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(106370,109375,116476,123297,114813,117925,126466,131235,120546,123791,129813,133463,122987,125418,130199,133016,121454,122044,128313,131556,120027,123001,130111,132524,123742,124931,133646,136557,127509,128945,137191,139716,129083,131604,139413,143125,133948,137116,144864,149277,138796,143258,150034,154708,144888,148762,156500,161088,152772,158011,163318,169969,162269,165765,170600,174681,166364,170240,176150,182056,172218,177856,182253,188090,176863,183273,187969,194650,183036,189516,193805,200499,188142,193732,197126,205140,191751,196700,199784,207360,196101,200824,205743,212489,200810,203683,207286,210910,194915,217920)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '1'
> par5 = '4'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> 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
      -0.1482
s.e.   0.1259

sigma^2 estimated as 1666927:  log likelihood = -523.52,  aic = 1051.05
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 67 
End = 90 
Frequency = 1 
 [1] 187555.6 193409.6 182180.0 188590.4 192873.0 198726.9 187497.4 193907.8
 [9] 198190.3 204044.3 192814.8 199225.2 203507.7 209361.7 198132.2 204542.5
[17] 208825.1 214679.0 203449.5 209859.9 214142.5 219996.4 208766.9 215177.3

$se
Time Series:
Start = 67 
End = 90 
Frequency = 1 
 [1]  1291.095  1696.011  2036.943  2326.448  3353.762  4024.301  4611.859
 [8]  5130.747  6233.542  7076.085  7840.641  8535.337  9726.790 10706.069
[15] 11613.954 12454.321 13734.026 14830.959 15862.206 16828.979 18193.725
[22] 19395.846 20536.995 21616.677

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 67 
End = 90 
Frequency = 1 
 [1] 185025.1 190085.4 178187.6 184030.6 186299.6 190839.3 178458.2 183851.5
 [9] 185972.6 190175.2 177447.1 182495.9 184443.2 188377.8 175368.8 180132.1
[17] 181906.4 185610.4 172359.6 176875.1 178482.7 181980.6 168514.4 172808.6
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 67 
End = 90 
Frequency = 1 
 [1] 190086.2 196733.7 186172.5 193150.3 199446.3 206614.6 196536.7 203964.1
 [9] 210408.1 217913.4 208182.4 215954.4 222572.2 230345.6 220895.5 228953.0
[17] 235743.8 243747.7 234539.4 242844.7 249802.2 258012.3 249019.4 257546.0
> 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$pred))
 [1] 106370.0 109375.0 116476.0 123297.0 114813.0 117925.0 126466.0 131235.0
 [9] 120546.0 123791.0 129813.0 133463.0 122987.0 125418.0 130199.0 133016.0
[17] 121454.0 122044.0 128313.0 131556.0 120027.0 123001.0 130111.0 132524.0
[25] 123742.0 124931.0 133646.0 136557.0 127509.0 128945.0 137191.0 139716.0
[33] 129083.0 131604.0 139413.0 143125.0 133948.0 137116.0 144864.0 149277.0
[41] 138796.0 143258.0 150034.0 154708.0 144888.0 148762.0 156500.0 161088.0
[49] 152772.0 158011.0 163318.0 169969.0 162269.0 165765.0 170600.0 174681.0
[57] 166364.0 170240.0 176150.0 182056.0 172218.0 177856.0 182253.0 188090.0
[65] 176863.0 183273.0 187555.6 193409.6 182180.0 188590.4 192873.0 198726.9
[73] 187497.4 193907.8 198190.3 204044.3 192814.8 199225.2 203507.7 209361.7
[81] 198132.2 204542.5 208825.1 214679.0 203449.5 209859.9 214142.5 219996.4
[89] 208766.9 215177.3
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 67 
End = 90 
Frequency = 1 
 [1] 0.006883800 0.008769013 0.011180932 0.012335980 0.017388452 0.020250404
 [7] 0.024596918 0.026459727 0.031452299 0.034679158 0.040664108 0.042842665
[13] 0.047795683 0.051136720 0.058617208 0.060888663 0.065768086 0.069084339
[19] 0.077966295 0.080191493 0.084960853 0.088164375 0.098372850 0.100459855
> postscript(file="/var/www/html/rcomp/tmp/1khr61260377730.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2y9521260377730.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/3744v1260377730.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/4cjzb1260377730.tab") 
> 
> system("convert tmp/1khr61260377730.ps tmp/1khr61260377730.png")
> system("convert tmp/2y9521260377730.ps tmp/2y9521260377730.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.616   0.330   0.846