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(90.2
+ ,90
+ ,88.8
+ ,85.8
+ ,84.2
+ ,80
+ ,77.8
+ ,76.8
+ ,86.4
+ ,89.2
+ ,86.2
+ ,84.6
+ ,83.2
+ ,83.2
+ ,82.6
+ ,79.8
+ ,77.2
+ ,74.8
+ ,73
+ ,73
+ ,83.6
+ ,85.6
+ ,84.8
+ ,84.2
+ ,83.4
+ ,84.6
+ ,84.6
+ ,83.8
+ ,81.2
+ ,79.6
+ ,78
+ ,78.2
+ ,88.8
+ ,92
+ ,91
+ ,91.2
+ ,90.4
+ ,91.8
+ ,92.2
+ ,90.2
+ ,88.6
+ ,87.8
+ ,86
+ ,87.2
+ ,97.6
+ ,101.2
+ ,100.4
+ ,100.2
+ ,100.2
+ ,103
+ ,104.2
+ ,104
+ ,102.4
+ ,101.8
+ ,101
+ ,102.2
+ ,114
+ ,118.4
+ ,118.8
+ ,117.2
+ ,117.2
+ ,118.4
+ ,118.8
+ ,117.2
+ ,114.4
+ ,112.6
+ ,111
+ ,110.8
+ ,120.2
+ ,124.4
+ ,123.4
+ ,121.2
+ ,119
+ ,119.8
+ ,120
+ ,118.4
+ ,115
+ ,113.4
+ ,111
+ ,111
+ ,121.6
+ ,126.2
+ ,125.8
+ ,124.8
+ ,122
+ ,123.2
+ ,124.2
+ ,120.8
+ ,116.8
+ ,114.8
+ ,111
+ ,109
+ ,119.8
+ ,124
+ ,121.6
+ ,118
+ ,115.8
+ ,116
+ ,115.8
+ ,114.4
+ ,112
+ ,110.2
+ ,107.4
+ ,108.2
+ ,117.6
+ ,121.4
+ ,119.8
+ ,115.6
+ ,112.6
+ ,113.2
+ ,112.2
+ ,110.8
+ ,108
+ ,105.2
+ ,102.4
+ ,101
+ ,110.8
+ ,116.8
+ ,113.8
+ ,108
+ ,104.4
+ ,105.2
+ ,105.4
+ ,103.2
+ ,100.6
+ ,97.8
+ ,95.8
+ ,95
+ ,104.8
+ ,110.4
+ ,106.4
+ ,102.2
+ ,98.4
+ ,98.4
+ ,98.6
+ ,96.2
+ ,92.4
+ ,91.4
+ ,88.4
+ ,87.8
+ ,97.6
+ ,104.2
+ ,100.2
+ ,97
+ ,92.8
+ ,92
+ ,93.4
+ ,92
+ ,89.6
+ ,88.6
+ ,87.2
+ ,86.2
+ ,96.8
+ ,102
+ ,102.6
+ ,100.6
+ ,94.2
+ ,94.2
+ ,95.2
+ ,95
+ ,94
+ ,92.2
+ ,91
+ ,91.2
+ ,103.4
+ ,105
+ ,104.6
+ ,103.8
+ ,101.8
+ ,102.4
+ ,103.8
+ ,103.4
+ ,102
+ ,101.8
+ ,100.2
+ ,101.4
+ ,113.8
+ ,116
+ ,115.6
+ ,113
+ ,109.4
+ ,111
+ ,112.4
+ ,112.2
+ ,111
+ ,108.8
+ ,107.4
+ ,108.6
+ ,118.8
+ ,122.2
+ ,122.6
+ ,122.2
+ ,118.8
+ ,119
+ ,118.2
+ ,117.8
+ ,116.8
+ ,114.6
+ ,113.4
+ ,113.8
+ ,124.2
+ ,125.8
+ ,125.6
+ ,122.4
+ ,119
+ ,119.4
+ ,118.6
+ ,118
+ ,116
+ ,114.8
+ ,114.6
+ ,114.6
+ ,124
+ ,125.2
+ ,124
+ ,117.6
+ ,113.2
+ ,111.4
+ ,112.2
+ ,109.8
+ ,106.4
+ ,105.2
+ ,102.2
+ ,99.8
+ ,111
+ ,113
+ ,108.4
+ ,105.4
+ ,102
+ ,102.8
+ ,103.4
+ ,101.6
+ ,98.6
+ ,98
+ ,93.8
+ ,95.6
+ ,105.6
+ ,106.8
+ ,103.6
+ ,101.2
+ ,100.4
+ ,103.2
+ ,105.6
+ ,106.6
+ ,107.2
+ ,107.4
+ ,104.8
+ ,107.2
+ ,117.4
+ ,119.4
+ ,116.2
+ ,112.8
+ ,111.6)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '1'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> par1 = '6'
> #'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    sar1     sma1
      0.9366  -0.8077  0.4138  -0.8979
s.e.  0.0477   0.0672  0.1045   0.0940

sigma^2 estimated as 1.305:  log likelihood = -368.41,  aic = 746.81
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 248 
End = 253 
Frequency = 1 
[1] 106.5429 117.6563 120.6553 119.0144 117.1544 115.8990

$se
Time Series:
Start = 248 
End = 253 
Frequency = 1 
[1] 1.143433 1.724376 2.239349 2.727957 3.203189 3.670469

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 248 
End = 253 
Frequency = 1 
[1] 104.3018 114.2765 116.2662 113.6676 110.8761 108.7048
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 248 
End = 253 
Frequency = 1 
[1] 108.7840 121.0360 125.0444 124.3612 123.4326 123.0931
> 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]  90.2000  90.0000  88.8000  85.8000  84.2000  80.0000  77.8000  76.8000
  [9]  86.4000  89.2000  86.2000  84.6000  83.2000  83.2000  82.6000  79.8000
 [17]  77.2000  74.8000  73.0000  73.0000  83.6000  85.6000  84.8000  84.2000
 [25]  83.4000  84.6000  84.6000  83.8000  81.2000  79.6000  78.0000  78.2000
 [33]  88.8000  92.0000  91.0000  91.2000  90.4000  91.8000  92.2000  90.2000
 [41]  88.6000  87.8000  86.0000  87.2000  97.6000 101.2000 100.4000 100.2000
 [49] 100.2000 103.0000 104.2000 104.0000 102.4000 101.8000 101.0000 102.2000
 [57] 114.0000 118.4000 118.8000 117.2000 117.2000 118.4000 118.8000 117.2000
 [65] 114.4000 112.6000 111.0000 110.8000 120.2000 124.4000 123.4000 121.2000
 [73] 119.0000 119.8000 120.0000 118.4000 115.0000 113.4000 111.0000 111.0000
 [81] 121.6000 126.2000 125.8000 124.8000 122.0000 123.2000 124.2000 120.8000
 [89] 116.8000 114.8000 111.0000 109.0000 119.8000 124.0000 121.6000 118.0000
 [97] 115.8000 116.0000 115.8000 114.4000 112.0000 110.2000 107.4000 108.2000
[105] 117.6000 121.4000 119.8000 115.6000 112.6000 113.2000 112.2000 110.8000
[113] 108.0000 105.2000 102.4000 101.0000 110.8000 116.8000 113.8000 108.0000
[121] 104.4000 105.2000 105.4000 103.2000 100.6000  97.8000  95.8000  95.0000
[129] 104.8000 110.4000 106.4000 102.2000  98.4000  98.4000  98.6000  96.2000
[137]  92.4000  91.4000  88.4000  87.8000  97.6000 104.2000 100.2000  97.0000
[145]  92.8000  92.0000  93.4000  92.0000  89.6000  88.6000  87.2000  86.2000
[153]  96.8000 102.0000 102.6000 100.6000  94.2000  94.2000  95.2000  95.0000
[161]  94.0000  92.2000  91.0000  91.2000 103.4000 105.0000 104.6000 103.8000
[169] 101.8000 102.4000 103.8000 103.4000 102.0000 101.8000 100.2000 101.4000
[177] 113.8000 116.0000 115.6000 113.0000 109.4000 111.0000 112.4000 112.2000
[185] 111.0000 108.8000 107.4000 108.6000 118.8000 122.2000 122.6000 122.2000
[193] 118.8000 119.0000 118.2000 117.8000 116.8000 114.6000 113.4000 113.8000
[201] 124.2000 125.8000 125.6000 122.4000 119.0000 119.4000 118.6000 118.0000
[209] 116.0000 114.8000 114.6000 114.6000 124.0000 125.2000 124.0000 117.6000
[217] 113.2000 111.4000 112.2000 109.8000 106.4000 105.2000 102.2000  99.8000
[225] 111.0000 113.0000 108.4000 105.4000 102.0000 102.8000 103.4000 101.6000
[233]  98.6000  98.0000  93.8000  95.6000 105.6000 106.8000 103.6000 101.2000
[241] 100.4000 103.2000 105.6000 106.6000 107.2000 107.4000 104.8000 106.5429
[249] 117.6563 120.6553 119.0144 117.1544 115.8990
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 248 
End = 253 
Frequency = 1 
[1] 0.01073214 0.01465605 0.01855989 0.02292124 0.02734161 0.03166956
> postscript(file="/var/www/html/rcomp/tmp/1pcl91264495294.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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.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/html/rcomp/tmp/25c9f1264495294.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: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/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/32get1264495295.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/html/rcomp/tmp/4hreh1264495295.tab") 
> 
> try(system("convert tmp/1pcl91264495294.ps tmp/1pcl91264495294.png",intern=TRUE))
character(0)
> try(system("convert tmp/25c9f1264495294.ps tmp/25c9f1264495294.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  2.229   0.329   5.560