R version 2.12.1 (2010-12-16)
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(1770,2203,2836,1976,2150,2180,2631,1781,2327,2260,2051,2250,2102,2957,2485,2871,2447,2570,2622,1840,2682,2369,2119,2531,2214,3206,2709,2734,2348,2702,2642,2064,2647,2534,2297,2718,2321,3112,2664,2808,2668,2934,2616,2228,2463,2416,2407,2582,2101,3305,2818,2401,3019,2507,2948,2210,2467,2596,2451,2233,2393,3122,2801,2656,2782,2604,2803,2178,2324,2536,2408,2261,2166,3243,2296,2719,2734,2297,2732,1904,2397,2473,1967,2471,2203,3053,2350,2807,2639,2646,2577,1860,2624,2590,2261,3342,2840,3328,3245,3025,2915,3579,2787,2397,3065,2154,2689,3187,2540,3469,3005,2573,2998,2768,2556,2414,2467,2136,2493,2735,2316,3042,2364,2248,2714,2583,2631,1965,2209,1964,2132)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '0'
> par6 = '1'
> par5 = '12'
> par4 = '0'
> par3 = '0'
> par2 = '1'
> 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    sma1
      0.9673  0.6155
s.e.  0.0198  0.0826

sigma^2 estimated as 153937:  log likelihood = -884.11,  aic = 1774.23
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 120 
End = 131 
Frequency = 1 
 [1] 2460.322 2189.059 2588.559 2248.349 2092.646 2289.827 1937.279 1973.798
 [9] 1928.464 1782.268 1880.282 1859.630

$se
Time Series:
Start = 120 
End = 131 
Frequency = 1 
 [1]  392.3550  545.8718  657.8264  747.5434  822.6730  887.2246  943.6310
 [8]  993.5110 1038.0122 1077.9868 1114.0903 1146.8412

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 120 
End = 131 
Frequency = 1 
 [1] 1691.30657 1119.15040 1299.21980  783.16400  480.20717  550.86674
 [7]   87.76220   26.51606 -106.04007 -330.58627 -303.33459 -388.17904
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 120 
End = 131 
Frequency = 1 
 [1] 3229.338 3258.968 3877.899 3713.534 3705.085 4028.787 3786.796 3921.079
 [9] 3962.968 3895.122 4063.899 4107.438
> 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$pred))
  [1] 1770.000 2203.000 2836.000 1976.000 2150.000 2180.000 2631.000 1781.000
  [9] 2327.000 2260.000 2051.000 2250.000 2102.000 2957.000 2485.000 2871.000
 [17] 2447.000 2570.000 2622.000 1840.000 2682.000 2369.000 2119.000 2531.000
 [25] 2214.000 3206.000 2709.000 2734.000 2348.000 2702.000 2642.000 2064.000
 [33] 2647.000 2534.000 2297.000 2718.000 2321.000 3112.000 2664.000 2808.000
 [41] 2668.000 2934.000 2616.000 2228.000 2463.000 2416.000 2407.000 2582.000
 [49] 2101.000 3305.000 2818.000 2401.000 3019.000 2507.000 2948.000 2210.000
 [57] 2467.000 2596.000 2451.000 2233.000 2393.000 3122.000 2801.000 2656.000
 [65] 2782.000 2604.000 2803.000 2178.000 2324.000 2536.000 2408.000 2261.000
 [73] 2166.000 3243.000 2296.000 2719.000 2734.000 2297.000 2732.000 1904.000
 [81] 2397.000 2473.000 1967.000 2471.000 2203.000 3053.000 2350.000 2807.000
 [89] 2639.000 2646.000 2577.000 1860.000 2624.000 2590.000 2261.000 3342.000
 [97] 2840.000 3328.000 3245.000 3025.000 2915.000 3579.000 2787.000 2397.000
[105] 3065.000 2154.000 2689.000 3187.000 2540.000 3469.000 3005.000 2573.000
[113] 2998.000 2768.000 2556.000 2414.000 2467.000 2136.000 2493.000 2460.322
[121] 2189.059 2588.559 2248.349 2092.646 2289.827 1937.279 1973.798 1928.464
[129] 1782.268 1880.282 1859.630
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 120 
End = 131 
Frequency = 1 
 [1] 0.1594730 0.2493637 0.2541284 0.3324855 0.3931257 0.3874636 0.4870909
 [8] 0.5033500 0.5382586 0.6048399 0.5925122 0.6167041
> postscript(file="/var/www/rcomp/tmp/1x1k71323973920.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2vbtc1323973920.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/316a81323973920.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/4setm1323973920.tab") 
> 
> try(system("convert tmp/1x1k71323973920.ps tmp/1x1k71323973920.png",intern=TRUE))
character(0)
> try(system("convert tmp/2vbtc1323973920.ps tmp/2vbtc1323973920.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.024   0.176   2.415