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(2072.65,2020.13,2032.76,2050.31,2128.98,2122.14,2122.89,2091.95,2002.97,1923.21,1834.44,1819.15,1792.00,1822.40,1900.70,1903.00,1958.80,1820.50,1719.80,1661.10,1664.40,1703.40,1774.90,1795.00,1816.30,1867.40,1900.00,1961.10,2065.70,2073.50,2080.80,2118.00,2099.00,2085.20,1937.70,1749.50,1750.30,1675.60,1697.50,1699.80,1655.90,1636.00,1614.20,1602.30,1548.70,1556.10,1526.90,1509.20,1566.30,1596.00,1654.50,1664.20,1687.70,1691.00,1664.60,1697.50,1685.10,1643.00,1559.60,1560.20,1590.16,1604.93,1661.80,1670.73,1692.40,1688.17,1658.04,1613.46,1595.11,1558.83,1526.65,1475.19)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '0'
> par6 = '1'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '-1.7'
> par1 = '24'
> #'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:
         ar1    sma1
      0.4415  0.0372
s.e.  0.1339  0.1615

sigma^2 estimated as 1.901e-14:  log likelihood = 675.65,  aic = -1345.3
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 49 
End = 72 
Frequency = 1 
 [1] 3.971861e-06 3.992354e-06 3.994857e-06 3.997020e-06 4.003761e-06
 [6] 4.006843e-06 4.010025e-06 4.011873e-06 4.019764e-06 4.018604e-06
[11] 4.022745e-06 4.024950e-06 4.025924e-06 4.026353e-06 4.026543e-06
[16] 4.026627e-06 4.026664e-06 4.026680e-06 4.026687e-06 4.026691e-06
[21] 4.026692e-06 4.026693e-06 4.026693e-06 4.026693e-06

$se
Time Series:
Start = 49 
End = 72 
Frequency = 1 
 [1] 1.378682e-07 2.418708e-07 3.307510e-07 4.071649e-07 4.740089e-07
 [6] 5.335850e-07 5.875734e-07 6.371765e-07 6.832594e-07 7.264546e-07
[11] 7.672341e-07 8.059582e-07 8.444248e-07 8.818655e-07 9.180581e-07
[16] 9.529957e-07 9.867475e-07 1.019404e-06 1.051056e-06 1.081786e-06
[21] 1.111668e-06 1.140769e-06 1.169146e-06 1.196850e-06

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 49 
End = 72 
Frequency = 1 
 [1] 3.701639e-06 3.518288e-06 3.346585e-06 3.198977e-06 3.074704e-06
 [6] 2.961016e-06 2.858381e-06 2.763007e-06 2.680576e-06 2.594753e-06
[11] 2.518966e-06 2.445272e-06 2.370851e-06 2.297897e-06 2.227149e-06
[16] 2.158755e-06 2.092639e-06 2.028648e-06 1.966618e-06 1.906391e-06
[21] 1.847823e-06 1.790786e-06 1.735167e-06 1.680867e-06
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 49 
End = 72 
Frequency = 1 
 [1] 4.242082e-06 4.466421e-06 4.643129e-06 4.795063e-06 4.932819e-06
 [6] 5.052669e-06 5.161669e-06 5.260739e-06 5.358953e-06 5.442455e-06
[11] 5.526524e-06 5.604628e-06 5.680996e-06 5.754810e-06 5.825937e-06
[16] 5.894498e-06 5.960689e-06 6.024712e-06 6.086756e-06 6.146990e-06
[21] 6.205561e-06 6.262599e-06 6.318218e-06 6.372519e-06
> 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$pred))
 [1] 2072.650 2020.130 2032.760 2050.310 2128.980 2122.140 2122.890 2091.950
 [9] 2002.970 1923.210 1834.440 1819.150 1792.000 1822.400 1900.700 1903.000
[17] 1958.800 1820.500 1719.800 1661.100 1664.400 1703.400 1774.900 1795.000
[25] 1816.300 1867.400 1900.000 1961.100 2065.700 2073.500 2080.800 2118.000
[33] 2099.000 2085.200 1937.700 1749.500 1750.300 1675.600 1697.500 1699.800
[41] 1655.900 1636.000 1614.200 1602.300 1548.700 1556.100 1526.900 1509.200
[49] 1503.358 1498.813 1498.261 1497.784 1496.300 1495.623 1494.925 1494.520
[57] 1492.793 1493.047 1492.143 1491.662 1491.449 1491.356 1491.314 1491.296
[65] 1491.288 1491.285 1491.283 1491.282 1491.282 1491.282 1491.282 1491.282
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 49 
End = 72 
Frequency = 1 
 [1] 0.02159048 0.03938326 0.05600763 0.07141832 0.08572402 0.09935445
 [7] 0.11242640 0.12515257 0.13732184 0.14972367 0.16173867 0.17379834
[13] 0.18644692 0.19941792 0.21261245 0.22600564 0.23960459 0.25343004
[19] 0.26750850 0.28186906 0.29654215 0.31155926 0.32695299 0.34275727
> postscript(file="/var/www/html/rcomp/tmp/16mvf1262201715.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2syk71262201715.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/3pwyk1262201715.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/4sodm1262201715.tab") 
> 
> try(system("convert tmp/16mvf1262201715.ps tmp/16mvf1262201715.png",intern=TRUE))
character(0)
> try(system("convert tmp/2syk71262201715.ps tmp/2syk71262201715.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.658   0.301   0.828