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(11974
+ ,10106
+ ,12069
+ ,11412
+ ,11180
+ ,10508
+ ,11288
+ ,10928
+ ,10199
+ ,11030
+ ,11234
+ ,13747
+ ,13912
+ ,12376
+ ,12264
+ ,11675
+ ,11271
+ ,10672
+ ,10933
+ ,10379
+ ,10187
+ ,10747
+ ,10970
+ ,12175
+ ,14200
+ ,11676
+ ,11258
+ ,10872
+ ,11148
+ ,10690
+ ,10684
+ ,11658
+ ,10178
+ ,10981
+ ,10773
+ ,11665
+ ,11359
+ ,10716
+ ,12928
+ ,12317
+ ,11641
+ ,10459
+ ,10953
+ ,10703
+ ,10703
+ ,11101
+ ,11334
+ ,13268
+ ,13145
+ ,12334
+ ,13153
+ ,11289
+ ,11374
+ ,10914
+ ,11299
+ ,11284
+ ,10694
+ ,11077
+ ,11104
+ ,12820
+ ,14915
+ ,11773
+ ,11608
+ ,11468
+ ,11511
+ ,11200
+ ,11164
+ ,10960
+ ,10667
+ ,11556
+ ,11372
+ ,12333
+ ,13102
+ ,11115
+ ,12572
+ ,11557
+ ,12059
+ ,11420
+ ,11185
+ ,11113
+ ,10706
+ ,11523
+ ,11391
+ ,12634
+ ,13469
+ ,11735
+ ,13281
+ ,11968
+ ,11623
+ ,11084
+ ,11509
+ ,11134
+ ,10438
+ ,11530
+ ,11491
+ ,13093
+ ,13106
+ ,11305
+ ,13113
+ ,12203
+ ,11309
+ ,11088
+ ,11234
+ ,11619
+ ,10942
+ ,11445
+ ,11291
+ ,13281
+ ,13726
+ ,11300
+ ,11983
+ ,11092
+ ,11093
+ ,10692
+ ,10786
+ ,11166
+ ,10553
+ ,11103
+ ,10969
+ ,12090
+ ,12544
+ ,12264
+ ,13783
+ ,11214
+ ,11453
+ ,10883
+ ,10381
+ ,10348
+ ,10024
+ ,10805
+ ,10796
+ ,11907
+ ,12261
+ ,11377
+ ,12689
+ ,11474
+ ,10992
+ ,10764
+ ,12164
+ ,10409
+ ,10398
+ ,10349
+ ,10865
+ ,11630
+ ,12221
+ ,10884
+ ,12019
+ ,11021
+ ,10799
+ ,10423
+ ,10484
+ ,10450
+ ,9906
+ ,11049
+ ,11281
+ ,12485
+ ,12849
+ ,11380
+ ,12079
+ ,11366
+ ,11328
+ ,10444
+ ,10854
+ ,10434
+ ,10137
+ ,10992
+ ,10906
+ ,12367
+ ,14371
+ ,11695
+ ,11546
+ ,10922
+ ,10670
+ ,10254
+ ,10573
+ ,10239
+ ,10253
+ ,11176
+ ,10719
+ ,11817)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '0'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> par2 = '1'
> par1 = '12'
> #'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:
         ma1     sma1
      0.4452  -1.0000
s.e.  0.0639   0.1093

sigma^2 estimated as 218650:  log likelihood = -1196.33,  aic = 2398.65
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 169 
End = 180 
Frequency = 1 
 [1] 13024.76 11452.93 12485.64 11494.86 11341.50 10802.93 11065.57 10898.93
 [9] 10409.43 11092.00 11126.93 12517.69

$se
Time Series:
Start = 169 
End = 180 
Frequency = 1 
 [1] 484.2085 529.8076 529.8076 529.8076 529.8076 529.8076 529.8076 529.8076
 [9] 529.8076 529.8076 529.8076 529.6136

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 169 
End = 180 
Frequency = 1 
 [1] 12075.707 10414.504 11447.218 10456.433 10303.075  9764.504 10027.147
 [8]  9860.504  9371.004 10053.575 10088.504 11479.651
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 169 
End = 180 
Frequency = 1 
 [1] 13973.80 12491.35 13524.06 12533.28 12379.92 11841.35 12103.99 11937.35
 [9] 11447.85 12130.42 12165.35 13555.74
> 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$pred))
  [1] 11974.00 10106.00 12069.00 11412.00 11180.00 10508.00 11288.00 10928.00
  [9] 10199.00 11030.00 11234.00 13747.00 13912.00 12376.00 12264.00 11675.00
 [17] 11271.00 10672.00 10933.00 10379.00 10187.00 10747.00 10970.00 12175.00
 [25] 14200.00 11676.00 11258.00 10872.00 11148.00 10690.00 10684.00 11658.00
 [33] 10178.00 10981.00 10773.00 11665.00 11359.00 10716.00 12928.00 12317.00
 [41] 11641.00 10459.00 10953.00 10703.00 10703.00 11101.00 11334.00 13268.00
 [49] 13145.00 12334.00 13153.00 11289.00 11374.00 10914.00 11299.00 11284.00
 [57] 10694.00 11077.00 11104.00 12820.00 14915.00 11773.00 11608.00 11468.00
 [65] 11511.00 11200.00 11164.00 10960.00 10667.00 11556.00 11372.00 12333.00
 [73] 13102.00 11115.00 12572.00 11557.00 12059.00 11420.00 11185.00 11113.00
 [81] 10706.00 11523.00 11391.00 12634.00 13469.00 11735.00 13281.00 11968.00
 [89] 11623.00 11084.00 11509.00 11134.00 10438.00 11530.00 11491.00 13093.00
 [97] 13106.00 11305.00 13113.00 12203.00 11309.00 11088.00 11234.00 11619.00
[105] 10942.00 11445.00 11291.00 13281.00 13726.00 11300.00 11983.00 11092.00
[113] 11093.00 10692.00 10786.00 11166.00 10553.00 11103.00 10969.00 12090.00
[121] 12544.00 12264.00 13783.00 11214.00 11453.00 10883.00 10381.00 10348.00
[129] 10024.00 10805.00 10796.00 11907.00 12261.00 11377.00 12689.00 11474.00
[137] 10992.00 10764.00 12164.00 10409.00 10398.00 10349.00 10865.00 11630.00
[145] 12221.00 10884.00 12019.00 11021.00 10799.00 10423.00 10484.00 10450.00
[153]  9906.00 11049.00 11281.00 12485.00 12849.00 11380.00 12079.00 11366.00
[161] 11328.00 10444.00 10854.00 10434.00 10137.00 10992.00 10906.00 12367.00
[169] 13024.76 11452.93 12485.64 11494.86 11341.50 10802.93 11065.57 10898.93
[177] 10409.43 11092.00 11126.93 12517.69
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 169 
End = 180 
Frequency = 1 
 [1] 0.03717601 0.04625958 0.04243335 0.04609084 0.04671407 0.04904297
 [7] 0.04787893 0.04861099 0.05089690 0.04776485 0.04761491 0.04230920
> postscript(file="/var/www/html/rcomp/tmp/1be951292936606.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2p5ow1292936606.ps",horizontal=F,onefile=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/3w73p1292936606.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/4hpkv1292936606.tab") 
> 
> try(system("convert tmp/1be951292936606.ps tmp/1be951292936606.png",intern=TRUE))
character(0)
> try(system("convert tmp/2p5ow1292936606.ps tmp/2p5ow1292936606.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.789   0.366   2.685