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(392,394,392,396,392,396,419,421,420,418,410,418,426,428,430,424,423,427,441,449,452,462,455,461,461,463,462,456,455,456,472,472,471,465,459,465,468,467,463,460,462,461,476,476,471,453,443,442,444,438,427,424,416,406,431,434,418,412,404,409,412,406,398,397,385,390,413,413,401,397,397,409)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '2'
> par7 = '2'
> par6 = '3'
> par5 = '1'
> 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      ar2      ar3      ma1      ma2     sar1     sar2    sma1
      0.4054  -0.1541  -0.5003  -0.0084  -0.6678  -1.2699  -0.5665  0.0458
s.e.  1.2377   1.2679   1.0105   0.5964   0.4721   0.4766   0.2898  0.4672

sigma^2 estimated as 36.42:  log likelihood = -149.68,  aic = 317.36
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 49 
End = 72 
Frequency = 1 
 [1] 447.3554 456.0698 454.4422 449.3291 440.6467 436.3610 437.1555 439.7682
 [9] 441.2811 438.8362 434.2737 430.1150 428.1679 428.3852 428.7401 427.8079
[17] 425.2382 422.0937 419.6702 418.3965 417.7966 416.9209 415.2508 412.9748

$se
Time Series:
Start = 49 
End = 72 
Frequency = 1 
 [1]  6.034880  9.302149 11.740906 13.233524 13.883738 14.972249 16.511756
 [8] 18.888730 21.395364 23.521638 25.354512 27.055178 28.998983 31.277770
[15] 33.781470 36.298455 38.675922 40.975209 43.316054 45.809223 48.463812
[22] 51.197742 53.929072 56.628699

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 49 
End = 72 
Frequency = 1 
 [1] 435.5271 437.8376 431.4300 423.3914 413.4346 407.0154 404.7925 402.7463
 [9] 399.3462 392.7337 384.5788 377.0868 371.3299 367.0807 362.5285 356.6629
[17] 349.4334 341.7823 334.7708 328.6104 322.8076 316.5734 309.5499 301.9825
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 49 
End = 72 
Frequency = 1 
 [1] 459.1838 474.3020 477.4544 475.2668 467.8588 465.7066 469.5185 476.7901
 [9] 483.2160 484.9386 483.9685 483.1431 485.0059 489.6896 494.9518 498.9529
[17] 501.0430 502.4051 504.5697 508.1825 512.7857 517.2685 520.9518 523.9670
> 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$pred))
 [1] 392.0000 394.0000 392.0000 396.0000 392.0000 396.0000 419.0000 421.0000
 [9] 420.0000 418.0000 410.0000 418.0000 426.0000 428.0000 430.0000 424.0000
[17] 423.0000 427.0000 441.0000 449.0000 452.0000 462.0000 455.0000 461.0000
[25] 461.0000 463.0000 462.0000 456.0000 455.0000 456.0000 472.0000 472.0000
[33] 471.0000 465.0000 459.0000 465.0000 468.0000 467.0000 463.0000 460.0000
[41] 462.0000 461.0000 476.0000 476.0000 471.0000 453.0000 443.0000 442.0000
[49] 447.3554 456.0698 454.4422 449.3291 440.6467 436.3610 437.1555 439.7682
[57] 441.2811 438.8362 434.2737 430.1150 428.1679 428.3852 428.7401 427.8079
[65] 425.2382 422.0937 419.6702 418.3965 417.7966 416.9209 415.2508 412.9748
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 49 
End = 72 
Frequency = 1 
 [1] 0.01349012 0.02039633 0.02583586 0.02945174 0.03150764 0.03431161
 [7] 0.03777090 0.04295156 0.04848466 0.05360005 0.05838372 0.06290220
[13] 0.06772806 0.07301319 0.07879241 0.08484756 0.09095120 0.09707610
[19] 0.10321450 0.10948760 0.11599857 0.12279964 0.12987107 0.13712387
> postscript(file="/var/www/html/rcomp/tmp/1g7af1260492966.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2qmhx1260492966.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/3h41d1260492966.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/4e0w61260492966.tab") 
> 
> system("convert tmp/1g7af1260492966.ps tmp/1g7af1260492966.png")
> system("convert tmp/2qmhx1260492966.ps tmp/2qmhx1260492966.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.784   0.324   1.130