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)

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> x <- c(14,14,15,13,8,7,3,3,4,4,0,-4,-14,-18,-8,-1,1,2,0,1,0,-1,-3,-3,-3,-4,-8,-9,-13,-18,-11,-9,-10,-13,-11,-5,-15,-6,-6,-3,-1,-3,-4,-6,0,-4,-2,-2,-6,-7,-6,-6,-3,-2,-5,-11,-11,-11,-10,-14,-8,-9,-5,-1,-2,-5,-4,-6,-2,-2,-2,-2,2,1,-8,-1,1,-1,2,2,1,-1,-2,-2,-1,-8,-4,-6,-3,-3,-7,-9,-11,-13,-11,-9,-17,-22,-25,-20,-24,-24,-22,-19,-18,-17,-11,-11,-12,-10,-15,-15,-15,-13,-8,-13,-9,-7,-4,-4,-2,0,-2,-3,1,-2,-1,1,-3,-4,-9,-9,-7,-14,-12,-16,-20,-12,-12,-10,-10,-13,-16)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '0'
> par5 = '4'
> par4 = '0'
> par3 = '1'
> par2 = '1'
> par1 = '24'
> par10 <- 'FALSE'
> par9 <- '0'
> par8 <- '0'
> par7 <- '0'
> par6 <- '0'
> par5 <- '4'
> par4 <- '0'
> 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")


sigma^2 estimated as 13.22:  log likelihood = -319.76,  aic = 641.52
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 120 
End = 143 
Frequency = 1 
 [1] -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4

$se
Time Series:
Start = 120 
End = 143 
Frequency = 1 
 [1]  3.635978  5.142050  6.297699  7.271957  8.130295  8.906292  9.619895
 [8] 10.284100 10.907935 11.497973 12.059176 12.595399 13.109707 13.604585
[15] 14.082084 14.543914 14.991523 15.426150 15.848862 16.260590 16.662146
[22] 17.054250 17.437540 17.812584

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 120 
End = 143 
Frequency = 1 
 [1] -11.12652 -14.07842 -16.34349 -18.25304 -19.93538 -21.45633 -22.85499
 [8] -24.15684 -25.37955 -26.53603 -27.63599 -28.68698 -29.69502 -30.66499
[15] -31.60088 -32.50607 -33.38339 -34.23525 -35.06377 -35.87076 -36.65781
[22] -37.42633 -38.17758 -38.91266
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 120 
End = 143 
Frequency = 1 
 [1]  3.126518  6.078418  8.343491 10.253035 11.935378 13.456332 14.854993
 [8] 16.156836 17.379553 18.536028 19.635985 20.686981 21.695025 22.664988
[15] 23.600884 24.506071 25.383385 26.235254 27.063770 27.870756 28.657807
[22] 29.426331 30.177578 30.912664
> 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$pred))
  [1]  14  14  15  13   8   7   3   3   4   4   0  -4 -14 -18  -8  -1   1   2
 [19]   0   1   0  -1  -3  -3  -3  -4  -8  -9 -13 -18 -11  -9 -10 -13 -11  -5
 [37] -15  -6  -6  -3  -1  -3  -4  -6   0  -4  -2  -2  -6  -7  -6  -6  -3  -2
 [55]  -5 -11 -11 -11 -10 -14  -8  -9  -5  -1  -2  -5  -4  -6  -2  -2  -2  -2
 [73]   2   1  -8  -1   1  -1   2   2   1  -1  -2  -2  -1  -8  -4  -6  -3  -3
 [91]  -7  -9 -11 -13 -11  -9 -17 -22 -25 -20 -24 -24 -22 -19 -18 -17 -11 -11
[109] -12 -10 -15 -15 -15 -13  -8 -13  -9  -7  -4  -4  -4  -4  -4  -4  -4  -4
[127]  -4  -4  -4  -4  -4  -4  -4  -4  -4  -4  -4  -4  -4  -4  -4  -4  -4
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 120 
End = 143 
Frequency = 1 
 [1] -0.9089946 -1.2855125 -1.5744248 -1.8179892 -2.0325737 -2.2265730
 [7] -2.4049737 -2.5710250 -2.7269838 -2.8744933 -3.0147940 -3.1488497
[13] -3.2774266 -3.4011464 -3.5205210 -3.6359784 -3.7478808 -3.8565375
[19] -3.9622156 -4.0651474 -4.1655366 -4.2635626 -4.3593850 -4.4531459
> postscript(file="/var/fisher/rcomp/tmp/1ye4n1353960087.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/fisher/rcomp/tmp/2bl9c1353960087.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/fisher/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/fisher/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/fisher/rcomp/tmp/3zjdf1353960087.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/fisher/rcomp/tmp/4gvdn1353960087.tab") 
> 
> try(system("convert tmp/1ye4n1353960087.ps tmp/1ye4n1353960087.png",intern=TRUE))
character(0)
> try(system("convert tmp/2bl9c1353960087.ps tmp/2bl9c1353960087.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.660   0.412   2.050