R version 2.13.0 (2011-04-13)
Copyright (C) 2011 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-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(374.92,375.63,376.51,377.75,378.54,378.21,376.65,374.28,373.12,373.1,374.67,375.97,377.03,377.87,378.88,380.42,380.62,379.66,377.48,376.07,374.1,374.47,376.15,377.51,378.43,379.7,380.91,382.2,382.45,382.14,380.6,378.6,376.72,376.98,378.29,380.07,381.36,382.19,382.65,384.65,384.94,384.01,382.15,380.33,378.81,379.06,380.17,381.85,382.88,383.77,384.42,386.36,386.53,386.01,384.45,381.96,380.81,381.09,382.37,383.84,385.42,385.72,385.96,387.18,388.5,387.88,386.38,384.15,383.07,382.98,384.11,385.54,386.92,387.41,388.77,389.46,390.18,389.43,387.74,385.91,384.77,384.38,385.99,387.26)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '1'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> 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      ma1     sar1
      0.2714  -0.7373  -0.6414
s.e.  0.3725   0.2986   0.1153

sigma^2 estimated as 0.08955:  log likelihood = -13.39,  aic = 34.78
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 61 
End = 84 
Frequency = 1 
 [1] 385.1018 385.9710 386.5039 388.4837 388.7310 387.9482 386.1958 384.1355
 [9] 382.7482 383.0090 384.1799 385.7846 386.8978 387.7803 388.3883 390.3426
[17] 390.5403 389.9260 388.2970 385.9611 384.7260 384.9991 386.2400 387.7583

$se
Time Series:
Start = 61 
End = 84 
Frequency = 1 
 [1] 0.2992506 0.3392617 0.3605292 0.3774435 0.3928494 0.4074721 0.4215352
 [8] 0.4351303 0.4483096 0.4611114 0.4735670 0.4857033 0.5312522 0.5563520
[15] 0.5766503 0.5953318 0.6132043 0.6305072 0.6473310 0.6637242 0.6797209
[22] 0.6953494 0.7106342 0.7255971

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 61 
End = 84 
Frequency = 1 
 [1] 384.5153 385.3060 385.7973 387.7439 387.9610 387.1495 385.3696 383.2826
 [9] 381.8695 382.1052 383.2517 384.8326 385.8565 386.6898 387.2581 389.1757
[17] 389.3384 388.6902 387.0283 384.6602 383.3938 383.6363 384.8472 386.3362
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 61 
End = 84 
Frequency = 1 
 [1] 385.6883 386.6359 387.2106 389.2235 389.5010 388.7468 387.0220 384.9884
 [9] 383.6269 383.9127 385.1081 386.7366 387.9390 388.8707 389.5185 391.5094
[17] 391.7422 391.1618 389.5658 387.2620 386.0583 386.3620 387.6329 389.1805
> 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$pred))
 [1] 374.9200 375.6300 376.5100 377.7500 378.5400 378.2100 376.6500 374.2800
 [9] 373.1200 373.1000 374.6700 375.9700 377.0300 377.8700 378.8800 380.4200
[17] 380.6200 379.6600 377.4800 376.0700 374.1000 374.4700 376.1500 377.5100
[25] 378.4300 379.7000 380.9100 382.2000 382.4500 382.1400 380.6000 378.6000
[33] 376.7200 376.9800 378.2900 380.0700 381.3600 382.1900 382.6500 384.6500
[41] 384.9400 384.0100 382.1500 380.3300 378.8100 379.0600 380.1700 381.8500
[49] 382.8800 383.7700 384.4200 386.3600 386.5300 386.0100 384.4500 381.9600
[57] 380.8100 381.0900 382.3700 383.8400 385.1018 385.9710 386.5039 388.4837
[65] 388.7310 387.9482 386.1958 384.1355 382.7482 383.0090 384.1799 385.7846
[73] 386.8978 387.7803 388.3883 390.3426 390.5403 389.9260 388.2970 385.9611
[81] 384.7260 384.9991 386.2400 387.7583
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 61 
End = 84 
Frequency = 1 
 [1] 0.0007770688 0.0008789823 0.0009327956 0.0009715812 0.0010105945
 [6] 0.0010503261 0.0010915065 0.0011327520 0.0011712911 0.0012039180
[11] 0.0012326698 0.0012590011 0.0013731076 0.0014347093 0.0014847263
[16] 0.0015251522 0.0015701434 0.0016169917 0.0016671027 0.0017196658
[21] 0.0017667661 0.0018061065 0.0018398772 0.0018712612
> postscript(file="/var/wessaorg/rcomp/tmp/116aa1324287037.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/20gle1324287037.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/34o6y1324287037.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/4k2at1324287037.tab") 
> 
> try(system("convert tmp/116aa1324287037.ps tmp/116aa1324287037.png",intern=TRUE))
character(0)
> try(system("convert tmp/20gle1324287037.ps tmp/20gle1324287037.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.963   0.161   1.120