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(1954,2302,3054,2414,2226,2725,2589,3470,2400,3180,4009,3924,2072,2434,2956,2828,2687,2629,3150,4119,3030,3055,3821,4001,2529,2472,3134,2789,2758,2993,3282,3437,2804,3076,3782,3889,2271,2452,3084,2522,2769,3438,2839,3746,2632,2851,3871,3618,2389,2344,2678,2492,2858,2246,2800,3869,3007,3023,3907,4209,2353,2570,2903,2910,3782,2759,2931,3641,2794,3070,3576,4106,2452,2206,2488,2416,2534,2521,3093,3903,2907,3025,3812,4209,2138,2419,2622,2912,2708,2798,3254,2895,3263,3736,4077,4097,2175,3138,2823,2498,2822,2738,4137,3515,3785,3632,4504,4451,2550,2867,3458,2961,3163,2880,3331,3062,3534,3622,4464,5411,2564,2820,3508,3088,3299,2939,3320,3418,3604,3495,4163,4882,2211,3260,2992,2425,2707,3244,3965,3315,3333,3583,4021,4904,2252,2952,3573,3048,3059,2731,3563,3092,3478,3478,4308,5029,2075,3264,3308,3688,3136,2824,3644,4694,2914,3686,4358,5587,2265,3685,3754,3708,3210,3517,3905,3670,4221,4404,5086,5725,2367,3819,4067,4022,3937,4365,4290)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> par2 = '-0.5'
> 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     sma1
      0.9616  -0.8240  -0.6444
s.e.  0.0431   0.0712   0.0791

sigma^2 estimated as 8.813e-07:  log likelihood = 901.91,  aic = -1795.83
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 176 
End = 187 
Frequency = 1 
 [1] 0.01575693 0.01688410 0.01605954 0.01467446 0.01336869 0.02053058
 [7] 0.01695604 0.01650512 0.01690268 0.01746496 0.01754287 0.01596451

$se
Time Series:
Start = 176 
End = 187 
Frequency = 1 
 [1] 0.0009387942 0.0009476370 0.0009557406 0.0009631729 0.0009699943
 [6] 0.0009762587 0.0009820160 0.0009873095 0.0009921789 0.0009966602
[11] 0.0010007859 0.0010045857

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 176 
End = 187 
Frequency = 1 
 [1] 0.01391690 0.01502673 0.01418628 0.01278664 0.01146751 0.01861711
 [7] 0.01503128 0.01456999 0.01495801 0.01551151 0.01558133 0.01399552
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 176 
End = 187 
Frequency = 1 
 [1] 0.01759697 0.01874147 0.01793279 0.01656227 0.01526988 0.02244405
 [7] 0.01888079 0.01844024 0.01884735 0.01941842 0.01950442 0.01793350
> 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$pred))
  [1] 1954.000 2302.000 3054.000 2414.000 2226.000 2725.000 2589.000 3470.000
  [9] 2400.000 3180.000 4009.000 3924.000 2072.000 2434.000 2956.000 2828.000
 [17] 2687.000 2629.000 3150.000 4119.000 3030.000 3055.000 3821.000 4001.000
 [25] 2529.000 2472.000 3134.000 2789.000 2758.000 2993.000 3282.000 3437.000
 [33] 2804.000 3076.000 3782.000 3889.000 2271.000 2452.000 3084.000 2522.000
 [41] 2769.000 3438.000 2839.000 3746.000 2632.000 2851.000 3871.000 3618.000
 [49] 2389.000 2344.000 2678.000 2492.000 2858.000 2246.000 2800.000 3869.000
 [57] 3007.000 3023.000 3907.000 4209.000 2353.000 2570.000 2903.000 2910.000
 [65] 3782.000 2759.000 2931.000 3641.000 2794.000 3070.000 3576.000 4106.000
 [73] 2452.000 2206.000 2488.000 2416.000 2534.000 2521.000 3093.000 3903.000
 [81] 2907.000 3025.000 3812.000 4209.000 2138.000 2419.000 2622.000 2912.000
 [89] 2708.000 2798.000 3254.000 2895.000 3263.000 3736.000 4077.000 4097.000
 [97] 2175.000 3138.000 2823.000 2498.000 2822.000 2738.000 4137.000 3515.000
[105] 3785.000 3632.000 4504.000 4451.000 2550.000 2867.000 3458.000 2961.000
[113] 3163.000 2880.000 3331.000 3062.000 3534.000 3622.000 4464.000 5411.000
[121] 2564.000 2820.000 3508.000 3088.000 3299.000 2939.000 3320.000 3418.000
[129] 3604.000 3495.000 4163.000 4882.000 2211.000 3260.000 2992.000 2425.000
[137] 2707.000 3244.000 3965.000 3315.000 3333.000 3583.000 4021.000 4904.000
[145] 2252.000 2952.000 3573.000 3048.000 3059.000 2731.000 3563.000 3092.000
[153] 3478.000 3478.000 4308.000 5029.000 2075.000 3264.000 3308.000 3688.000
[161] 3136.000 2824.000 3644.000 4694.000 2914.000 3686.000 4358.000 5587.000
[169] 2265.000 3685.000 3754.000 3708.000 3210.000 3517.000 3905.000 4027.695
[177] 3507.875 3877.341 4643.827 5595.283 2372.453 3478.174 3670.817 3500.167
[185] 3278.420 3249.365 3923.637
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 176 
End = 187 
Frequency = 1 
 [1] 0.1438332 0.1339217 0.1436376 0.1617743 0.1831962 0.1102672 0.1390286
 [8] 0.1445265 0.1412855 0.1365976 0.1365455 0.1536565
> postscript(file="/var/www/rcomp/tmp/13rdy1324218902.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2l8cq1324218902.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/387w11324218902.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/4bxnp1324218902.tab") 
> 
> try(system("convert tmp/13rdy1324218902.ps tmp/13rdy1324218902.png",intern=TRUE))
character(0)
> try(system("convert tmp/2l8cq1324218902.ps tmp/2l8cq1324218902.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.330   0.060   1.392