R version 2.12.0 (2010-10-15)
Copyright (C) 2010 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(377,370,358,357,349,348,369,381,368,361,351,351,358,354,347,345,343,340,362,370,373,371,354,357,363,364,363,358,357,357,380,378,376,380,379,384,392,394,392,396,392,396,419,421,420,418,410,418,426,428,430,424,423,427,441,449,452,462,455,461,461,463,462,456,455,456,472,472,471,465,459,465,468,467,463,460,462,461,476,476,471,453,443,442,444,438,427,424,416,406,431,434,418,412,404,409,412,406,398,397,385,390,413,413,401,397,397,409,419,424,428,430,424,433,456,459,446,441,439,454,460,457,451,444,437,443,471,469,454,444,436)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '1'
> 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      ma1     sma1
      0.9377  -0.8057  -0.6271
s.e.  0.0582   0.0831   0.1492

sigma^2 estimated as 26.79:  log likelihood = -327.55,  aic = 663.09
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 120 
End = 131 
Frequency = 1 
 [1] 447.4579 454.6415 455.6726 454.3856 454.8247 449.6399 453.9395 476.7377
 [9] 479.7484 470.0784 465.5122 462.3534

$se
Time Series:
Start = 120 
End = 131 
Frequency = 1 
 [1]  5.176070  7.818322 10.167607 12.401993 14.579473 16.724054 18.846586
 [8] 20.951989 23.042268 25.117941 27.178768 29.224131

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 120 
End = 131 
Frequency = 1 
 [1] 437.3129 439.3176 435.7441 430.0777 426.2489 416.8607 417.0001 435.6718
 [9] 434.5856 420.8473 412.2418 405.0741
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 120 
End = 131 
Frequency = 1 
 [1] 457.6030 469.9654 475.6011 478.6935 483.4005 482.4190 490.8788 517.8036
 [9] 524.9113 519.3096 518.7826 519.6327
> 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$pred))
  [1] 377.0000 370.0000 358.0000 357.0000 349.0000 348.0000 369.0000 381.0000
  [9] 368.0000 361.0000 351.0000 351.0000 358.0000 354.0000 347.0000 345.0000
 [17] 343.0000 340.0000 362.0000 370.0000 373.0000 371.0000 354.0000 357.0000
 [25] 363.0000 364.0000 363.0000 358.0000 357.0000 357.0000 380.0000 378.0000
 [33] 376.0000 380.0000 379.0000 384.0000 392.0000 394.0000 392.0000 396.0000
 [41] 392.0000 396.0000 419.0000 421.0000 420.0000 418.0000 410.0000 418.0000
 [49] 426.0000 428.0000 430.0000 424.0000 423.0000 427.0000 441.0000 449.0000
 [57] 452.0000 462.0000 455.0000 461.0000 461.0000 463.0000 462.0000 456.0000
 [65] 455.0000 456.0000 472.0000 472.0000 471.0000 465.0000 459.0000 465.0000
 [73] 468.0000 467.0000 463.0000 460.0000 462.0000 461.0000 476.0000 476.0000
 [81] 471.0000 453.0000 443.0000 442.0000 444.0000 438.0000 427.0000 424.0000
 [89] 416.0000 406.0000 431.0000 434.0000 418.0000 412.0000 404.0000 409.0000
 [97] 412.0000 406.0000 398.0000 397.0000 385.0000 390.0000 413.0000 413.0000
[105] 401.0000 397.0000 397.0000 409.0000 419.0000 424.0000 428.0000 430.0000
[113] 424.0000 433.0000 456.0000 459.0000 446.0000 441.0000 439.0000 447.4579
[121] 454.6415 455.6726 454.3856 454.8247 449.6399 453.9395 476.7377 479.7484
[129] 470.0784 465.5122 462.3534
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 120 
End = 131 
Frequency = 1 
 [1] 0.01156772 0.01719668 0.02231341 0.02729398 0.03205515 0.03719433
 [7] 0.04151784 0.04394867 0.04802990 0.05343351 0.05838465 0.06320734
> postscript(file="/var/www/rcomp/tmp/1urla1293187220.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/rcomp/tmp/2q1ij1293187220.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/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/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/rcomp/tmp/3fkxv1293187220.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/rcomp/tmp/4j3w11293187220.tab") 
> 
> try(system("convert tmp/1urla1293187220.ps tmp/1urla1293187220.png",intern=TRUE))
character(0)
> try(system("convert tmp/2q1ij1293187220.ps tmp/2q1ij1293187220.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.970   0.470   1.422