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(17848,19592,21092,20899,25890,24965,22225,20977,22897,22785,22769,19637,20203,20450,23083,21738,26766,25280,22574,22729,21378,22902,24989,21116,15169,15846,20927,18273,22538,15596,14034,11366,14861,15149,13577,13026,13190,13196,15826,14733,16307,15703,14589,12043,15057,14053,12698,10888,10045,11549,13767,12434,13116,14211,12266,12602,15714,13742,12745,10491,10057,10900,11771,11992,11933,14504,11727,11477,13578,11555,11846,11397,10066,10269,14279,13870,13695,14420,11424,9704,12464,14301,13464,9893,11572,12380,16692,16052,16459,14761,13654,13480,18068,16560,14530,10650,11651,13735,13360,17818,20613,16231,13862,12004,17734,15034,12609,12320,10833,11350,13648,14890,16325,18045,15616,11926,16855,15083,12520,12355)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '0'
> par6 = '0'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> par1 = '24'
> #'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:
         sma1
      -0.6384
s.e.   0.1240

sigma^2 estimated as 3308536:  log likelihood = -743.91,  aic = 1491.81
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 97 
End = 120 
Frequency = 1 
 [1] 10547.698 11238.219 14571.782 13922.616 14648.893 14286.420 12302.441
 [8] 11535.874 14792.723 14175.991 13106.599 10254.091 10151.788 10842.310
[15] 14175.873 13526.707 14252.984 13890.511 11906.532 11139.964 14396.814
[22] 13780.082 12710.690  9858.182

$se
Time Series:
Start = 97 
End = 120 
Frequency = 1 
 [1]  1819.946  2573.370  3151.549  3638.996  4068.454  4456.719  4813.769
 [8]  5146.106  5458.245  5753.474  6034.276  6302.580  6772.553  7211.513
[15]  7625.244  8017.655  8391.735  8749.838  9093.849  9425.313  9745.510
[22] 10055.516 10356.246 10648.487

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 97 
End = 120 
Frequency = 1 
 [1]   6980.6036   6194.4144   8394.7461   6790.1849   6674.7234   5551.2505
 [7]   2867.4533   1449.5063   4094.5635   2899.1820   1279.4178  -2098.9666
[13]  -3122.4160  -3292.2547   -769.6059  -2187.8959  -2194.8172  -3259.1705
[19]  -5917.4124  -7333.6496  -4704.3861  -5928.7297  -7587.5526 -11012.8527
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 97 
End = 120 
Frequency = 1 
 [1] 14114.79 16282.02 20748.82 21055.05 22623.06 23021.59 21737.43 21622.24
 [9] 25490.88 25452.80 24933.78 22607.15 23425.99 24976.87 29121.35 29241.31
[17] 30700.79 31040.19 29730.48 29613.58 33498.01 33488.89 33008.93 30729.22
> 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$pred))
  [1] 17848.000 19592.000 21092.000 20899.000 25890.000 24965.000 22225.000
  [8] 20977.000 22897.000 22785.000 22769.000 19637.000 20203.000 20450.000
 [15] 23083.000 21738.000 26766.000 25280.000 22574.000 22729.000 21378.000
 [22] 22902.000 24989.000 21116.000 15169.000 15846.000 20927.000 18273.000
 [29] 22538.000 15596.000 14034.000 11366.000 14861.000 15149.000 13577.000
 [36] 13026.000 13190.000 13196.000 15826.000 14733.000 16307.000 15703.000
 [43] 14589.000 12043.000 15057.000 14053.000 12698.000 10888.000 10045.000
 [50] 11549.000 13767.000 12434.000 13116.000 14211.000 12266.000 12602.000
 [57] 15714.000 13742.000 12745.000 10491.000 10057.000 10900.000 11771.000
 [64] 11992.000 11933.000 14504.000 11727.000 11477.000 13578.000 11555.000
 [71] 11846.000 11397.000 10066.000 10269.000 14279.000 13870.000 13695.000
 [78] 14420.000 11424.000  9704.000 12464.000 14301.000 13464.000  9893.000
 [85] 11572.000 12380.000 16692.000 16052.000 16459.000 14761.000 13654.000
 [92] 13480.000 18068.000 16560.000 14530.000 10650.000 10547.698 11238.219
 [99] 14571.782 13922.616 14648.893 14286.420 12302.441 11535.874 14792.723
[106] 14175.991 13106.599 10254.091 10151.788 10842.310 14175.873 13526.707
[113] 14252.984 13890.511 11906.532 11139.964 14396.814 13780.082 12710.690
[120]  9858.182
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 97 
End = 120 
Frequency = 1 
 [1] 0.1725444 0.2289838 0.2162775 0.2613730 0.2777312 0.3119549 0.3912857
 [8] 0.4460959 0.3689817 0.4058604 0.4603998 0.6146406 0.6671291 0.6651270
[15] 0.5379030 0.5927277 0.5887704 0.6299147 0.7637698 0.8460811 0.6769213
[22] 0.7297138 0.8147666 1.0801674
> postscript(file="/var/www/html/rcomp/tmp/14c3j1292072378.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2tv0c1292072378.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/30xxo1292072378.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/43xec1292072378.tab") 
> 
> try(system("convert tmp/14c3j1292072378.ps tmp/14c3j1292072378.png",intern=TRUE))
character(0)
> try(system("convert tmp/2tv0c1292072378.ps tmp/2tv0c1292072378.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.717   0.412   1.715