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(112,118,132,129,121,135,148,148,136,119,104,118,115,126,141,135,125,149,170,170,158,133,114,140,145,150,178,163,172,178,199,199,184,162,146,166,171,180,193,181,183,218,230,242,209,191,172,194,196,196,236,235,229,243,264,272,237,211,180,201,204,188,235,227,234,264,302,293,259,229,203,229,242,233,267,269,270,315,364,347,312,274,237,278,284,277,317,313,318,374,413,405,355,306,271,306,315,301,356,348,355,422,465,467,404,347,305,336,340,318,362,348,363,435,491,505,404,359,310,337,360,342,406,396,420,472,548,559,463,407,362,405,417,391,419,461,472,535,622,606,508,461,390,432)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '1'
> par6 = '0'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '0.0'
> 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:
          ma1
      -0.3452
s.e.   0.0938

sigma^2 estimated as 0.001806:  log likelihood = 206.93,  aic = -409.85
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 133 
End = 144 
Frequency = 1 
 [1] 6.056443 6.005150 6.176692 6.151753 6.210594 6.327318 6.476614 6.496489
 [9] 6.308066 6.179152 6.061983 6.174226

$se
Time Series:
Start = 133 
End = 144 
Frequency = 1 
 [1] 0.04249568 0.05079622 0.05791915 0.06425730 0.07002409 0.07535082
 [7] 0.08032508 0.08500877 0.08944755 0.09367623 0.09772210 0.10160699

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 133 
End = 144 
Frequency = 1 
 [1] 5.973152 5.905589 6.063171 6.025809 6.073347 6.179630 6.319177 6.329871
 [9] 6.132749 5.995547 5.870448 5.975076
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 133 
End = 144 
Frequency = 1 
 [1] 6.139735 6.104710 6.290214 6.277698 6.347841 6.475006 6.634052 6.663106
 [9] 6.483383 6.362758 6.253519 6.373376
> 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$pred))
  [1] 112.0000 118.0000 132.0000 129.0000 121.0000 135.0000 148.0000 148.0000
  [9] 136.0000 119.0000 104.0000 118.0000 115.0000 126.0000 141.0000 135.0000
 [17] 125.0000 149.0000 170.0000 170.0000 158.0000 133.0000 114.0000 140.0000
 [25] 145.0000 150.0000 178.0000 163.0000 172.0000 178.0000 199.0000 199.0000
 [33] 184.0000 162.0000 146.0000 166.0000 171.0000 180.0000 193.0000 181.0000
 [41] 183.0000 218.0000 230.0000 242.0000 209.0000 191.0000 172.0000 194.0000
 [49] 196.0000 196.0000 236.0000 235.0000 229.0000 243.0000 264.0000 272.0000
 [57] 237.0000 211.0000 180.0000 201.0000 204.0000 188.0000 235.0000 227.0000
 [65] 234.0000 264.0000 302.0000 293.0000 259.0000 229.0000 203.0000 229.0000
 [73] 242.0000 233.0000 267.0000 269.0000 270.0000 315.0000 364.0000 347.0000
 [81] 312.0000 274.0000 237.0000 278.0000 284.0000 277.0000 317.0000 313.0000
 [89] 318.0000 374.0000 413.0000 405.0000 355.0000 306.0000 271.0000 306.0000
 [97] 315.0000 301.0000 356.0000 348.0000 355.0000 422.0000 465.0000 467.0000
[105] 404.0000 347.0000 305.0000 336.0000 340.0000 318.0000 362.0000 348.0000
[113] 363.0000 435.0000 491.0000 505.0000 404.0000 359.0000 310.0000 337.0000
[121] 360.0000 342.0000 406.0000 396.0000 420.0000 472.0000 548.0000 559.0000
[129] 463.0000 407.0000 362.0000 405.0000 426.8545 405.5117 481.3970 469.5399
[137] 497.9969 559.6536 649.7674 662.8101 548.9823 482.5827 429.2259 480.2113
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 133 
End = 144 
Frequency = 1 
 [1] 0.04431562 0.05341091 0.06133470 0.06847908 0.07505699 0.08119935
 [7] 0.08699347 0.09250100 0.09776741 0.10282735 0.10770796 0.11243094
> postscript(file="/var/www/html/rcomp/tmp/1i6o21259942981.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2macd1259942981.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/3wxz41259942981.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/4d0i91259942981.tab") 
> 
> system("convert tmp/1i6o21259942981.ps tmp/1i6o21259942981.png")
> system("convert tmp/2macd1259942981.ps tmp/2macd1259942981.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.602   0.307   0.711