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(153.3
+ ,154.5
+ ,155.2
+ ,156.9
+ ,157
+ ,157.4
+ ,157.2
+ ,157.5
+ ,158
+ ,158.5
+ ,159
+ ,159.3
+ ,160
+ ,160.8
+ ,161.9
+ ,162.5
+ ,162.7
+ ,162.8
+ ,162.9
+ ,163
+ ,164
+ ,164.7
+ ,164.8
+ ,164.9
+ ,165
+ ,165.8
+ ,166.1
+ ,167.2
+ ,167.7
+ ,168.3
+ ,168.6
+ ,168.9
+ ,169.1
+ ,169.5
+ ,169.6
+ ,169.7
+ ,169.8
+ ,170.4
+ ,170.9
+ ,171.9
+ ,171.9
+ ,172
+ ,172
+ ,172.4
+ ,173
+ ,173.7
+ ,173.8
+ ,173.8
+ ,173.9
+ ,174.6
+ ,175
+ ,175.9
+ ,176
+ ,175.1
+ ,175.6
+ ,175.9
+ ,176.7
+ ,176.1
+ ,176.1
+ ,176.2
+ ,176.3
+ ,177.8
+ ,178.5
+ ,179.4
+ ,179.5
+ ,179.6
+ ,179.7
+ ,179.7
+ ,179.8
+ ,179.9
+ ,180.2
+ ,180.4
+ ,180.4
+ ,181.3
+ ,181.9
+ ,182.5
+ ,182.7
+ ,183.1
+ ,183.6
+ ,183.7
+ ,183.8
+ ,183.9
+ ,184.1
+ ,184.4
+ ,184.5
+ ,185.9
+ ,186.6
+ ,187.6
+ ,187.8
+ ,187.9
+ ,188
+ ,188.3
+ ,188.4
+ ,188.5
+ ,188.5
+ ,188.6
+ ,188.6
+ ,189.4
+ ,190
+ ,191.9
+ ,192.5
+ ,193
+ ,193.5
+ ,193.9
+ ,194.2
+ ,194.9
+ ,194.9
+ ,194.9
+ ,194.9
+ ,195.5
+ ,196
+ ,196.2
+ ,196.2
+ ,196.2
+ ,196.2
+ ,197
+ ,197.7
+ ,198
+ ,198.2
+ ,198.5
+ ,198.6
+ ,199.5
+ ,200
+ ,201.3
+ ,202.2
+ ,202.9
+ ,203.5
+ ,203.5
+ ,204
+ ,204.1
+ ,204.3
+ ,204.5
+ ,204.8
+ ,205.1
+ ,205.7
+ ,206.5
+ ,206.9
+ ,207.1
+ ,207.8
+ ,208
+ ,208.5
+ ,208.6
+ ,209
+ ,209.1
+ ,209.7
+ ,209.8
+ ,209.9
+ ,210
+ ,210.8
+ ,211.4
+ ,211.7
+ ,212
+ ,212.2
+ ,212.4
+ ,212.9
+ ,213.4
+ ,213.7
+ ,214
+ ,214.3
+ ,214.8
+ ,215
+ ,215.9
+ ,216.4
+ ,216.9
+ ,217.2
+ ,217.5
+ ,217.9
+ ,218.1
+ ,218.6
+ ,218.9
+ ,219.3
+ ,220.4
+ ,220.9
+ ,221
+ ,221.8
+ ,222
+ ,222.2
+ ,222.5
+ ,222.9
+ ,223.1
+ ,223.4
+ ,224
+ ,225.1
+ ,225.5
+ ,225.9
+ ,226.3
+ ,226.5
+ ,227
+ ,227.3
+ ,227.8
+ ,228.1
+ ,228.4
+ ,228.5
+ ,228.8
+ ,229
+ ,229.1
+ ,229.3
+ ,229.6
+ ,229.9
+ ,230
+ ,230.2
+ ,230.8
+ ,231
+ ,231.7
+ ,231.9
+ ,233
+ ,235.1
+ ,236
+ ,236.9
+ ,237.1
+ ,237.5
+ ,238.2
+ ,238.9
+ ,239.1
+ ,240
+ ,240.2
+ ,240.5
+ ,240.7
+ ,241.1
+ ,241.4
+ ,242.2
+ ,242.9
+ ,243.2
+ ,243.9)
> par20 = ''
> par19 = ''
> par18 = ''
> par17 = ''
> par16 = ''
> par15 = ''
> par14 = ''
> par13 = ''
> par12 = ''
> par11 = ''
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '0'
> par6 = '2'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> par1 = '12'
> ylab = ''
> xlab = ''
> main = ''
> #'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     sma1
      0.1433  0.1447  -0.7904
s.e.  0.0706  0.0703   0.0607

sigma^2 estimated as 0.1081:  log likelihood = -66.95,  aic = 141.9
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 213 
End = 224 
Frequency = 1 
 [1] 238.5618 238.9931 239.2994 239.6442 239.8947 240.5078 241.3397 241.9953
 [9] 242.4786 242.8067 243.2021 243.5786

$se
Time Series:
Start = 213 
End = 224 
Frequency = 1 
 [1] 0.3288492 0.4995082 0.6593066 0.7953915 0.9162790 1.0245542 1.1232296
 [8] 1.2142107 1.2989746 1.3785936 1.4538849 1.5254756

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 213 
End = 224 
Frequency = 1 
 [1] 237.9173 238.0141 238.0072 238.0852 238.0987 238.4997 239.1382 239.6155
 [9] 239.9326 240.1047 240.3525 240.5887
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 213 
End = 224 
Frequency = 1 
 [1] 239.2064 239.9721 240.5917 241.2032 241.6906 242.5159 243.5412 244.3752
 [9] 245.0245 245.5088 246.0517 246.5686
> 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] 153.3000 154.5000 155.2000 156.9000 157.0000 157.4000 157.2000 157.5000
  [9] 158.0000 158.5000 159.0000 159.3000 160.0000 160.8000 161.9000 162.5000
 [17] 162.7000 162.8000 162.9000 163.0000 164.0000 164.7000 164.8000 164.9000
 [25] 165.0000 165.8000 166.1000 167.2000 167.7000 168.3000 168.6000 168.9000
 [33] 169.1000 169.5000 169.6000 169.7000 169.8000 170.4000 170.9000 171.9000
 [41] 171.9000 172.0000 172.0000 172.4000 173.0000 173.7000 173.8000 173.8000
 [49] 173.9000 174.6000 175.0000 175.9000 176.0000 175.1000 175.6000 175.9000
 [57] 176.7000 176.1000 176.1000 176.2000 176.3000 177.8000 178.5000 179.4000
 [65] 179.5000 179.6000 179.7000 179.7000 179.8000 179.9000 180.2000 180.4000
 [73] 180.4000 181.3000 181.9000 182.5000 182.7000 183.1000 183.6000 183.7000
 [81] 183.8000 183.9000 184.1000 184.4000 184.5000 185.9000 186.6000 187.6000
 [89] 187.8000 187.9000 188.0000 188.3000 188.4000 188.5000 188.5000 188.6000
 [97] 188.6000 189.4000 190.0000 191.9000 192.5000 193.0000 193.5000 193.9000
[105] 194.2000 194.9000 194.9000 194.9000 194.9000 195.5000 196.0000 196.2000
[113] 196.2000 196.2000 196.2000 197.0000 197.7000 198.0000 198.2000 198.5000
[121] 198.6000 199.5000 200.0000 201.3000 202.2000 202.9000 203.5000 203.5000
[129] 204.0000 204.1000 204.3000 204.5000 204.8000 205.1000 205.7000 206.5000
[137] 206.9000 207.1000 207.8000 208.0000 208.5000 208.6000 209.0000 209.1000
[145] 209.7000 209.8000 209.9000 210.0000 210.8000 211.4000 211.7000 212.0000
[153] 212.2000 212.4000 212.9000 213.4000 213.7000 214.0000 214.3000 214.8000
[161] 215.0000 215.9000 216.4000 216.9000 217.2000 217.5000 217.9000 218.1000
[169] 218.6000 218.9000 219.3000 220.4000 220.9000 221.0000 221.8000 222.0000
[177] 222.2000 222.5000 222.9000 223.1000 223.4000 224.0000 225.1000 225.5000
[185] 225.9000 226.3000 226.5000 227.0000 227.3000 227.8000 228.1000 228.4000
[193] 228.5000 228.8000 229.0000 229.1000 229.3000 229.6000 229.9000 230.0000
[201] 230.2000 230.8000 231.0000 231.7000 231.9000 233.0000 235.1000 236.0000
[209] 236.9000 237.1000 237.5000 238.2000 238.5618 238.9931 239.2994 239.6442
[217] 239.8947 240.5078 241.3397 241.9953 242.4786 242.8067 243.2021 243.5786
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 213 
End = 224 
Frequency = 1 
 [1] 0.001378465 0.002090053 0.002755153 0.003319052 0.003819506 0.004259963
 [7] 0.004654143 0.005017497 0.005357070 0.005677741 0.005978094 0.006262764
> postscript(file="/var/www/html/rcomp/tmp/1zj051260537772.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/28fir1260537772.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/3igeo1260537772.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/4x03y1260537772.tab") 
> 
> system("convert tmp/1zj051260537772.ps tmp/1zj051260537772.png")
> system("convert tmp/28fir1260537772.ps tmp/28fir1260537772.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.877   0.311   1.092