R version 3.0.2 (2013-09-25) -- "Frisbee Sailing"
Copyright (C) 2013 The R Foundation for Statistical Computing
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(46,62,66,59,58,61,41,27,58,70,49,59,44,36,72,45,56,54,53,35,61,52,47,51,52,63,74,45,51,64,36,30,55,64,39,40,63,45,59,55,40,64,27,28,45,57,45,69,60,56,58,50,51,53,37,22,55,70,62,58,39,49,58,47,42,62,39,40,72,70,54,65)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '1'
> par6 = '0'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> par2 = '1.0'
> par1 = '12'
> par10 <- 'FALSE'
> par9 <- '0'
> par8 <- '0'
> par7 <- '1'
> par6 <- '0'
> par5 <- '12'
> par4 <- '1'
> par3 <- '0'
> par2 <- '1.0'
> par1 <- '12'
> #'GNU S' R Code compiled by R2WASP v. 1.2.327 ()
> #Author: root
> #To cite this work: Wessa P., (2013), ARIMA Forecasting (v1.0.9) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_arimaforecasting.wasp/
> #Source of accompanying publication: 
> #
> 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:
          ma1
      -0.0719
s.e.   0.1349

sigma^2 estimated as 132.3:  log likelihood = -185.36,  aic = 374.72
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 61 
End = 72 
Frequency = 1 
 [1] 60.69781 56.00000 58.00000 50.00000 51.00000 53.00000 37.00000 22.00000
 [9] 55.00000 70.00000 62.00000 58.00000

$se
Time Series:
Start = 61 
End = 72 
Frequency = 1 
 [1] 11.50321 11.53289 11.53289 11.53289 11.53289 11.53289 11.53289 11.53289
 [9] 11.53289 11.53289 11.53289 11.53289

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 61 
End = 72 
Frequency = 1 
 [1] 38.1515162 33.3955319 35.3955319 27.3955319 28.3955319 30.3955319
 [7] 14.3955319 -0.6044681 32.3955319 47.3955319 39.3955319 35.3955319
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 61 
End = 72 
Frequency = 1 
 [1] 83.24409 78.60447 80.60447 72.60447 73.60447 75.60447 59.60447 44.60447
 [9] 77.60447 92.60447 84.60447 80.60447
> 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$pred))
 [1] 46.00000 62.00000 66.00000 59.00000 58.00000 61.00000 41.00000 27.00000
 [9] 58.00000 70.00000 49.00000 59.00000 44.00000 36.00000 72.00000 45.00000
[17] 56.00000 54.00000 53.00000 35.00000 61.00000 52.00000 47.00000 51.00000
[25] 52.00000 63.00000 74.00000 45.00000 51.00000 64.00000 36.00000 30.00000
[33] 55.00000 64.00000 39.00000 40.00000 63.00000 45.00000 59.00000 55.00000
[41] 40.00000 64.00000 27.00000 28.00000 45.00000 57.00000 45.00000 69.00000
[49] 60.00000 56.00000 58.00000 50.00000 51.00000 53.00000 37.00000 22.00000
[57] 55.00000 70.00000 62.00000 58.00000 60.69781 56.00000 58.00000 50.00000
[65] 51.00000 53.00000 37.00000 22.00000 55.00000 70.00000 62.00000 58.00000
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 61 
End = 72 
Frequency = 1 
 [1] 0.1895161 0.2059445 0.1988430 0.2306578 0.2261351 0.2176017 0.3116998
 [8] 0.5242224 0.2096889 0.1647556 0.1860144 0.1988430
> postscript(file="/var/fisher/rcomp/tmp/1we6t1385985692.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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.spe <- array(0, dim=fx)
> perf.scalederr <- array(0, dim=fx)
> perf.mase <- array(0, dim=fx)
> perf.mase1 <- array(0, dim=fx)
> perf.mape <- array(0, dim=fx)
> perf.smape <- array(0, dim=fx)
> perf.mape1 <- array(0, dim=fx)
> perf.smape1 <- 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)
> perf.scaleddenom <- 0
> for (i in 2:fx) {
+ perf.scaleddenom = perf.scaleddenom + abs(x[nx+i] - x[nx+i-1])
+ }
> perf.scaleddenom = perf.scaleddenom / (fx-1)
> for (i in 1:fx) {
+ locSD <- (ub[i] - forecast$pred[i]) / 1.96
+ perf.scalederr[i] = (x[nx+i] - forecast$pred[i]) / perf.scaleddenom
+ perf.pe[i] = (x[nx+i] - forecast$pred[i]) / x[nx+i]
+ perf.spe[i] = 2*(x[nx+i] - forecast$pred[i]) / (x[nx+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.smape[1] = abs(perf.spe[1])
> perf.mape1[1] = perf.mape[1]
> perf.smape1[1] = perf.smape[1]
> perf.mse[1] = perf.se[1]
> perf.mase[1] = abs(perf.scalederr[1])
> perf.mase1[1] = perf.mase[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.smape[i] = perf.smape[i-1] + abs(perf.spe[i])
+ perf.smape1[i] = perf.smape[i] / i
+ perf.mse[i] = perf.mse[i-1] + perf.se[i]
+ perf.mse1[i] = perf.mse[i] / i
+ perf.mase[i] = perf.mase[i-1] + abs(perf.scalederr[i])
+ perf.mase1[i] = perf.mase[i] / i
+ }
> perf.rmse = sqrt(perf.mse1)
> postscript(file="/var/fisher/rcomp/tmp/2tify1385985692.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/3yo5z1385985692.tab") 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Univariate ARIMA Extrapolation Forecast Performance',10,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,'sMAPE',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.element(a,'ScaledE',1,header=TRUE)
> a<-table.element(a,'MASE',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.smape1[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.element(a,round(perf.scalederr[i],4))
+ a<-table.element(a,round(perf.mase1[i],4))
+ a<-table.row.end(a)
+ }
> a<-table.end(a)
> table.save(a,file="/var/fisher/rcomp/tmp/4dktd1385985692.tab") 
> 
> try(system("convert tmp/1we6t1385985692.ps tmp/1we6t1385985692.png",intern=TRUE))
character(0)
> try(system("convert tmp/2tify1385985692.ps tmp/2tify1385985692.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  2.596   0.641   3.175