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(451,450,444,429,421,400,389,384,432,446,431,423,416,416,413,399,386,374,365,365,418,428,424,421,417,423,423,419,406,398,390,391,444,460,455,456,452,459,461,451,443,439,430,436,488,506,502,501,501,515,521,520,512,509,505,511,570,592,594,586,586,592,594,586,572,563,555,554,601,622,617,606,595,599,600,592,575,567,555,555,608,631,629,624,610,616,621,604,584,574,555,545,599,620,608,590,579,580,579,572,560,551,537,541,588,607,599,578,563,566,561,554,540,526,512,505,554,584,569,540,522,526,527,516,503,489,479,475,524,552,532,511,492,492,493,481,462,457,442,439,488,521,501,485,464,460,467,460,448,443,436,431,484,510,513,503,471,471,476,475,470,461,455,456,517,525,523,519,509,512,519,517,510,509,501,507,569,580,578,565,547,555,562,561,555,544,537,543,594,611,613,611,594,595,591,589,584,573,567,569,621,629,628,612,595,597,593,590,580,574,573,573,620,626,620,588,566,557,561,549,532,526,511,499,555,565,542,527,510,514,517,508,493,490,469,478,528,534,518,506,502)
> par20 = ''
> par19 = ''
> par18 = ''
> par17 = ''
> par16 = ''
> par15 = ''
> par14 = ''
> par13 = ''
> par12 = ''
> par11 = ''
> par10 = 'FALSE'
> par9 = '1'
> par8 = '2'
> par7 = '0'
> par6 = '0'
> 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:
        sar1    sar2     sma1
      0.5277  0.0439  -0.9999
s.e.  0.0749  0.0791   0.0991

sigma^2 estimated as 30.95:  log likelihood = -687.71,  aic = 1383.41
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 230 
End = 241 
Frequency = 1 
 [1] 506.0805 508.4387 498.4543 484.0170 476.5947 464.3524 457.2827 511.3028
 [9] 524.1810 508.0851 493.5491 477.8996

$se
Time Series:
Start = 230 
End = 241 
Frequency = 1 
 [1]  5.688430  8.044655  9.852650 11.376860 12.719716 13.933751 15.050171
 [8] 16.089309 17.065289 17.988394 18.866387 19.705298

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 230 
End = 241 
Frequency = 1 
 [1] 494.9312 492.6712 479.1431 461.7183 451.6640 437.0423 427.7843 479.7678
 [9] 490.7330 472.8279 456.5710 439.2772
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 230 
End = 241 
Frequency = 1 
 [1] 517.2298 524.2062 517.7655 506.3156 501.5253 491.6626 486.7810 542.8378
 [9] 557.6289 543.3424 530.5272 516.5220
> 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] 451.0000 450.0000 444.0000 429.0000 421.0000 400.0000 389.0000 384.0000
  [9] 432.0000 446.0000 431.0000 423.0000 416.0000 416.0000 413.0000 399.0000
 [17] 386.0000 374.0000 365.0000 365.0000 418.0000 428.0000 424.0000 421.0000
 [25] 417.0000 423.0000 423.0000 419.0000 406.0000 398.0000 390.0000 391.0000
 [33] 444.0000 460.0000 455.0000 456.0000 452.0000 459.0000 461.0000 451.0000
 [41] 443.0000 439.0000 430.0000 436.0000 488.0000 506.0000 502.0000 501.0000
 [49] 501.0000 515.0000 521.0000 520.0000 512.0000 509.0000 505.0000 511.0000
 [57] 570.0000 592.0000 594.0000 586.0000 586.0000 592.0000 594.0000 586.0000
 [65] 572.0000 563.0000 555.0000 554.0000 601.0000 622.0000 617.0000 606.0000
 [73] 595.0000 599.0000 600.0000 592.0000 575.0000 567.0000 555.0000 555.0000
 [81] 608.0000 631.0000 629.0000 624.0000 610.0000 616.0000 621.0000 604.0000
 [89] 584.0000 574.0000 555.0000 545.0000 599.0000 620.0000 608.0000 590.0000
 [97] 579.0000 580.0000 579.0000 572.0000 560.0000 551.0000 537.0000 541.0000
[105] 588.0000 607.0000 599.0000 578.0000 563.0000 566.0000 561.0000 554.0000
[113] 540.0000 526.0000 512.0000 505.0000 554.0000 584.0000 569.0000 540.0000
[121] 522.0000 526.0000 527.0000 516.0000 503.0000 489.0000 479.0000 475.0000
[129] 524.0000 552.0000 532.0000 511.0000 492.0000 492.0000 493.0000 481.0000
[137] 462.0000 457.0000 442.0000 439.0000 488.0000 521.0000 501.0000 485.0000
[145] 464.0000 460.0000 467.0000 460.0000 448.0000 443.0000 436.0000 431.0000
[153] 484.0000 510.0000 513.0000 503.0000 471.0000 471.0000 476.0000 475.0000
[161] 470.0000 461.0000 455.0000 456.0000 517.0000 525.0000 523.0000 519.0000
[169] 509.0000 512.0000 519.0000 517.0000 510.0000 509.0000 501.0000 507.0000
[177] 569.0000 580.0000 578.0000 565.0000 547.0000 555.0000 562.0000 561.0000
[185] 555.0000 544.0000 537.0000 543.0000 594.0000 611.0000 613.0000 611.0000
[193] 594.0000 595.0000 591.0000 589.0000 584.0000 573.0000 567.0000 569.0000
[201] 621.0000 629.0000 628.0000 612.0000 595.0000 597.0000 593.0000 590.0000
[209] 580.0000 574.0000 573.0000 573.0000 620.0000 626.0000 620.0000 588.0000
[217] 566.0000 557.0000 561.0000 549.0000 532.0000 526.0000 511.0000 499.0000
[225] 555.0000 565.0000 542.0000 527.0000 510.0000 506.0805 508.4387 498.4543
[233] 484.0170 476.5947 464.3524 457.2827 511.3028 524.1810 508.0851 493.5491
[241] 477.8996
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 230 
End = 241 
Frequency = 1 
 [1] 0.01124017 0.01582227 0.01976641 0.02350508 0.02668875 0.03000684
 [7] 0.03291218 0.03146728 0.03255610 0.03540429 0.03822596 0.04123313
> postscript(file="/var/www/html/rcomp/tmp/1heeu1229960804.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/24nas1229960804.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/3wmej1229960804.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/4nzs21229960804.tab") 
> 
> system("convert tmp/1heeu1229960804.ps tmp/1heeu1229960804.png")
> system("convert tmp/24nas1229960804.ps tmp/24nas1229960804.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.776   0.336   1.896