R version 2.15.2 (2012-10-26) -- "Trick or Treat"
Copyright (C) 2012 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i686-pc-linux-gnu (32-bit)

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> x <- c(369.07,369.32,370.38,371.63,371.32,371.51,369.69,368.18,366.87,366.94,368.27,369.62,370.47,371.44,372.39,373.32,373.77,373.13,371.51,369.59,368.12,368.38,369.64,371.11,372.38,373.08,373.87,374.93,375.58,375.44,373.91,371.77,370.72,370.5,372.19,373.71,374.92,375.63,376.51,377.75,378.54,378.21,376.65,374.28,373.12,373.1,374.67,375.97,377.03,377.87,378.88,380.42,380.62,379.66,377.48,376.07,374.1,374.47,376.15,377.51,378.43,379.7,380.91,382.2,382.45,382.14,380.6,378.6,376.72,376.98,378.29,380.07,381.36,382.19,382.65,384.65,384.94,384.01,382.15,380.33,378.81,379.06,380.17,381.85,382.88,383.77,384.42,386.36,386.53,386.01,384.45,381.96,380.81,381.09,382.37,383.84,385.42,385.72,385.96,387.18,388.5,387.88,386.38,384.15,383.07,382.98,384.11,385.54,386.92,387.41,388.77,389.46,390.18,389.43,387.74,385.91,384.77,384.38,385.99,387.26,388.45,389.7,391.08,392.46,392.96,392.03,390.13,388.15,386.8,387.18,388.59)
> par10 = 'TRUE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '0'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '-0.9'
> par1 = '24'
> par10 <- 'TRUE'
> par9 <- '1'
> par8 <- '0'
> par7 <- '1'
> par6 <- '0'
> par5 <- '12'
> par4 <- '1'
> par3 <- '1'
> par2 <- '-0.9'
> par1 <- '24'
> #'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:
          ma1     sma1
      -0.4698  -0.7839
s.e.   0.1108   0.1753

sigma^2 estimated as 1.22e-11:  log likelihood = 1041.95,  aic = -2077.9
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 108 
End = 131 
Frequency = 1 
 [1] 0.004701487 0.004687738 0.004679450 0.004671546 0.004655133 0.004649360
 [7] 0.004655390 0.004674019 0.004697325 0.004712944 0.004711443 0.004696419
[13] 0.004678716 0.004664967 0.004656679 0.004648774 0.004632361 0.004626589
[19] 0.004632618 0.004651247 0.004674554 0.004690173 0.004688672 0.004673647

$se
Time Series:
Start = 108 
End = 131 
Frequency = 1 
 [1] 3.506835e-06 3.968246e-06 4.381065e-06 4.758203e-06 5.107568e-06
 [6] 5.434521e-06 5.742889e-06 6.035523e-06 6.314610e-06 6.581873e-06
[11] 6.838700e-06 7.086225e-06 7.560976e-06 7.895179e-06 8.213196e-06
[16] 8.519351e-06 8.814879e-06 9.100815e-06 9.378038e-06 9.647297e-06
[21] 9.909243e-06 1.016444e-05 1.041338e-05 1.065652e-05

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 108 
End = 131 
Frequency = 1 
 [1] 0.004694614 0.004679960 0.004670863 0.004662219 0.004645122 0.004638709
 [7] 0.004644134 0.004662189 0.004684949 0.004700044 0.004698040 0.004682530
[13] 0.004663896 0.004649492 0.004640581 0.004632076 0.004615084 0.004608751
[19] 0.004614237 0.004632338 0.004655132 0.004670250 0.004668262 0.004652760
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 108 
End = 131 
Frequency = 1 
 [1] 0.004708361 0.004695516 0.004688037 0.004680872 0.004665144 0.004660012
 [7] 0.004666646 0.004685848 0.004709702 0.004725845 0.004724847 0.004710308
[13] 0.004693535 0.004680441 0.004672776 0.004665472 0.004649639 0.004644426
[19] 0.004650999 0.004670156 0.004693976 0.004710095 0.004709082 0.004694534
> 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$pred))
  [1] 369.0700 369.3200 370.3800 371.6300 371.3200 371.5100 369.6900 368.1800
  [9] 366.8700 366.9400 368.2700 369.6200 370.4700 371.4400 372.3900 373.3200
 [17] 373.7700 373.1300 371.5100 369.5900 368.1200 368.3800 369.6400 371.1100
 [25] 372.3800 373.0800 373.8700 374.9300 375.5800 375.4400 373.9100 371.7700
 [33] 370.7200 370.5000 372.1900 373.7100 374.9200 375.6300 376.5100 377.7500
 [41] 378.5400 378.2100 376.6500 374.2800 373.1200 373.1000 374.6700 375.9700
 [49] 377.0300 377.8700 378.8800 380.4200 380.6200 379.6600 377.4800 376.0700
 [57] 374.1000 374.4700 376.1500 377.5100 378.4300 379.7000 380.9100 382.2000
 [65] 382.4500 382.1400 380.6000 378.6000 376.7200 376.9800 378.2900 380.0700
 [73] 381.3600 382.1900 382.6500 384.6500 384.9400 384.0100 382.1500 380.3300
 [81] 378.8100 379.0600 380.1700 381.8500 382.8800 383.7700 384.4200 386.3600
 [89] 386.5300 386.0100 384.4500 381.9600 380.8100 381.0900 382.3700 383.8400
 [97] 385.4200 385.7200 385.9600 387.1800 388.5000 387.8800 386.3800 384.1500
[105] 383.0700 382.9800 384.1100 385.8382 387.0958 387.8577 388.5870 390.1095
[113] 390.6477 390.0856 388.3585 386.2181 384.7962 384.9324 386.3009 387.9253
[121] 389.1959 389.9657 390.7025 392.2409 392.7847 392.2167 390.4717 388.3091
[129] 386.8726 387.0102 388.3928
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 108 
End = 131 
Frequency = 1 
 [1] 0.0008300576 0.0009422235 0.0010422800 0.0011341121 0.0012218743
 [6] 0.0013018981 0.0013741737 0.0014386120 0.0014978311 0.0015562211
[11] 0.0016176447 0.0016817574 0.0018016193 0.0018870966 0.0019668941
[16] 0.0020439732 0.0021226795 0.0021945617 0.0022587362 0.0023145215
[21] 0.0023657371 0.0024188201 0.0024791314 0.0025454830
> postscript(file="/var/wessaorg/rcomp/tmp/1qwyg1355690725.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/wessaorg/rcomp/tmp/2ph5x1355690725.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/3jg8e1355690725.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/wessaorg/rcomp/tmp/4hsuu1355690726.tab") 
> 
> try(system("convert tmp/1qwyg1355690725.ps tmp/1qwyg1355690725.png",intern=TRUE))
character(0)
> try(system("convert tmp/2ph5x1355690725.ps tmp/2ph5x1355690725.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.558   0.265   1.799