
+ ,316.85
+ ,317.78
+ ,318.40
+ ,319.53
+ ,320.41
+ ,320.85
+ ,320.45
+ ,319.44
+ ,317.25
+ ,316.12
+ ,315.27
+ ,316.53
+ ,317.53
+ ,318.58
+ ,318.92
+ ,319.70
+ ,321.22
+ ,322.08
+ ,321.31
+ ,319.58
+ ,317.61
+ ,316.05
+ ,315.83
+ ,316.91
+ ,318.20
+ ,319.41
+ ,320.07
+ ,320.74
+ ,321.40
+ ,322.06
+ ,321.73
+ ,320.27
+ ,318.54
+ ,316.54
+ ,316.71
+ ,317.53
+ ,318.55
+ ,319.27
+ ,320.28
+ ,320.73
+ ,321.97
+ ,322.00
+ ,321.71
+ ,321.05
+ ,318.71
+ ,317.65
+ ,317.14
+ ,318.71
+ ,319.25
+ ,320.46
+ ,321.43
+ ,322.22
+ ,323.54
+ ,323.91
+ ,323.59
+ ,322.26
+ ,320.21
+ ,318.48
+ ,317.94
+ ,319.63
+ ,320.87
+ ,322.17
+ ,322.34
+ ,322.88
+ ,324.25
+ ,324.83
+ ,323.93
+ ,322.39
+ ,320.76
+ ,319.10
+ ,319.23
+ ,320.56
+ ,321.80
+ ,322.40
+ ,322.99
+ ,323.73
+ ,324.86
+ ,325.41
+ ,325.19
+ ,323.97
+ ,321.92
+ ,320.10
+ ,319.96
+ ,320.97
+ ,322.48
+ ,323.52
+ ,323.89
+ ,325.04
+ ,326.01
+ ,326.67
+ ,325.96
+ ,325.13
+ ,322.90
+ ,321.61
+ ,321.01
+ ,322.08
+ ,323.37
+ ,324.34
+ ,325.30
+ ,326.29
+ ,327.54
+ ,327.54
+ ,327.21
+ ,325.98
+ ,324.42
+ ,322.91
+ ,322.90
+ ,323.85
+ ,324.96
+ ,326.01
+ ,326.51
+ ,327.01
+ ,327.62
+ ,328.76
+ ,328.40
+ ,327.20
+ ,325.28
+ ,323.20
+ ,323.40
+ ,324.64
+ ,325.85
+ ,326.60
+ ,327.47
+ ,327.58
+ ,329.56
+ ,329.90
+ ,328.92
+ ,327.89
+ ,326.17
+ ,324.68
+ ,325.04
+ ,326.34
+ ,327.39
+ ,328.37
+ ,329.40
+ ,330.14
+ ,331.33
+ ,332.31
+ ,331.90
+ ,330.70
+ ,329.15
+ ,327.34
+ ,327.02
+ ,327.99
+ ,328.48
+ ,329.18
+ ,330.55
+ ,331.32
+ ,332.48
+ ,332.92
+ ,332.08
+ ,331.02
+ ,329.24
+ ,327.28
+ ,327.21
+ ,328.29
+ ,329.41
+ ,330.23
+ ,331.24
+ ,331.87
+ ,333.14
+ ,333.80
+ ,333.42
+ ,331.73
+ ,329.90
+ ,328.40
+ ,328.17
+ ,329.32
+ ,330.59
+ ,331.58
+ ,332.39
+ ,333.33
+ ,334.41
+ ,334.71
+ ,334.17
+ ,332.88
+ ,330.77
+ ,329.14
+ ,328.77
+ ,330.14
+ ,331.52
+ ,332.75
+ ,333.25
+ ,334.53
+ ,335.90
+ ,336.57
+ ,336.10
+ ,334.76
+ ,332.59
+ ,331.41
+ ,330.98
+ ,332.24
+ ,333.68
+ ,334.80
+ ,335.22
+ ,336.47
+ ,337.59
+ ,337.84
+ ,337.72
+ ,336.37
+ ,334.51
+ ,332.60
+ ,332.37
+ ,333.75
+ ,334.79
+ ,336.05
+ ,336.59
+ ,337.79
+ ,338.71
+ ,339.30
+ ,339.12
+ ,337.56
+ ,335.92
+ ,333.74
+ ,333.70
+ ,335.13
+ ,336.56
+ ,337.84
+ ,338.19
+ ,339.90
+ ,340.60
+ ,341.29
+ ,341.00
+ ,339.39
+ ,337.43
+ ,335.72
+ ,335.84
+ ,336.93
+ ,338.04
+ ,339.06
+ ,340.30
+ ,341.21
+ ,342.33
+ ,342.74
+ ,342.07
+ ,340.32
+ ,338.27
+ ,336.52
+ ,336.68
+ ,338.19
+ ,339.44
+ ,340.57
+ ,341.44
+ ,342.53
+ ,343.39
+ ,343.96
+ ,343.18
+ ,341.88
+ ,339.65
+ ,337.80
+ ,337.69
+ ,339.09
+ ,340.32
+ ,341.20
+ ,342.35
+ ,342.93
+ ,344.77
+ ,345.58
+ ,345.14
+ ,343.81
+ ,342.22
+ ,339.69
+ ,339.82
+ ,340.98
+ ,342.82
+ ,343.52
+ ,344.33
+ ,345.11
+ ,346.88
+ ,347.25
+ ,346.61
+ ,345.22
+ ,343.11
+ ,340.90
+ ,341.17
+ ,342.80
+ ,344.04
+ ,344.79
+ ,345.82
+ ,347.25
+ ,348.17
+ ,348.75
+ ,348.07
+ ,346.38
+ ,344.52
+ ,342.92
+ ,342.63
+ ,344.06
+ ,345.38
+ ,346.12
+ ,346.79
+ ,347.69
+ ,349.38
+ ,350.04
+ ,349.38
+ ,347.78
+ ,345.75
+ ,344.70
+ ,344.01
+ ,345.50
+ ,346.75
+ ,347.86
+ ,348.32
+ ,349.26
+ ,350.84
+ ,351.70
+ ,351.11
+ ,349.37
+ ,347.97
+ ,346.31
+ ,346.22
+ ,347.68
+ ,348.82
+ ,350.29
+ ,351.58
+ ,352.08
+ ,353.45
+ ,354.08
+ ,353.66
+ ,352.25
+ ,350.30
+ ,348.58
+ ,348.74
+ ,349.93
+ ,351.21
+ ,352.62
+ ,352.93
+ ,353.54
+ ,355.27
+ ,355.52
+ ,354.97
+ ,353.74
+ ,351.51
+ ,349.63
+ ,349.82
+ ,351.12
+ ,352.35
+ ,353.47
+ ,354.51
+ ,355.18
+ ,355.98
+ ,356.94
+ ,355.99
+ ,354.58
+ ,352.68
+ ,350.72
+ ,350.92
+ ,352.55
+ ,353.91)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '0'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '0.2'
> 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:
          ma1    sma1
      -0.3717  -0.912
s.e.   0.0550   0.035

sigma^2 estimated as 2.881e-07:  log likelihood = 2183.11,  aic = -4360.22
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 373 
End = 384 
Frequency = 1 
 [1] 3.233431 3.234883 3.236530 3.239008 3.240079 3.239092 3.236423 3.232790
 [9] 3.229499 3.229329 3.231824 3.234161

$se
Time Series:
Start = 373 
End = 384 
Frequency = 1 
 [1] 0.0005369305 0.0006340953 0.0007182335 0.0007934998 0.0008622206
 [6] 0.0009258547 0.0009853880 0.0010415239 0.0010947852 0.0011455728
[11] 0.0011942025 0.0012409279

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 373 
End = 384 
Frequency = 1 
 [1] 3.232378 3.233640 3.235122 3.237453 3.238389 3.237278 3.234492 3.230749
 [9] 3.227354 3.227083 3.229483 3.231729
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 373 
End = 384 
Frequency = 1 
 [1] 3.234483 3.236125 3.237938 3.240563 3.241769 3.240907 3.238355 3.234831
 [9] 3.231645 3.231574 3.234164 3.236593
> 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] 315.4200 316.3200 316.4900 317.5600 318.1300 318.0000 316.3900 314.6600
  [9] 313.6800 313.1800 314.6600 315.4300 316.2700 316.8100 317.4200 318.8700
 [17] 319.8700 319.4300 318.0100 315.7500 314.0000 313.6800 314.8400 316.0300
 [25] 316.7300 317.5400 318.3800 319.3100 320.4200 319.6100 318.4200 316.6400
 [33] 314.8300 315.1500 315.9500 316.8500 317.7800 318.4000 319.5300 320.4100
 [41] 320.8500 320.4500 319.4400 317.2500 316.1200 315.2700 316.5300 317.5300
 [49] 318.5800 318.9200 319.7000 321.2200 322.0800 321.3100 319.5800 317.6100
 [57] 316.0500 315.8300 316.9100 318.2000 319.4100 320.0700 320.7400 321.4000
 [65] 322.0600 321.7300 320.2700 318.5400 316.5400 316.7100 317.5300 318.5500
 [73] 319.2700 320.2800 320.7300 321.9700 322.0000 321.7100 321.0500 318.7100
 [81] 317.6500 317.1400 318.7100 319.2500 320.4600 321.4300 322.2200 323.5400
 [89] 323.9100 323.5900 322.2600 320.2100 318.4800 317.9400 319.6300 320.8700
 [97] 322.1700 322.3400 322.8800 324.2500 324.8300 323.9300 322.3900 320.7600
[105] 319.1000 319.2300 320.5600 321.8000 322.4000 322.9900 323.7300 324.8600
[113] 325.4100 325.1900 323.9700 321.9200 320.1000 319.9600 320.9700 322.4800
[121] 323.5200 323.8900 325.0400 326.0100 326.6700 325.9600 325.1300 322.9000
[129] 321.6100 321.0100 322.0800 323.3700 324.3400 325.3000 326.2900 327.5400
[137] 327.5400 327.2100 325.9800 324.4200 322.9100 322.9000 323.8500 324.9600
[145] 326.0100 326.5100 327.0100 327.6200 328.7600 328.4000 327.2000 325.2800
[153] 323.2000 323.4000 324.6400 325.8500 326.6000 327.4700 327.5800 329.5600
[161] 329.9000 328.9200 327.8900 326.1700 324.6800 325.0400 326.3400 327.3900
[169] 328.3700 329.4000 330.1400 331.3300 332.3100 331.9000 330.7000 329.1500
[177] 327.3400 327.0200 327.9900 328.4800 329.1800 330.5500 331.3200 332.4800
[185] 332.9200 332.0800 331.0200 329.2400 327.2800 327.2100 328.2900 329.4100
[193] 330.2300 331.2400 331.8700 333.1400 333.8000 333.4200 331.7300 329.9000
[201] 328.4000 328.1700 329.3200 330.5900 331.5800 332.3900 333.3300 334.4100
[209] 334.7100 334.1700 332.8800 330.7700 329.1400 328.7700 330.1400 331.5200
[217] 332.7500 333.2500 334.5300 335.9000 336.5700 336.1000 334.7600 332.5900
[225] 331.4100 330.9800 332.2400 333.6800 334.8000 335.2200 336.4700 337.5900
[233] 337.8400 337.7200 336.3700 334.5100 332.6000 332.3700 333.7500 334.7900
[241] 336.0500 336.5900 337.7900 338.7100 339.3000 339.1200 337.5600 335.9200
[249] 333.7400 333.7000 335.1300 336.5600 337.8400 338.1900 339.9000 340.6000
[257] 341.2900 341.0000 339.3900 337.4300 335.7200 335.8400 336.9300 338.0400
[265] 339.0600 340.3000 341.2100 342.3300 342.7400 342.0700 340.3200 338.2700
[273] 336.5200 336.6800 338.1900 339.4400 340.5700 341.4400 342.5300 343.3900
[281] 343.9600 343.1800 341.8800 339.6500 337.8000 337.6900 339.0900 340.3200
[289] 341.2000 342.3500 342.9300 344.7700 345.5800 345.1400 343.8100 342.2200
[297] 339.6900 339.8200 340.9800 342.8200 343.5200 344.3300 345.1100 346.8800
[305] 347.2500 346.6100 345.2200 343.1100 340.9000 341.1700 342.8000 344.0400
[313] 344.7900 345.8200 347.2500 348.1700 348.7500 348.0700 346.3800 344.5200
[321] 342.9200 342.6300 344.0600 345.3800 346.1200 346.7900 347.6900 349.3800
[329] 350.0400 349.3800 347.7800 345.7500 344.7000 344.0100 345.5000 346.7500
[337] 347.8600 348.3200 349.2600 350.8400 351.7000 351.1100 349.3700 347.9700
[345] 346.3100 346.2200 347.6800 348.8200 350.2900 351.5800 352.0800 353.4500
[353] 354.0800 353.6600 352.2500 350.3000 348.5800 348.7400 349.9300 351.2100
[361] 352.6200 352.9300 353.5400 355.2700 355.5200 354.9700 353.7400 351.5100
[369] 349.6300 349.8200 351.1200 352.3500 353.4417 354.2359 355.1388 356.5003
[377] 357.0903 356.5469 355.0803 353.0916 351.2983 351.2055 352.5642 353.8410
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 373 
End = 384 
Frequency = 1 
 [1] 0.0008308205 0.0009808436 0.0011105391 0.0012260887 0.0013319436
 [6] 0.0014307908 0.0015241590 0.0016129104 0.0016972304 0.0017761693
[11] 0.0018502457 0.0019213574
> postscript(file="/var/www/wessaorg/rcomp/tmp/1rm1y1293672611.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/wessaorg/rcomp/tmp/2xmgs1293672611.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/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/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/www/wessaorg/rcomp/tmp/34ovm1293672611.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/wessaorg/rcomp/tmp/40yxn1293672612.tab") 
> 
> try(system("convert tmp/1rm1y1293672611.ps tmp/1rm1y1293672611.png",intern=TRUE))
character(0)
> try(system("convert tmp/2xmgs1293672611.ps tmp/2xmgs1293672611.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
   1.25    0.14    1.43