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(3030.29,2803.47,2767.63,2882.6,2863.36,2897.06,3012.61,3142.95,3032.93,3045.78,3110.52,3013.24,2987.1,2995.55,2833.18,2848.96,2794.83,2845.26,2915.02,2892.63,2604.42,2641.65,2659.81,2638.53,2720.25,2745.88,2735.7,2811.7,2799.43,2555.28,2304.98,2214.95,2065.81,1940.49,2042,1995.37,1946.81,1765.9,1635.25,1833.42,1910.43,1959.67,1969.6,2061.41,2093.48,2120.88,2174.56,2196.72,2350.44,2440.25,2408.64,2472.81,2407.6,2454.62,2448.05,2497.84,2645.64,2756.76,2849.27,2921.44)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '1.5'
> 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    sma1
      -0.3504  0.2298  0.4651  0.7627  -0.3450  -0.8387  0.2791
s.e.   0.3384  0.3891  0.3027  0.4863   0.4422   0.4968  0.3568

sigma^2 estimated as 56279886:  log likelihood = -322.74,  aic = 661.48
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 102136.5 104021.3 105710.3 107266.4 109483.7 110520.8 111662.9 113716.6
 [9] 114160.8 108724.3 103507.1 102232.2 103235.0 103687.3 104193.5 104586.5
[17] 104775.4 105034.9 105170.2 105270.3 105387.0 105432.1 105489.7 105534.1
[25] 105552.7 105583.2 105597.4 105608.1

$se
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1]  7683.423 13060.333 15610.999 17254.226 19298.106 20521.462 21781.863
 [8] 23008.016 23955.768 24987.316 25905.123 26753.820 28233.375 29819.647
[15] 31174.284 32384.813 33621.479 34712.370 35782.822 36824.940 37797.755
[22] 38766.009 39696.184 40596.901 41486.282 42346.110 43190.808 44019.808

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 87076.97 78423.04 75112.72 73448.13 71659.43 70298.69 68970.44 68620.93
 [9] 67207.46 59749.13 52733.05 49794.71 47897.60 45240.80 43091.88 41112.22
[17] 38877.33 36998.69 35035.87 33093.45 31303.42 29450.67 27685.14 25964.17
[25] 24239.59 22584.81 20943.46 19329.29
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 117196.0 129619.5 136307.8 141084.7 147308.0 150742.8 154355.3 158812.3
 [9] 161114.1 157699.4 154281.1 154669.7 158572.4 162133.8 165295.1 168060.7
[17] 170673.5 173071.2 175304.5 177447.2 179470.6 181413.4 183294.2 185104.0
[25] 186865.8 188581.6 190251.4 191886.9
> 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$pred))
 [1] 3030.290 2803.470 2767.630 2882.600 2863.360 2897.060 3012.610 3142.950
 [9] 3032.930 3045.780 3110.520 3013.240 2987.100 2995.550 2833.180 2848.960
[17] 2794.830 2845.260 2915.020 2892.630 2604.420 2641.650 2659.810 2638.530
[25] 2720.250 2745.880 2735.700 2811.700 2799.430 2555.280 2304.980 2214.950
[33] 2185.013 2211.812 2235.689 2257.577 2288.581 2303.010 2318.850 2347.196
[41] 2353.303 2277.986 2204.517 2186.377 2200.652 2207.075 2214.252 2219.816
[49] 2222.489 2226.157 2228.068 2229.482 2231.129 2231.765 2232.578 2233.205
[57] 2233.467 2233.897 2234.098 2234.249
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 33 
End = 60 
Frequency = 1 
 [1] 0.04899335 0.08059901 0.09422637 0.10227044 0.11161179 0.11728445
 [7] 0.12291556 0.12725273 0.13172689 0.14354783 0.15553758 0.16218749
[13] 0.16901680 0.17714274 0.18379172 0.18975243 0.19613799 0.20156302
[19] 0.20705748 0.21243159 0.21737704 0.22240975 0.22719590 0.23183362
[25] 0.23644682 0.24086562 0.24522483 0.24949690
> postscript(file="/var/www/html/rcomp/tmp/1r57w1260453827.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2kyjn1260453828.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/3lben1260453828.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/4ozx81260453828.tab") 
> system("convert tmp/1r57w1260453827.ps tmp/1r57w1260453827.png")
> system("convert tmp/2kyjn1260453828.ps tmp/2kyjn1260453828.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.023   0.326   2.339