R version 2.12.0 (2010-10-15)
Copyright (C) 2010 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(4.785,4.109,4.026,4.44,3.828,3.953,4.801,4.104,4.57,4.411,4.839,4.736,3.83,4.248,5.657,3.809,4.578,4.3,5.103,4.121,4.205,5.116,4.219,4.736,4.625,4.146,5.299,5.011,4.731,4.619,5.578,5.369,4.904,6.102,5.04,5.731,5.732,4.491,4.755,5.208,4.962,4.163,5.592,5.761,4.929,5.219,4.429,4.143,4.308,3.996,4.634,4.138,3.759,3.922,5.56,4.004,3.937,5.25,3.908,4.814,4.407,3.243,3.74,3.949,3.711,3.796,4.145,3.499,4.164,3.902,3.186,3.353,3.475,3.032,3.341,3.811,3.655,4.058,3.682,3.348,3.848,3.289,3.851,2.766,2.837,2.734,3.764,3.215,3.287,3.507,3.06,3.734,3.849,4.404,3.497,3.389,2.944,3.098,3.48,3.353,3.958,3.504,3.446,3.794,3.676,4.159,3.914,3.595)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '0.0'
> par1 = '12'
> #'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
      -0.0884  -0.7183
s.e.   0.1350   0.0940

sigma^2 estimated as 0.01508:  log likelihood = 64,  aic = -122
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 97 
End = 108 
Frequency = 1 
 [1] 1.284254 1.278624 1.279122 1.279078 1.279082 1.279081 1.279081 1.279081
 [9] 1.279081 1.279081 1.279081 1.279081

$se
Time Series:
Start = 97 
End = 108 
Frequency = 1 
 [1] 0.1228076 0.1250821 0.1292348 0.1330716 0.1368167 0.1404607 0.1440126
 [8] 0.1474790 0.1508657 0.1541781 0.1574208 0.1605980

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 97 
End = 108 
Frequency = 1 
 [1] 1.0435515 1.0334634 1.0258216 1.0182574 1.0109208 1.0037783 0.9968167
 [8] 0.9900226 0.9833846 0.9768923 0.9705367 0.9643093
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 97 
End = 108 
Frequency = 1 
 [1] 1.524957 1.523785 1.532422 1.539898 1.547242 1.554384 1.561346 1.568140
 [9] 1.574778 1.581270 1.587626 1.593853
> 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$pred))
  [1] 4.785000 4.109000 4.026000 4.440000 3.828000 3.953000 4.801000 4.104000
  [9] 4.570000 4.411000 4.839000 4.736000 3.830000 4.248000 5.657000 3.809000
 [17] 4.578000 4.300000 5.103000 4.121000 4.205000 5.116000 4.219000 4.736000
 [25] 4.625000 4.146000 5.299000 5.011000 4.731000 4.619000 5.578000 5.369000
 [33] 4.904000 6.102000 5.040000 5.731000 5.732000 4.491000 4.755000 5.208000
 [41] 4.962000 4.163000 5.592000 5.761000 4.929000 5.219000 4.429000 4.143000
 [49] 4.308000 3.996000 4.634000 4.138000 3.759000 3.922000 5.560000 4.004000
 [57] 3.937000 5.250000 3.908000 4.814000 4.407000 3.243000 3.740000 3.949000
 [65] 3.711000 3.796000 4.145000 3.499000 4.164000 3.902000 3.186000 3.353000
 [73] 3.475000 3.032000 3.341000 3.811000 3.655000 4.058000 3.682000 3.348000
 [81] 3.848000 3.289000 3.851000 2.766000 2.837000 2.734000 3.764000 3.215000
 [89] 3.287000 3.507000 3.060000 3.734000 3.849000 4.404000 3.497000 3.389000
 [97] 3.611974 3.591695 3.593482 3.593324 3.593338 3.593337 3.593337 3.593337
[105] 3.593337 3.593337 3.593337 3.593337
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 97 
End = 108 
Frequency = 1 
 [1] 0.1388485 0.1417484 0.1470765 0.1520380 0.1569170 0.1616988 0.1663927
 [8] 0.1710052 0.1755421 0.1800086 0.1844094 0.1887485
> postscript(file="/var/www/rcomp/tmp/1esy31292532913.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/www/rcomp/tmp/2akwc1292532913.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/www/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/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/rcomp/tmp/3g3t51292532913.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/rcomp/tmp/42msb1292532913.tab") 
> 
> try(system("convert tmp/1esy31292532913.ps tmp/1esy31292532913.png",intern=TRUE))
character(0)
> try(system("convert tmp/2akwc1292532913.ps tmp/2akwc1292532913.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
   0.72    0.38    1.09