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

[michael.sankowski at gmail.com]

Also be aware that while the square of time may hold, you need to start thinking about the whole day once you go to sub daily intervals. 

Should you include the time from 5pm to the open of the asian markets?  If you do your result will be artifically low. If not you will exclude data that could be informative. 
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-----Original Message-----
From: "Brian G. Peterson" <brian at braverock.com>

Date: Fri, 10 Oct 2008 16:28:45 
To: Shane Conway<shane.conway at gmail.com>
Cc: <r-sig-finance at stat.math.ethz.ch>; Chiquoine, Ben<BChiquoine at tiff.org>
Subject: Re: [R-SIG-Finance] Scaling risk for irregularly spaced time series?


Eric Zivot has previously posted some research to this list about 
intraday implied and realized volatility.  Scaling volatility using the 
square root of time rule assumes independent observations, something 
which is often not true on shorter time spans.

As for your question on irregularly spaced data, yes, in most cases, 
some method of regularizing the data is used to create a regular series 
to do other scaling calculations on.  While this can introduce problems, 
as long as you're aware of things like day/week boundaries, then you're 
usually OK. 

I definitely suggest that you take a look at some of Eric's earlier 
posts on this topic, and maybe some of the other literature on intraday 
volatility.

Regards,

   - Brian

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


Shane Conway wrote:
> 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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