intraday volatility

I have a question regarding calculating the intraday volatility.

I have a dataset that is sub minute, and about 2-3k long.

The normal calculation would be
sigma = sd(diff(log(data)))
but when producing a GBM w.o drift, the process is way out of scale of what
I would expect.

any comments? or hints for calculating the intraday vol. adjusted for my
timescale?

What you see is typical for high frequency data.  See the package 
'realized' and the references therein for more information on the 
literature regarding volatility calculations on high frequency data.

Regards,

   - Brian

Brian G. Peterson
http://braverock.com/brian/
Ph: 773-459-4973
IM: bgpbraverock

Andres Susrud <andres.susrud at gmail.com> [2010-10-28 06:06]:

I have a question regarding calculating the intraday volatility.

I have a dataset that is sub minute, and about 2-3k long.

The normal calculation would be
sigma = sd(diff(log(data)))
but when producing a GBM w.o drift, the process is way out of scale of what
I would expect.

As Brian noted, noise is predominant in HF data. The URLs below
link to a recent (2010) paper on the problem. Google will turn up
a free draft version of the paper.

http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VC0-4YJ6GKX-G&_user=10&_coverDate=03%2F06%2F2010&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1517805192&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=9311c44ddcdeb2111516631a7781fc0b&searchtype=a

http://tinyurl.com/2bsrd9b

-rex

Impartial, adj.:
        Unable to perceive any promise of personal advantage from
        espousing either side of a controversy or adopting either of two
        conflicting opinions.
                -- Ambrose Bierce, "The Devil's Dictionary"

rex <rex at nosyntax.net> [2010-10-28 07:09]:

As Brian noted, noise is predominant in HF data. The URLs below
link to a recent (2010) paper on the problem. Google will turn up
a free draft version of the paper.

The URLs fail. :( Here's a reference:

Ultra High Frequency Volatility Estimation with Dependent
Microstructure Noise
Yacine Ait-Sahalia, Per A. Mykland, Lan Zhang
First Draft: November 2004. This Version: October 28, 2008.
                    Abstract
We analyze the impact of time series dependence in market
microstructure noise on the properties of estimators of the
integrated volatility of an asset price based on data sampled at
frequencies high enough for that noise to be a dominant
consideration. We show that combining two time scales for that
purpose will work even when the noise exhibits time series
dependence, analyze in that context a refinement of this approach
based on multiple time scales, and compare empirically our
different estimators to the standard realized volatility.

Google Scholar advanced search ( author:Mykland) will find the
full text.

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.143.972&rep=rep1&type=pdf

(Tested, it works in FF.)

-rex

Mathematician: noun, someone who disavows certainty when their
uncertainty set is non-empty, even if that set has measure zero.