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

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> x <- c(77.7,78.89,90.2,77.26,80.76,84.93,66.08,71.56,80.78,83.31,85.3,73.94,78.7,81.32,86.8,80.76,84.46,84.21,73.64,70.85,83.78,89.12,78.93,80.54,81.67,82.53,88.2,89.17,83.7,89.79,77.58,70.11,88.07,92.49,83.33,90.05,82.91,88.52,96.42,90.87,86.4,97.47,85.67,79.91,95.73,94.6,91.92,90.38,82.31,87.82,101.29,89.58,87.83,99.95,82.67,84.65,97.83,97.47,97.66,99.14,90.02,100.97,112.48,91.44,108.46,98.41,89.35,92.8,100.43,104.85,108.36,101.54,105.26,101.8,112.36,99.5,104.65,101.13,89.8,87.84,96.41,103.26,100.31,92.33,96.19,96.37,103.06,101.5,101.88,100.85,95.56,87.6,101.18,110.8,101.1,104.42,103.27,100.87,107.8,104.99,100.76,104.46,100.62,87.84,107.31,115.61,103.43,109.93,104.43,106.69,123.1,109.42,101.46,124.48,101.49,100.46,115.51,113.37,115.4,118.2,106.82,110.17,119.91,112.31,110.62,120.37,97.94,103.02,116.36,108.51,122.54,121.32,112.25,109.89,129.58,107.2,118.68,118.25,102.67,104.19,117.74,123.3,122.2,112.71,118.53,115.32,127.36,110.45,122.22,123.39,116.2,109.22,116.98,132.89,125.24,115.68)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '2'
> par7 = '0'
> par6 = '3'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> par2 = '0.3'
> 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     ar2     ar3    sar1     sar2     sma1
      0.0246  0.3819  0.5904  0.2059  -0.2454  -0.8951
s.e.  0.0788  0.0632  0.0771  0.1315   0.1049   0.2235

sigma^2 estimated as 0.001915:  log likelihood = 214.89,  aic = -415.78
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 145 
End = 156 
Frequency = 1 
 [1] 4.180124 4.151943 4.283700 4.168417 4.187357 4.222348 4.088699 4.035749
 [9] 4.210776 4.282797 4.209449 4.178876

$se
Time Series:
Start = 145 
End = 156 
Frequency = 1 
 [1] 0.04417201 0.04418137 0.04728668 0.05435919 0.05490224 0.05855215
 [7] 0.06163282 0.06294248 0.06593402 0.06801268 0.06974289 0.07209858

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 145 
End = 156 
Frequency = 1 
 [1] 4.093547 4.065348 4.191018 4.061873 4.079748 4.107585 3.967898 3.912382
 [9] 4.081545 4.149492 4.072753 4.037563
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 145 
End = 156 
Frequency = 1 
 [1] 4.266701 4.238539 4.376381 4.274961 4.294965 4.337110 4.209499 4.159116
 [9] 4.340007 4.416102 4.346145 4.320189
> 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$pred))
  [1]  77.7000  78.8900  90.2000  77.2600  80.7600  84.9300  66.0800  71.5600
  [9]  80.7800  83.3100  85.3000  73.9400  78.7000  81.3200  86.8000  80.7600
 [17]  84.4600  84.2100  73.6400  70.8500  83.7800  89.1200  78.9300  80.5400
 [25]  81.6700  82.5300  88.2000  89.1700  83.7000  89.7900  77.5800  70.1100
 [33]  88.0700  92.4900  83.3300  90.0500  82.9100  88.5200  96.4200  90.8700
 [41]  86.4000  97.4700  85.6700  79.9100  95.7300  94.6000  91.9200  90.3800
 [49]  82.3100  87.8200 101.2900  89.5800  87.8300  99.9500  82.6700  84.6500
 [57]  97.8300  97.4700  97.6600  99.1400  90.0200 100.9700 112.4800  91.4400
 [65] 108.4600  98.4100  89.3500  92.8000 100.4300 104.8500 108.3600 101.5400
 [73] 105.2600 101.8000 112.3600  99.5000 104.6500 101.1300  89.8000  87.8400
 [81]  96.4100 103.2600 100.3100  92.3300  96.1900  96.3700 103.0600 101.5000
 [89] 101.8800 100.8500  95.5600  87.6000 101.1800 110.8000 101.1000 104.4200
 [97] 103.2700 100.8700 107.8000 104.9900 100.7600 104.4600 100.6200  87.8400
[105] 107.3100 115.6100 103.4300 109.9300 104.4300 106.6900 123.1000 109.4200
[113] 101.4600 124.4800 101.4900 100.4600 115.5100 113.3700 115.4000 118.2000
[121] 106.8200 110.1700 119.9100 112.3100 110.6200 120.3700  97.9400 103.0200
[129] 116.3600 108.5100 122.5400 121.3200 112.2500 109.8900 129.5800 107.2000
[137] 118.6800 118.2500 102.6700 104.1900 117.7400 123.3000 122.2000 112.7100
[145] 117.6604 115.0371 127.6625 116.5656 118.3404 121.6690 109.2992 104.6519
[153] 120.5611 127.5729 120.4345 117.5434
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 145 
End = 156 
Frequency = 1 
 [1] 0.03608282 0.03634154 0.03773358 0.04478009 0.04503010 0.04770750
 [7] 0.05200124 0.05386675 0.05408908 0.05488368 0.05734987 0.05981345
> postscript(file="/var/www/html/rcomp/tmp/1tva81229251634.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2jq5l1229251634.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/3lx2y1229251634.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/4r3af1229251634.tab") 
> 
> system("convert tmp/1tva81229251634.ps tmp/1tva81229251634.png")
> system("convert tmp/2jq5l1229251634.ps tmp/2jq5l1229251634.png")
> 
> 
> proc.time()
   user  system elapsed 
  3.337   0.418   4.291