R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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(24,22,25,24,29,26,26,21,23,22,21,16,19,16,25,27,23,22,23,20,24,23,20,21,22,17,21,19,23,22,15,23,21,18,18,18,18,10,13,10,9,9,6,11,9,10,9,16,10,7,7,14,11,10,6,8,13,12,15,16,16)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '1'
> par5 = '1'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> par1 = '22'
> #'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
      -0.6785
s.e.   0.1246

sigma^2 estimated as 22.24:  log likelihood = -110.2,  aic = 224.4
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 40 
End = 61 
Frequency = 1 
 [1]   8.5363447   9.1368849   6.3012969   5.7971704   3.7111144   2.6984199
 [7]   0.9574345  -0.2893953  -1.8715167  -3.2261379  -4.7351212  -6.1393677
[13]  -7.6146796  -9.0417726 -10.5015828 -11.9391939 -13.3918675 -14.8343209
[19] -16.2837088 -17.7283916 -19.1762669 -20.6219761

$se
Time Series:
Start = 40 
End = 61 
Frequency = 1 
 [1]   4.716388   7.816017  12.629374  17.514225  23.287854  29.362689
 [7]  36.029771  43.051039  50.531981  58.367459  66.592934  75.157682
[13]  84.070255  93.303479 102.855787 112.710784 122.863421 133.302578
[19] 144.022329 155.014359 166.272842 177.791108

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 40 
End = 61 
Frequency = 1 
 [1]   -0.7077764   -6.1825091  -18.4522769  -28.5307109  -41.9330791
 [6]  -54.8524499  -69.6609164  -84.6694310 -100.9141988 -117.6263583
[11] -135.2572724 -153.4484242 -172.3923800 -191.9165907 -212.0989258
[16] -232.8523297 -254.2041727 -276.1073744 -298.5674741 -321.5565359
[21] -345.0710375 -369.0925474
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 40 
End = 61 
Frequency = 1 
 [1]  17.78047  24.45628  31.05487  40.12505  49.35531  60.24929  71.57579
 [8]  84.09064  97.17117 111.17408 125.78703 141.16969 157.16302 173.83305
[15] 191.09576 208.97394 227.42044 246.43873 266.00006 286.09975 306.71850
[22] 327.84860
> 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$pred))
 [1]  24.0000000  22.0000000  25.0000000  24.0000000  29.0000000  26.0000000
 [7]  26.0000000  21.0000000  23.0000000  22.0000000  21.0000000  16.0000000
[13]  19.0000000  16.0000000  25.0000000  27.0000000  23.0000000  22.0000000
[19]  23.0000000  20.0000000  24.0000000  23.0000000  20.0000000  21.0000000
[25]  22.0000000  17.0000000  21.0000000  19.0000000  23.0000000  22.0000000
[31]  15.0000000  23.0000000  21.0000000  18.0000000  18.0000000  18.0000000
[37]  18.0000000  10.0000000  13.0000000   8.5363447   9.1368849   6.3012969
[43]   5.7971704   3.7111144   2.6984199   0.9574345  -0.2893953  -1.8715167
[49]  -3.2261379  -4.7351212  -6.1393677  -7.6146796  -9.0417726 -10.5015828
[55] -11.9391939 -13.3918675 -14.8343209 -16.2837088 -17.7283916 -19.1762669
[61] -20.6219761
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 40 
End = 61 
Frequency = 1 
 [1]    0.5525068    0.8554357    2.0042500    3.0211679    6.2751646
 [6]   10.8814379   37.6315791 -148.7620588  -27.0005509  -18.0920533
[11]  -14.0636176  -12.2419255  -11.0405506  -10.3191578   -9.7943128
[16]   -9.4404014   -9.1744801   -8.9860924   -8.8445655   -8.7438479
[21]   -8.6707618   -8.6214390
> postscript(file="/var/www/html/rcomp/tmp/1p8bf1260470548.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2drxi1260470548.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/3g28z1260470548.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/4iilg1260470548.tab") 
> 
> system("convert tmp/1p8bf1260470548.ps tmp/1p8bf1260470548.png")
> system("convert tmp/2drxi1260470548.ps tmp/2drxi1260470548.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.625   0.334   0.818