garch() uncertainty

May 16, 2012

(This article was first published on Xi'an's Og » R, and kindly contributed to R-bloggers)

As part of an on-going paper with Kerrie Mengersen and Pierre Pudlo, we are using a GARCH(1,1) model as a target. Thus, the model is of the form

y_t=\sigma_t \epsilon_t \qquad \sigma^2_t = \alpha_0 + \alpha_1 y_{t-1}^2 + \beta_1 \sigma_{t-1}^2

which is a somehow puzzling object: the latent (variance) part is deterministic and can be reconstructed exactly given the series and the parameters. However, estimation is not such an easy task and using the garch() function in the tseries package leads to puzzling results! Indeed, simulating data shows some high variability of the procedure against starting values:


   for (t in 2:nobs){
> x = genedata(c(1, 0.3, 0.2),1000)$pata
> garch(x,trace=FALSE)

garch(x = x, trace = FALSE)

       a0         a1         b1
4.362e+00  1.976e-01  6.805e-14
> garch(x,trace=FALSE,start=c(1,.3,.2))

garch(x = x, trace = FALSE, start = c(1, 0.3, 0.2))

    a0      a1      b1
0.8025  0.2592  0.3255
> simgarch=genedata(c(1, 0.2, 0.7),1000)

garch(x = simgarch$pat, trace = FALSE)

a0         a1         b1
8.044e+00  1.826e-01  4.051e-14
> garch(simgarch$pat,trace=FALSE,star=c(1, 0.2, 0.7))

garch(x = simgarch$pat, trace = FALSE, star = c(1, 0.2, 0.7))

a0      a1      b1
1.1814  0.2079  0.6590

The above code clearly shows the huge impact of the starting value on the final estimate….

Filed under: R, Statistics, University life Tagged: GARCH, R, times series, tseries

To leave a comment for the author, please follow the link and comment on their blog: Xi'an's Og » R. offers daily e-mail updates about R news and tutorials on topics such as: Data science, Big Data, R jobs, visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...

If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Tags: , , , , ,

Comments are closed.


Mango solutions

RStudio homepage

Zero Inflated Models and Generalized Linear Mixed Models with R

Quantide: statistical consulting and training


CRC R books series

Contact us if you wish to help support R-bloggers, and place your banner here.

Never miss an update!
Subscribe to R-bloggers to receive
e-mails with the latest R posts.
(You will not see this message again.)

Click here to close (This popup will not appear again)