R version 2.8.0 (2008-10-20)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(143827,145191,146832,148577,149873,151847,153252,154292,155657,156523,156416,156693,160312,160438,160882,161668,164391,168556,169738,170387,171294,172202,172651,172770,178366,180014,181067,182586,184957,186417,188599,189490,190264,191221,191110,190674,195438,196393,197172,198760,200945,203845,204613,205487,206100,206315,206291,207801,211653,211325,211893,212056,214696,217455,218884,219816,219984,219062,218550,218179,222218,222196,223393,223292,226236,228831,228745,229140,229270,229359,230006,228810,232677,232961,234629,235660,240024,243554,244368,244356,245126,246321,246797,246735,251083,251786,252732,255051,259022,261698,263891,265247,262228,263429,264305,266371,273248,275472,278146,279506,283991,286794,288703,289285,288869,286942,285833,284095,289229,289389,290793,291454,294733,293853,294056,293982,293075,292391)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> 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: 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     ar2      ma1     sma1
      0.2763  0.0514  -0.0521  -0.7139
s.e.  0.7638  0.2132   0.7590   0.1146

sigma^2 estimated as 880645:  log likelihood = -772.76,  aic = 1555.53
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 107 
End = 118 
Frequency = 1 
 [1] 286765.4 286954.1 291840.1 292772.8 294301.3 295565.1 299214.6 302040.3
 [9] 303496.9 304206.2 303755.0 303680.7

$se
Time Series:
Start = 107 
End = 118 
Frequency = 1 
 [1]  939.478 1485.029 1945.262 2337.471 2680.807 2987.837 3267.216 3524.926
 [9] 3765.190 3991.074 4204.861 4408.298

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 107 
End = 118 
Frequency = 1 
 [1] 284924.0 284043.5 288027.4 288191.3 289046.9 289709.0 292810.9 295131.4
 [9] 296117.1 296383.7 295513.5 295040.4
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 107 
End = 118 
Frequency = 1 
 [1] 288606.8 289864.8 295652.8 297354.2 299555.7 301421.3 305618.4 308949.1
 [9] 310876.6 312028.7 311996.5 312321.0
> 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$pred))
  [1] 143827.0 145191.0 146832.0 148577.0 149873.0 151847.0 153252.0 154292.0
  [9] 155657.0 156523.0 156416.0 156693.0 160312.0 160438.0 160882.0 161668.0
 [17] 164391.0 168556.0 169738.0 170387.0 171294.0 172202.0 172651.0 172770.0
 [25] 178366.0 180014.0 181067.0 182586.0 184957.0 186417.0 188599.0 189490.0
 [33] 190264.0 191221.0 191110.0 190674.0 195438.0 196393.0 197172.0 198760.0
 [41] 200945.0 203845.0 204613.0 205487.0 206100.0 206315.0 206291.0 207801.0
 [49] 211653.0 211325.0 211893.0 212056.0 214696.0 217455.0 218884.0 219816.0
 [57] 219984.0 219062.0 218550.0 218179.0 222218.0 222196.0 223393.0 223292.0
 [65] 226236.0 228831.0 228745.0 229140.0 229270.0 229359.0 230006.0 228810.0
 [73] 232677.0 232961.0 234629.0 235660.0 240024.0 243554.0 244368.0 244356.0
 [81] 245126.0 246321.0 246797.0 246735.0 251083.0 251786.0 252732.0 255051.0
 [89] 259022.0 261698.0 263891.0 265247.0 262228.0 263429.0 264305.0 266371.0
 [97] 273248.0 275472.0 278146.0 279506.0 283991.0 286794.0 288703.0 289285.0
[105] 288869.0 286942.0 286765.4 286954.1 291840.1 292772.8 294301.3 295565.1
[113] 299214.6 302040.3 303496.9 304206.2 303755.0 303680.7
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 107 
End = 118 
Frequency = 1 
 [1] 0.003276120 0.005175144 0.006665504 0.007983910 0.009109058 0.010108895
 [7] 0.010919306 0.011670383 0.012406025 0.013119631 0.013842937 0.014516226
> postscript(file="/var/www/html/freestat/rcomp/tmp/1ar0a1292951481.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/html/freestat/rcomp/tmp/2c7qg1292951481.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/html/freestat/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/freestat/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/freestat/rcomp/tmp/31q5a1292951481.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/freestat/rcomp/tmp/448lx1292951481.tab") 
> 
> try(system("convert tmp/1ar0a1292951481.ps tmp/1ar0a1292951481.png",intern=TRUE))
character(0)
> try(system("convert tmp/2c7qg1292951481.ps tmp/2c7qg1292951481.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.568   0.421   1.650