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

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> x <- c(2360,2214,2825,2355,2333,3016,2155,2172,2150,2533,2058,2160,2260,2498,2695,2799,2947,2930,2318,2540,2570,2669,2450,2842,3440,2678,2981,2260,2844,2546,2456,2295,2379,2479,2057,2280,2351,2276,2548,2311,2201,2725,2408,2139,1898,2537,2069,2063,2524,2437,2189,2793,2074,2622,2278,2144,2427,2139,1828,2072,1800)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> par1 = '12'
> par1 <- as.numeric(par1) #cut off periods
> par1 <- 28
> 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
> par6 <- 3
> par7 <- as.numeric(par7) #q
> par7 <- 3
> 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     ar2     ar3   ma1      ma2     ma3
      -1.3458  0.2185  0.6178  0.96  -0.9544  -0.998
s.e.   0.2111  0.4200  0.2137   NaN   0.5350     NaN

sigma^2 estimated as 97190:  log likelihood = -145.88,  aic = 305.76
Warning message:
In sqrt(diag(x$var.coef)) : NaNs produced
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 34 
End = 61 
Frequency = 1 
 [1] 2474.076 2452.210 2874.248 3472.475 2838.532 2987.803 2501.813 2815.066
 [9] 2837.808 2402.194 2609.125 2320.614 2783.874 2412.434 3155.226 3472.880
[17] 3070.636 3044.955 2671.693 2938.163 2940.404 2591.805 2648.247 2568.610
[25] 2771.648 2703.077 3110.459 3784.908

$se
Time Series:
Start = 34 
End = 61 
Frequency = 1 
 [1] 329.9159 380.9833 412.3419 419.4004 428.9785 429.2294 433.7076 432.3259
 [9] 435.0209 433.1973 434.9238 433.2480 565.4728 606.9105 633.5366 641.5323
[17] 649.9491 651.2921 654.6143 654.6231 655.8704 656.1098 656.1463 657.1300
[25] 757.2394 801.5063 823.6084 835.1085

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 34 
End = 61 
Frequency = 1 
 [1] 1827.441 1705.482 2066.058 2650.451 1997.734 2146.514 1651.746 1967.707
 [9] 1985.167 1553.128 1756.674 1471.448 1675.548 1222.889 1913.494 2215.477
[17] 1796.736 1768.423 1388.649 1655.101 1654.898 1305.830 1362.201 1280.635
[25] 1287.459 1132.124 1496.186 2148.096
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 34 
End = 61 
Frequency = 1 
 [1] 3120.711 3198.937 3682.438 4294.500 3679.330 3829.093 3351.880 3662.425
 [9] 3690.449 3251.261 3461.576 3169.780 3892.201 3601.979 4396.957 4730.283
[17] 4344.536 4321.488 3954.737 4221.224 4225.910 3877.780 3934.294 3856.585
[25] 4255.837 4274.029 4724.732 5421.721
> 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$pred))
 [1] 2360.000 2214.000 2825.000 2355.000 2333.000 3016.000 2155.000 2172.000
 [9] 2150.000 2533.000 2058.000 2160.000 2260.000 2498.000 2695.000 2799.000
[17] 2947.000 2930.000 2318.000 2540.000 2570.000 2669.000 2450.000 2842.000
[25] 3440.000 2678.000 2981.000 2260.000 2844.000 2546.000 2456.000 2295.000
[33] 2379.000 2474.076 2452.210 2874.248 3472.475 2838.532 2987.803 2501.813
[41] 2815.066 2837.808 2402.194 2609.125 2320.614 2783.874 2412.434 3155.226
[49] 3472.880 3070.636 3044.955 2671.693 2938.163 2940.404 2591.805 2648.247
[57] 2568.610 2771.648 2703.077 3110.459 3784.908
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 34 
End = 61 
Frequency = 1 
 [1] 0.1333491 0.1553633 0.1434608 0.1207785 0.1511269 0.1436605 0.1733573
 [8] 0.1535758 0.1532947 0.1803340 0.1666934 0.1866954 0.2031244 0.2515760
[15] 0.2007896 0.1847263 0.2116659 0.2138922 0.2450185 0.2228002 0.2230545
[22] 0.2531478 0.2477662 0.2558310 0.2732091 0.2965163 0.2647868 0.2206417
> postscript(file="/var/www/html/rcomp/tmp/1qtb41260735824.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2jfmw1260735824.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/38dzk1260735824.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/41v6l1260735824.tab") 
> try(system("convert tmp/1qtb41260735824.ps tmp/1qtb41260735824.png",intern=TRUE))
character(0)
> try(system("convert tmp/2jfmw1260735824.ps tmp/2jfmw1260735824.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.134   0.322   1.266