R version 2.8.0 (2008-10-20)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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Type 'demo()' for some demos, 'help()' for on-line help, or
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> x <- c(14525.87
+ ,14295.79
+ ,13830.14
+ ,14153.22
+ ,15418.03
+ ,16666.97
+ ,16505.21
+ ,17135.96
+ ,18033.25
+ ,17671
+ ,17544.22
+ ,17677.9
+ ,18470.97
+ ,18409.96
+ ,18941.6
+ ,19685.53
+ ,19834.71
+ ,19598.93
+ ,17039.97
+ ,16969.28
+ ,16973.38
+ ,16329.89
+ ,16153.34
+ ,15311.7
+ ,14760.87
+ ,14452.93
+ ,13720.95
+ ,13266.27
+ ,12708.47
+ ,13411.84
+ ,13975.55
+ ,12974.89
+ ,12151.11
+ ,11576.21
+ ,9996.83
+ ,10438.9
+ ,10511.22
+ ,10496.2
+ ,10300.79
+ ,9981.65
+ ,11448.79
+ ,11384.49
+ ,11717.46
+ ,10965.88
+ ,10352.27
+ ,9751.2
+ ,9354.01
+ ,8792.5
+ ,8721.14
+ ,8692.94
+ ,8570.73
+ ,8538.47
+ ,8169.75
+ ,7905.84
+ ,8145.82
+ ,8895.71
+ ,9676.31
+ ,9884.59
+ ,10637.44
+ ,10717.13
+ ,10205.29
+ ,10295.98
+ ,10892.76
+ ,10631.92
+ ,11441.08
+ ,11950.95
+ ,11037.54
+ ,11527.72
+ ,11383.89
+ ,10989.34
+ ,11079.42
+ ,11028.93
+ ,10973
+ ,11068.05
+ ,11394.84
+ ,11545.71
+ ,11809.38
+ ,11395.64
+ ,11082.38
+ ,11402.75
+ ,11716.87
+ ,12204.98
+ ,12986.62
+ ,13392.79
+ ,14368.05
+ ,15650.83
+ ,16102.64
+ ,16187.64
+ ,16311.54
+ ,17232.97
+ ,16397.83
+ ,14990.31
+ ,15147.55
+ ,15786.78
+ ,15934.09
+ ,16519.44
+ ,16101.07
+ ,16775.08
+ ,17286.32
+ ,17741.23
+ ,17128.37
+ ,17460.53
+ ,17611.14
+ ,18001.37
+ ,17974.77
+ ,16460.95
+ ,16235.39
+ ,16903.36
+ ,15543.76
+ ,15532.18
+ ,13731.31
+ ,13547.84
+ ,12602.93
+ ,13357.7
+ ,13995.33
+ ,14084.6
+ ,13168.91
+ ,12989.35
+ ,12123.53
+ ,9117.03
+ ,8531.45)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '1'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '1'
> par1 = '12'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> 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
      0.2161
s.e.  0.0955

sigma^2 estimated as 402252:  log likelihood = -850.13,  aic = 1704.26
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 110 
End = 121 
Frequency = 1 
 [1] 15249.92 15186.41 15172.68 15169.72 15169.07 15168.94 15168.91 15168.90
 [9] 15168.90 15168.90 15168.90 15168.90

$se
Time Series:
Start = 110 
End = 121 
Frequency = 1 
 [1]  634.2335  998.5830 1280.1023 1513.4244 1715.9490 1897.1011 2062.4279
 [8] 2215.4565 2358.5782 2493.4987 2621.4844 2743.5061

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 110 
End = 121 
Frequency = 1 
 [1] 14006.817 13229.185 12663.682 12203.404 11805.814 11450.618 11126.547
 [8] 10826.605 10546.085 10281.640 10030.788  9791.626
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 110 
End = 121 
Frequency = 1 
 [1] 16493.01 17143.63 17681.68 18136.03 18532.33 18887.25 19211.26 19511.19
 [9] 19791.71 20056.16 20307.01 20546.17
> 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$pred))
  [1] 14525.87 14295.79 13830.14 14153.22 15418.03 16666.97 16505.21 17135.96
  [9] 18033.25 17671.00 17544.22 17677.90 18470.97 18409.96 18941.60 19685.53
 [17] 19834.71 19598.93 17039.97 16969.28 16973.38 16329.89 16153.34 15311.70
 [25] 14760.87 14452.93 13720.95 13266.27 12708.47 13411.84 13975.55 12974.89
 [33] 12151.11 11576.21  9996.83 10438.90 10511.22 10496.20 10300.79  9981.65
 [41] 11448.79 11384.49 11717.46 10965.88 10352.27  9751.20  9354.01  8792.50
 [49]  8721.14  8692.94  8570.73  8538.47  8169.75  7905.84  8145.82  8895.71
 [57]  9676.31  9884.59 10637.44 10717.13 10205.29 10295.98 10892.76 10631.92
 [65] 11441.08 11950.95 11037.54 11527.72 11383.89 10989.34 11079.42 11028.93
 [73] 10973.00 11068.05 11394.84 11545.71 11809.38 11395.64 11082.38 11402.75
 [81] 11716.87 12204.98 12986.62 13392.79 14368.05 15650.83 16102.64 16187.64
 [89] 16311.54 17232.97 16397.83 14990.31 15147.55 15786.78 15934.09 16519.44
 [97] 16101.07 16775.08 17286.32 17741.23 17128.37 17460.53 17611.14 18001.37
[105] 17974.77 16460.95 16235.39 16903.36 15543.76 15249.92 15186.41 15172.68
[113] 15169.72 15169.07 15168.94 15168.91 15168.90 15168.90 15168.90 15168.90
[121] 15168.90
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 110 
End = 121 
Frequency = 1 
 [1] 0.04158932 0.06575505 0.08436889 0.09976617 0.11312154 0.12506488
 [7] 0.13596418 0.14605255 0.15548777 0.16438232 0.17281970 0.18086390
> postscript(file="/var/www/html/rcomp/tmp/138um1229686652.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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.se <- array(0, dim=fx)
> perf.mse <- 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$pred[i]
+ perf.mape[i] = perf.mape[i] + abs(perf.pe[i])
+ perf.se[i] = (x[nx+i] - forecast$pred[i])^2
+ perf.mse[i] = perf.mse[i] + perf.se[i]
+ 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 = perf.mape / fx
> perf.mse = perf.mse / fx
> perf.rmse = sqrt(perf.mse)
> postscript(file="/var/www/html/rcomp/tmp/2y6iq1229686652.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[1:12] <- 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/3qiqc1229686652.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.mape[i],4))
+ a<-table.element(a,round(perf.se[i],4))
+ a<-table.element(a,round(perf.mse[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/474ee1229686652.tab") 
> 
> system("convert tmp/138um1229686652.ps tmp/138um1229686652.png")
> system("convert tmp/2y6iq1229686652.ps tmp/2y6iq1229686652.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.585   0.329   0.847