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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Type 'demo()' for some demos, 'help()' for on-line help, or
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Type 'q()' to quit R.

> x <- c(349
+ ,336
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+ ,558)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '1'
> par7 = '2'
> par6 = '3'
> par5 = '1'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> par1 = '12'
> 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 <- 3
> 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      ma2     ma3     sar1     sma1
      1.5123  -0.6641  -0.1472  -1.2426  -0.0715  0.5598  -0.1595  -0.9463
s.e.  0.1965   0.3279   0.1834   0.0931   0.1612  0.0857   0.1972   0.0189

sigma^2 estimated as 242.7:  log likelihood = -1440.63,  aic = 2899.26
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 348 
End = 359 
Frequency = 1 
 [1] 489.2535 473.8027 463.5648 458.7874 460.0826 466.0276 474.1903 481.7216
 [9] 486.1412 485.9479 480.9380 472.1653

$se
Time Series:
Start = 348 
End = 359 
Frequency = 1 
 [1] 15.58022 23.90804 27.54769 29.70024 30.94252 31.90291 33.02234 34.74752
 [9] 37.49201 41.40458 46.20895 51.33137

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 348 
End = 359 
Frequency = 1 
 [1] 458.7163 426.9429 409.5713 400.5749 399.4353 403.4979 409.4666 413.6164
 [9] 412.6568 404.7949 390.3685 371.5559
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 348 
End = 359 
Frequency = 1 
 [1] 519.7908 520.6625 517.5583 516.9999 520.7299 528.5573 538.9141 549.8267
 [9] 559.6255 567.1009 571.5076 572.7748
> 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] 349.0000 336.0000 331.0000 327.0000 323.0000 322.0000 385.0000 405.0000
  [9] 412.0000 411.0000 410.0000 415.0000 414.0000 411.0000 408.0000 410.0000
 [17] 411.0000 416.0000 479.0000 498.0000 502.0000 498.0000 499.0000 506.0000
 [25] 510.0000 509.0000 502.0000 495.0000 490.0000 490.0000 553.0000 570.0000
 [33] 573.0000 572.0000 575.0000 580.0000 580.0000 574.0000 563.0000 556.0000
 [41] 546.0000 545.0000 605.0000 628.0000 631.0000 626.0000 614.0000 606.0000
 [49] 602.0000 589.0000 574.0000 558.0000 552.0000 546.0000 607.0000 636.0000
 [57] 631.0000 623.0000 618.0000 605.0000 619.0000 596.0000 570.0000 546.0000
 [65] 528.0000 506.0000 555.0000 568.0000 564.0000 553.0000 541.0000 542.0000
 [73] 540.0000 521.0000 505.0000 491.0000 482.0000 478.0000 523.0000 531.0000
 [81] 532.0000 540.0000 525.0000 533.0000 531.0000 508.0000 495.0000 482.0000
 [89] 470.0000 466.0000 515.0000 518.0000 516.0000 511.0000 500.0000 498.0000
 [97] 494.0000 476.0000 458.0000 443.0000 430.0000 424.0000 476.0000 481.0000
[105] 470.0000 460.0000 451.0000 450.0000 444.0000 429.0000 421.0000 400.0000
[113] 389.0000 384.0000 432.0000 446.0000 431.0000 423.0000 416.0000 416.0000
[121] 413.0000 399.0000 386.0000 374.0000 365.0000 365.0000 418.0000 428.0000
[129] 424.0000 421.0000 417.0000 423.0000 423.0000 419.0000 406.0000 398.0000
[137] 390.0000 391.0000 444.0000 460.0000 455.0000 456.0000 452.0000 459.0000
[145] 461.0000 451.0000 443.0000 439.0000 430.0000 436.0000 488.0000 506.0000
[153] 502.0000 501.0000 501.0000 515.0000 521.0000 520.0000 512.0000 509.0000
[161] 505.0000 511.0000 570.0000 592.0000 594.0000 586.0000 586.0000 592.0000
[169] 594.0000 586.0000 572.0000 563.0000 555.0000 554.0000 601.0000 622.0000
[177] 617.0000 606.0000 595.0000 599.0000 600.0000 592.0000 575.0000 567.0000
[185] 555.0000 555.0000 608.0000 631.0000 629.0000 624.0000 610.0000 616.0000
[193] 621.0000 604.0000 584.0000 574.0000 555.0000 545.0000 599.0000 620.0000
[201] 608.0000 590.0000 579.0000 580.0000 579.0000 572.0000 560.0000 551.0000
[209] 537.0000 541.0000 588.0000 607.0000 599.0000 578.0000 563.0000 566.0000
[217] 561.0000 554.0000 540.0000 526.0000 512.0000 505.0000 554.0000 584.0000
[225] 569.0000 540.0000 522.0000 526.0000 527.0000 516.0000 503.0000 489.0000
[233] 479.0000 475.0000 524.0000 552.0000 532.0000 511.0000 492.0000 492.0000
[241] 493.0000 481.0000 462.0000 457.0000 442.0000 439.0000 488.0000 521.0000
[249] 501.0000 485.0000 464.0000 460.0000 467.0000 460.0000 448.0000 443.0000
[257] 436.0000 431.0000 484.0000 510.0000 513.0000 503.0000 471.0000 471.0000
[265] 476.0000 475.0000 470.0000 461.0000 455.0000 456.0000 517.0000 525.0000
[273] 523.0000 519.0000 509.0000 512.0000 519.0000 517.0000 510.0000 509.0000
[281] 501.0000 507.0000 569.0000 580.0000 578.0000 565.0000 547.0000 555.0000
[289] 562.0000 561.0000 555.0000 544.0000 537.0000 543.0000 594.0000 611.0000
[297] 613.0000 611.0000 594.0000 595.0000 591.0000 589.0000 584.0000 573.0000
[305] 567.0000 569.0000 621.0000 629.0000 628.0000 612.0000 595.0000 597.0000
[313] 593.0000 590.0000 580.0000 574.0000 573.0000 573.0000 620.0000 626.0000
[321] 620.0000 588.0000 566.0000 557.0000 561.0000 549.0000 532.0000 526.0000
[329] 511.0000 499.0000 555.0000 565.0000 542.0000 527.0000 510.0000 514.0000
[337] 517.0000 508.0000 493.0000 490.0000 469.0000 478.0000 528.0000 534.0000
[345] 518.0000 506.0000 502.0000 489.2535 473.8027 463.5648 458.7874 460.0826
[353] 466.0276 474.1903 481.7216 486.1412 485.9479 480.9380 472.1653
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 348 
End = 359 
Frequency = 1 
 [1] 0.03184488 0.05045991 0.05942577 0.06473639 0.06725426 0.06845712
 [7] 0.06963942 0.07213195 0.07712165 0.08520374 0.09608088 0.10871482
> postscript(file="/var/www/html/rcomp/tmp/1f9ln1260741792.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2aesd1260741792.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/33e3t1260741792.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/4skbg1260741792.tab") 
> 
> try(system("convert tmp/1f9ln1260741792.ps tmp/1f9ln1260741792.png",intern=TRUE))
character(0)
> try(system("convert tmp/2aesd1260741792.ps tmp/2aesd1260741792.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.417   0.331   1.593