R version 2.8.0 (2008-10-20)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(1775,2197,2920,4240,5415,6136,6719,6234,7152,3646,2165,2803,1615,2350,3350,3536,5834,6767,5993,7276,5641,3477,2247,2466,1567,2237,2598,3729,5715,5776,5852,6878,5488,3583,2054,2282,1552,2261,2446,3519,5161,5085,5711,6057,5224,3363,1899,2115,1491,2061,2419,3430,4778,4862,6176,5664,5529,3418,1941,2402,1579,2146,2462,3695,4831,5134,6250,5760,6249,2917,1741,2359,1511,2059,2635,2867,4403,5720,4502,5749,5627,2846,1762,2429,1169,2154,2249,2687,4359,5382,4459,6398,4596,3024,1887,2070,1351,2218,2461,3028,4784,4975,4607,6249,4809,3157,1910,2228,1594,2467,2222,3607,4685,4962,5770,5480,5000,3228,1993,2288,1588,2105,2191,3591,4668,4885,5822,5599,5340,3082,2010,2301)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '3'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> par2 = '0.0'
> 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#output/
> #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     ar2     ar3      ma1     sma1
      -0.0552  0.2748  0.6330  -0.1633  -0.6349
s.e.   0.1229  0.0710  0.0832   0.1733   0.1027

sigma^2 estimated as 0.005399:  log likelihood = 124.99,  aic = -237.99
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 121 
End = 132 
Frequency = 1 
 [1] 7.314747 7.767992 7.787049 8.116678 8.481218 8.563606 8.582716 8.703338
 [9] 8.549009 8.076004 7.577596 7.740748

$se
Time Series:
Start = 121 
End = 132 
Frequency = 1 
 [1] 0.07348031 0.07521431 0.07811224 0.08818888 0.08843791 0.09189261
 [7] 0.09465784 0.09466819 0.09718273 0.09812273 0.09831695 0.09982495

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 121 
End = 132 
Frequency = 1 
 [1] 7.170725 7.620572 7.633949 7.943828 8.307880 8.383497 8.397187 8.517789
 [9] 8.358531 7.883683 7.384895 7.545091
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 121 
End = 132 
Frequency = 1 
 [1] 7.458768 7.915412 7.940149 8.289528 8.654556 8.743716 8.768246 8.888888
 [9] 8.739487 8.268324 7.770298 7.936405
> 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$pred))
  [1] 1775.000 2197.000 2920.000 4240.000 5415.000 6136.000 6719.000 6234.000
  [9] 7152.000 3646.000 2165.000 2803.000 1615.000 2350.000 3350.000 3536.000
 [17] 5834.000 6767.000 5993.000 7276.000 5641.000 3477.000 2247.000 2466.000
 [25] 1567.000 2237.000 2598.000 3729.000 5715.000 5776.000 5852.000 6878.000
 [33] 5488.000 3583.000 2054.000 2282.000 1552.000 2261.000 2446.000 3519.000
 [41] 5161.000 5085.000 5711.000 6057.000 5224.000 3363.000 1899.000 2115.000
 [49] 1491.000 2061.000 2419.000 3430.000 4778.000 4862.000 6176.000 5664.000
 [57] 5529.000 3418.000 1941.000 2402.000 1579.000 2146.000 2462.000 3695.000
 [65] 4831.000 5134.000 6250.000 5760.000 6249.000 2917.000 1741.000 2359.000
 [73] 1511.000 2059.000 2635.000 2867.000 4403.000 5720.000 4502.000 5749.000
 [81] 5627.000 2846.000 1762.000 2429.000 1169.000 2154.000 2249.000 2687.000
 [89] 4359.000 5382.000 4459.000 6398.000 4596.000 3024.000 1887.000 2070.000
 [97] 1351.000 2218.000 2461.000 3028.000 4784.000 4975.000 4607.000 6249.000
[105] 4809.000 3157.000 1910.000 2228.000 1594.000 2467.000 2222.000 3607.000
[113] 4685.000 4962.000 5770.000 5480.000 5000.000 3228.000 1993.000 2288.000
[121] 1502.291 2363.720 2409.197 3349.874 4823.321 5237.535 5338.587 6022.985
[129] 5161.638 3216.354 1953.927 2300.193
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 121 
End = 132 
Frequency = 1 
 [1] 0.07903512 0.08104113 0.08440893 0.09626941 0.09656550 0.10068800
 [7] 0.10400793 0.10402040 0.10705507 0.10819336 0.10842881 0.11025999
> postscript(file="/var/www/html/freestat/rcomp/tmp/14t7w1292941542.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/freestat/rcomp/tmp/2aum71292941542.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/freestat/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/freestat/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/freestat/rcomp/tmp/3hdj11292941542.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/freestat/rcomp/tmp/42ehp1292941542.tab") 
> try(system("convert tmp/14t7w1292941542.ps tmp/14t7w1292941542.png",intern=TRUE))
character(0)
> try(system("convert tmp/2aum71292941542.ps tmp/2aum71292941542.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.703   0.450   1.775