[R-SIG-Finance] Scaling risk for irregularly spaced time series?

[Eric Zivot]

There is ia huge literature on calculating daily volatility using
irregularly spaced intra-day data. This literature is called "realized
variance". Go to Neil Shephard's website at Oxford and you can learn all
about it. I have some introductory lectures on this subject on my website

http://faculty.washington.edu/ezivot/econ512/econ512.htm

Typically, people align intra-day data to a regular time clock (e.g every 5
seconds or every 15 seconds) prior to analysis. This simplifies calculations
and using irregularly spaced data does not necessarily better results. To
get good results you should use kernel type estimators or use subsampling
techniques. My former Phd student Scott Payseur has implemented most of
realized variance techniques in his realized package on CRAN.


-----Original Message-----
From: r-sig-finance-bounces at stat.math.ethz.ch
[mailto:r-sig-finance-bounces at stat.math.ethz.ch] On Behalf Of Shane Conway
Sent: Friday, October 10, 2008 2:16 PM
To: Chiquoine, Ben
Cc: r-sig-finance at stat.math.ethz.ch
Subject: Re: [R-SIG-Finance] Scaling risk for irregularly spaced time
series?

Thanks!

That's my problem: I can't rely on the observations being evenly spaced
(hence my reference to "irregularly spaced").  Do most people interpolate
their data so that it's regularly spaced first, and if so, won't that also
bias the calculation?

Any suggestions for how to produce a daily volatility calculation using an
irregularly spaced intraday time series?  I'm not married to using the
square-root rule if there's a better alternative...


On Fri, Oct 10, 2008 at 5:06 PM, Chiquoine, Ben <BChiquoine at tiff.org> wrote:
> I believe Davids suggestion is correct if your 8 hours are consecutive.
> This may be pointing out the obvious but if your observations are 
> unevenly separated throughout the day your return series will not be 
> hourly and if there is mean reversion or momentum (evidence of both 
> have been found in fx data depending on the frequency of observation) 
> your results will be biased.  Unfortunately I don't have a better way 
> for you to approach the problem this is just a heads up
>
> Good luck,
>
> Ben
>
> -----Original Message-----
> From: r-sig-finance-bounces at stat.math.ethz.ch
> [mailto:r-sig-finance-bounces at stat.math.ethz.ch] On Behalf Of 
> davidr at rhotrading.com
> Sent: Friday, October 10, 2008 4:52 PM
> To: Shane Conway; r-sig-finance at stat.math.ethz.ch
> Subject: Re: [R-SIG-Finance] Scaling risk for irregularly spaced time 
> series?
>
> You basically said it: scale by the 'activity'.
> If you are measuring activity for 8 hours and that is your day, then 
> sigma{1 hour} * sqrt(8) is your daily vol, assuming lots of untrue 
> things, of course ;-)
>
> -- David
>
> -----Original Message-----
> From: r-sig-finance-bounces at stat.math.ethz.ch
> [mailto:r-sig-finance-bounces at stat.math.ethz.ch] On Behalf Of Shane 
> Conway
> Sent: Friday, October 10, 2008 3:41 PM
> To: r-sig-finance at stat.math.ethz.ch
> Subject: [R-SIG-Finance] Scaling risk for irregularly spaced time 
> series?
>
> I'm working with intraday FX price data (primarily hourly bars).  I 
> want to scale my volatility calculations up to the daily level.
> Ordinarily I would us the square-root-of-time rule and multiple by the 
> sqrt(T).
>
> The question is: how do people deal with this scaling factor when the 
> time series is irregularly spaced?  If I apply sqrt(24) for hourly 
> data but I only have 8 hours of data (for instance), my calculation 
> will be way off.
>
> Thanks,
> Shane
>
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