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)

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> x <- c(1954,2302,3054,2414,2226,2725,2589,3470,2400,3180,4009,3924,2072,2434,2956,2828,2687,2629,3150,4119,3030,3055,3821,4001,2529,2472,3134,2789,2758,2993,3282,3437,2804,3076,3782,3889,2271,2452,3084,2522,2769,3438,2839,3746,2632,2851,3871,3618,2389,2344,2678,2492,2858,2246,2800,3869,3007,3023,3907,4209)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '2'
> par7 = '0'
> par6 = '1'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> par2 = '1'
> par1 = '12'
> par10 <- 'FALSE'
> par9 <- '0'
> par8 <- '2'
> par7 <- '0'
> par6 <- '1'
> par5 <- '12'
> par4 <- '1'
> par3 <- '0'
> par2 <- '1'
> 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:
         ar1     sar1     sar2
      0.3367  -0.5858  -0.5474
s.e.  0.1771   0.2289   0.1989

sigma^2 estimated as 55347:  log likelihood = -252.93,  aic = 513.86
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 49 
End = 60 
Frequency = 1 
 [1] 2072.836 2409.542 3004.616 2695.968 2722.417 2977.646 3026.096 3938.279
 [9] 2856.450 2971.298 3840.213 3838.053

$se
Time Series:
Start = 49 
End = 60 
Frequency = 1 
 [1] 235.2591 248.2327 249.6606 249.8219 249.8401 249.8422 249.8424 249.8425
 [9] 249.8425 249.8425 249.8425 249.8425

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 49 
End = 60 
Frequency = 1 
 [1] 1611.728 1923.006 2515.281 2206.317 2232.731 2487.956 2536.404 3448.587
 [9] 2366.759 2481.607 3350.522 3348.362
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 49 
End = 60 
Frequency = 1 
 [1] 2533.944 2896.078 3493.950 3185.619 3212.104 3467.337 3515.787 4427.970
 [9] 3346.142 3460.989 4329.904 4327.745
> 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$pred))
 [1] 1954.000 2302.000 3054.000 2414.000 2226.000 2725.000 2589.000 3470.000
 [9] 2400.000 3180.000 4009.000 3924.000 2072.000 2434.000 2956.000 2828.000
[17] 2687.000 2629.000 3150.000 4119.000 3030.000 3055.000 3821.000 4001.000
[25] 2529.000 2472.000 3134.000 2789.000 2758.000 2993.000 3282.000 3437.000
[33] 2804.000 3076.000 3782.000 3889.000 2271.000 2452.000 3084.000 2522.000
[41] 2769.000 3438.000 2839.000 3746.000 2632.000 2851.000 3871.000 3618.000
[49] 2072.836 2409.542 3004.616 2695.968 2722.417 2977.646 3026.096 3938.279
[57] 2856.450 2971.298 3840.213 3838.053
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 49 
End = 60 
Frequency = 1 
 [1] 0.11349623 0.10302070 0.08309234 0.09266499 0.09177143 0.08390594
 [7] 0.08256264 0.06343951 0.08746606 0.08408530 0.06505953 0.06509614
> postscript(file="/var/wessaorg/rcomp/tmp/1f0os1387113718.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/wessaorg/rcomp/tmp/2l4qm1387113718.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/3svtv1387113718.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/wessaorg/rcomp/tmp/45ci71387113719.tab") 
> 
> try(system("convert tmp/1f0os1387113718.ps tmp/1f0os1387113718.png",intern=TRUE))
character(0)
> try(system("convert tmp/2l4qm1387113718.ps tmp/2l4qm1387113718.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  2.500   0.413   2.885