R version 2.9.0 (2009-04-17)
Copyright (C) 2009 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(100
+ ,108.1560276
+ ,114.0150276
+ ,102.1880309
+ ,110.3672031
+ ,96.8602511
+ ,94.1944583
+ ,99.51621961
+ ,94.06333487
+ ,97.5541476
+ ,78.15062422
+ ,81.2434643
+ ,92.36262465
+ ,96.06324371
+ ,114.0523777
+ ,110.6616666
+ ,104.9171949
+ ,90.00187193
+ ,95.7008067
+ ,86.02741157
+ ,84.85287668
+ ,100.04328
+ ,80.91713823
+ ,74.06539709
+ ,77.30281369
+ ,97.23043249
+ ,90.75515676
+ ,100.5614455
+ ,92.01293267
+ ,99.24012138
+ ,105.8672755
+ ,90.9920463
+ ,93.30624423
+ ,91.17419413
+ ,77.33295039
+ ,91.1277721
+ ,85.01249943
+ ,83.90390242
+ ,104.8626302
+ ,110.9039108
+ ,95.43714373
+ ,111.6238727
+ ,108.8925403
+ ,96.17511682
+ ,101.9740205
+ ,99.11953031
+ ,86.78158147
+ ,118.4195003
+ ,118.7441447
+ ,106.5296192
+ ,134.7772694
+ ,104.6778714
+ ,105.2954304
+ ,139.4139849
+ ,103.6060491
+ ,99.78182974
+ ,103.4610301
+ ,120.0594945
+ ,96.71377168
+ ,107.1308929
+ ,105.3608372
+ ,111.6942359
+ ,132.0519998
+ ,126.8037879
+ ,154.4824253
+ ,141.5570984
+ ,109.9506882
+ ,127.904198
+ ,133.0888617
+ ,120.0796299
+ ,117.5557142
+ ,143.0362309
+ ,159.982927
+ ,128.5991124
+ ,149.7373327
+ ,126.8169313
+ ,140.9639674
+ ,137.6691981
+ ,117.9402337
+ ,122.3095247
+ ,127.7804207
+ ,136.1677176
+ ,116.2405856
+ ,123.1576893
+ ,116.3400234
+ ,108.6119282
+ ,125.8982264
+ ,112.8003105
+ ,107.5182447
+ ,135.0955413
+ ,115.5096488
+ ,115.8640759
+ ,104.5883906
+ ,163.7213386
+ ,113.4482275
+ ,98.0428844
+ ,116.7868521
+ ,126.5330444
+ ,113.0336597
+ ,124.3392163
+ ,109.8298759
+ ,124.4434777
+ ,111.5039454
+ ,102.0350019
+ ,116.8726598
+ ,112.2073122
+ ,101.1513902
+ ,124.4255108)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '1'
> par6 = '0'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> 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
      -0.6960
s.e.   0.0948

sigma^2 estimated as 238.6:  log likelihood = -345.31,  aic = 694.63
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 97 
End = 108 
Frequency = 1 
 [1] 107.34847  99.62037 116.90667 103.80875  98.52669 126.10399 106.51809
 [8] 106.87252  95.59683 154.72978 104.45667  89.05133

$se
Time Series:
Start = 97 
End = 108 
Frequency = 1 
 [1] 15.44782 16.14574 16.81472 17.45808 18.07856 18.67844 19.25965 19.82382
 [9] 20.37237 20.90654 21.42739 21.93589

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 97 
End = 108 
Frequency = 1 
 [1]  77.07074  67.97472  83.94982  69.59092  63.09271  89.49424  68.76918
 [8]  68.01783  55.66698 113.75296  62.45898  46.05699
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 97 
End = 108 
Frequency = 1 
 [1] 137.6262 131.2660 149.8635 138.0266 133.9607 162.7137 144.2670 145.7272
 [9] 135.5267 195.7066 146.4544 132.0457
> 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$pred))
  [1] 100.00000 108.15603 114.01503 102.18803 110.36720  96.86025  94.19446
  [8]  99.51622  94.06333  97.55415  78.15062  81.24346  92.36262  96.06324
 [15] 114.05238 110.66167 104.91719  90.00187  95.70081  86.02741  84.85288
 [22] 100.04328  80.91714  74.06540  77.30281  97.23043  90.75516 100.56145
 [29]  92.01293  99.24012 105.86728  90.99205  93.30624  91.17419  77.33295
 [36]  91.12777  85.01250  83.90390 104.86263 110.90391  95.43714 111.62387
 [43] 108.89254  96.17512 101.97402  99.11953  86.78158 118.41950 118.74414
 [50] 106.52962 134.77727 104.67787 105.29543 139.41398 103.60605  99.78183
 [57] 103.46103 120.05949  96.71377 107.13089 105.36084 111.69424 132.05200
 [64] 126.80379 154.48243 141.55710 109.95069 127.90420 133.08886 120.07963
 [71] 117.55571 143.03623 159.98293 128.59911 149.73733 126.81693 140.96397
 [78] 137.66920 117.94023 122.30952 127.78042 136.16772 116.24059 123.15769
 [85] 116.34002 108.61193 125.89823 112.80031 107.51824 135.09554 115.50965
 [92] 115.86408 104.58839 163.72134 113.44823  98.04288 107.34847  99.62037
 [99] 116.90667 103.80875  98.52669 126.10399 106.51809 106.87252  95.59683
[106] 154.72978 104.45667  89.05133
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 97 
End = 108 
Frequency = 1 
 [1] 0.1439035 0.1620727 0.1438303 0.1681754 0.1834890 0.1481194 0.1808110
 [8] 0.1854903 0.2131072 0.1351165 0.2051319 0.2463286
> postscript(file="/var/www/html/rcomp/tmp/1hpix1260537933.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2bpin1260537933.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/3z7vu1260537933.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/4z7jb1260537933.tab") 
> system("convert tmp/1hpix1260537933.ps tmp/1hpix1260537933.png")
> system("convert tmp/2bpin1260537933.ps tmp/2bpin1260537933.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.606   0.331   0.737