R version 2.15.2 (2012-10-26) -- "Trick or Treat"
Copyright (C) 2012 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i686-pc-linux-gnu (32-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> x <- c(112,118,132,129,121,135,148,148,136,119,104,118,115,126,141,135,125,149,170,170,158,133,114,140,145,150,178,163,172,178,199,199,184,162,146,166,171,180,193,181,183,218,230,242,209,191,172,194,196,196,236,235,229,243,264,272,237,211,180,201,204,188,235,227,234,264,302,293,259,229,203,229,242,233,267,269,270,315,364,347,312,274,237,278,284,277,317,313,318,374,413,405,355,306,271,306,315,301,356,348,355,422,465,467,404,347,305,336,340,318,362,348,363,435,491,505,404,359,310,337,360,342,406,396,420,472,548,559,463,407,362,405,417,391,419,461,472,535,622,606,508,461,390,432)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '2'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '0.5'
> par1 = '24'
> par10 <- 'FALSE'
> par9 <- '1'
> par8 <- '0'
> par7 <- '1'
> par6 <- '2'
> par5 <- '12'
> par4 <- '1'
> par3 <- '1'
> par2 <- '0.5'
> 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     ma1     sma1
      -0.6182  -0.0465  0.3613  -0.3017
s.e.   0.7219   0.2296  0.7124   0.0927

sigma^2 estimated as 0.08907:  log likelihood = -23.06,  aic = 56.12
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 121 
End = 144 
Frequency = 1 
 [1] 18.53242 17.99579 19.25921 18.94526 19.27385 21.01963 22.24020 22.44678
 [9] 20.36337 19.13387 17.85736 18.66117 18.82857 18.29408 19.55652 19.24308
[17] 19.57140 21.31732 22.53782 22.74443 20.66101 19.43152 18.15501 18.95881

$se
Time Series:
Start = 121 
End = 144 
Frequency = 1 
 [1] 0.2984509 0.3718340 0.4510400 0.5100490 0.5667914 0.6164482 0.6633273
 [8] 0.7066393 0.7476791 0.7864628 0.8234815 0.8588757 0.9707763 1.0495425
[15] 1.1313288 1.2034492 1.2735391 1.3389301 1.4017980 1.4616975 1.5193736
[22] 1.5748692 1.6285104 1.6804218

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 121 
End = 144 
Frequency = 1 
 [1] 17.94745 17.26700 18.37517 17.94557 18.16293 19.81139 20.94008 21.06176
 [9] 18.89792 17.59240 16.24334 16.97777 16.92585 16.23698 17.33912 16.88432
[17] 17.07526 18.69302 19.79030 19.87951 17.68304 16.34478 14.96313 15.66518
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 121 
End = 144 
Frequency = 1 
 [1] 19.11738 18.72458 20.14324 19.94496 20.38476 22.22786 23.54032 23.83179
 [9] 21.82882 20.67534 19.47139 20.34456 20.73129 20.35118 21.77393 21.60184
[17] 22.06754 23.94162 25.28535 25.60936 23.63898 22.51826 21.34689 22.25244
> 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$pred))
  [1] 112.0000 118.0000 132.0000 129.0000 121.0000 135.0000 148.0000 148.0000
  [9] 136.0000 119.0000 104.0000 118.0000 115.0000 126.0000 141.0000 135.0000
 [17] 125.0000 149.0000 170.0000 170.0000 158.0000 133.0000 114.0000 140.0000
 [25] 145.0000 150.0000 178.0000 163.0000 172.0000 178.0000 199.0000 199.0000
 [33] 184.0000 162.0000 146.0000 166.0000 171.0000 180.0000 193.0000 181.0000
 [41] 183.0000 218.0000 230.0000 242.0000 209.0000 191.0000 172.0000 194.0000
 [49] 196.0000 196.0000 236.0000 235.0000 229.0000 243.0000 264.0000 272.0000
 [57] 237.0000 211.0000 180.0000 201.0000 204.0000 188.0000 235.0000 227.0000
 [65] 234.0000 264.0000 302.0000 293.0000 259.0000 229.0000 203.0000 229.0000
 [73] 242.0000 233.0000 267.0000 269.0000 270.0000 315.0000 364.0000 347.0000
 [81] 312.0000 274.0000 237.0000 278.0000 284.0000 277.0000 317.0000 313.0000
 [89] 318.0000 374.0000 413.0000 405.0000 355.0000 306.0000 271.0000 306.0000
 [97] 315.0000 301.0000 356.0000 348.0000 355.0000 422.0000 465.0000 467.0000
[105] 404.0000 347.0000 305.0000 336.0000 340.0000 318.0000 362.0000 348.0000
[113] 363.0000 435.0000 491.0000 505.0000 404.0000 359.0000 310.0000 337.0000
[121] 343.4505 323.8484 370.9170 358.9230 371.4811 441.8247 494.6266 503.8577
[129] 414.6669 366.1050 318.8854 348.2391 354.5150 334.6734 382.4575 370.2963
[137] 383.0396 454.4281 507.9534 517.3093 426.8773 377.5839 329.6042 359.4365
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 121 
End = 144 
Frequency = 1 
 [1] 0.03271685 0.04216133 0.04791390 0.05526511 0.06050955 0.06034030
 [7] 0.06139475 0.06490374 0.07607606 0.08551771 0.09639680 0.09620136
[13] 0.10832764 0.12119233 0.12225756 0.13274451 0.13844210 0.13335125
[19] 0.13197750 0.13662740 0.15767584 0.17496882 0.19517117 0.19266902
> postscript(file="/var/wessaorg/rcomp/tmp/1j71l1355583081.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/wessaorg/rcomp/tmp/2va801355583081.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/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/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/wessaorg/rcomp/tmp/3h4741355583081.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/wessaorg/rcomp/tmp/4x77y1355583081.tab") 
> 
> try(system("convert tmp/1j71l1355583081.ps tmp/1j71l1355583081.png",intern=TRUE))
character(0)
> try(system("convert tmp/2va801355583081.ps tmp/2va801355583081.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  2.311   0.271   2.595