[R-SIG-Finance] Interpolating/comparing two irregulartime/price sequences?

[Adrian Trapletti]

It really depends on the application what methods are appropriate. 
Possibilities include interpolation schemes (linear, previous tick, 
other), modelling in a framework that allows missing values (e.g. state 
space and Kalman filter), model prices/changes and time increments (e.g. 
Rob Engle published some work in this area).

For exmple, when important macro announcements are released, liquid 
instruments are traded immediately and the prices adjust very quickly 
(within less than a 1/10th of a second) to the new information. For less 
liquid instruments there is maybe for a longer time (several seconds up 
to several minutes) no trade. However, that does not mean that the price 
for the less liquid instrument did not update (you cannot trade anymore 
on the last observed price). It just means that there is no observation. 
Previous tick interpolation would lead to wrong conclusions (spurious 
lead/lag) in this example.

There is a lot of research in high-frequency finance in the hedge fund 
and investment bank industry (e.g. algorithmic trading, automatic market 
making). However, due to the nature of the business most is proprietary 
research.

Best regards
Adrian

Rory Winston wrote:

>Thanks everyone for their extremely helpful comments on this issue.
>Eric, that is a very interesting point you have raised. Did Peter
>publish a paper on this topic? If so, do you happen to know the
>title? I feel intuitively that the previous tick method should be more
>reliable than interpolation for high-frequency data, although it would
>be nice to see some research on this topic confirming this to be the
>case.
>
>Thanks
>Rory
>
>
>On Nov 8, 2007 9:33 PM, Eric Zivot <ezivot at u.washington.edu> wrote:
>  
>
>>Just a few quick comments on this issue
>>
>>The Olsen group book, Introduction to High Frequency Finance, discusses
>>various interpolation schemes to align multiple irregularly spaced data. For
>>realized variance modeling Peter Hansen at Stanford showed that one should
>>use the "previous tick" method for aligning data to a common time clock and
>>not an linear interpolation around neighboring ticks. The latter method
>>leads to degenerate results as you sample more frequently since the
>>quadratic variation of a line is zero.
>>
>>The type of alignment discussed below is handled in the timeSeries class in
>>S-PLUS using the align() function. Diethelm Wuertz implemented a subset of
>>this class in R and I think the align() function is there too.
>>
>>
>> ________________________________
>> From: r-sig-finance-bounces at stat.math.ethz.ch
>>[mailto:r-sig-finance-bounces at stat.math.ethz.ch] On Behalf Of Adrian
>>Trapletti
>>Sent: Thursday, November 08, 2007 3:37 AM
>>To: rory.winston at gmail.com
>>Cc: R-Finance
>>Subject: Re: [R-SIG-Finance] Interpolating/comparing two irregulartime/price
>>sequences?
>>
>>
>>
>>Rory,
>>
>>There is no best method for synchronizing high frequency data. It depends on
>>the application. One of the pioneers for high frequency financial data
>>modelling was http://www.olsen.ch . In the 90ies they published some
>>articles where they used interpolation schemes to model irregularly spaced
>>high frequency data with standard discrete time series methods. You can find
>>some articles on their website. Currently, there is a lot of work on the
>>topic realized variance/volatility, and when it comes to multivariate
>>applications, you may find some methods there
>>http://www.google.ch/search?hl=en&q=%22realized+covariance%22&btnG=Search&meta=
>>
>>Best regards
>>Adrian
>>
>>
>>
>>Message: 1
>>Date: Wed, 7 Nov 2007 18:31:16 +0000
>>From: "Rory Winston" <rory.winston at gmail.com>
>>Subject: [R-SIG-Finance] Interpolating/comparing two irregular
>> time/price sequences?
>>To: r-sig-finance at stat.math.ethz.ch
>>Message-ID:
>> <3f446aa30711071031j37936e36i933be63c90f9ce4c at mail.gmail.com>
>>Content-Type: text/plain; charset=ISO-8859-1
>>
>>Hi all
>>
>>I have two data frames, that both look like the following:
>>
>>
>>
>>    
>>
>>>head(series1)
>>>      
>>>
>> timestamp mid spread
>>1 1.194438e+12 2.10011 0.000260
>>2 1.194438e+12 2.10010 0.000290
>>...
>>
>>These two time sequences are sampled on price ticks, so the interval
>>between ticks is stochastic and irregular. The time sequences are also
>>of different lengths, i.e. one may have 8 hours worth of data, the
>>other may have 4. My issue is that I want to compare these two series
>>for similarity - they should be producing almost exactly the same
>>data, although potentially at slightly different timestamps (hence the
>>sampling irregularity). I can subset the data so that they span
>>roughly the same time intervals, but the number of ticks in each
>>series will be different. Basically what I am trying to achieve is
>>some sort of constant interpolation based on a time index - so that if
>>series A starts at 08:01, contains 10,000 ticks, and ends at 16:05,
>>and series B starts at 08:00, contains 7,000 ticks, and ends at 16:06,
>>I would like to be able to index from series A into series B at say,
>>each timestamp in A. Using a simple example, for the following series
>>A and B:
>>
>>A:
>>time tick
>>16:01 2.05
>>16:02 2.06
>>
>>
>>B:
>>time tick
>>16:00 2.04
>>16:02 2.06
>>
>>I would like to be able to index from A into B at each tick from A, so
>>I would get an output series that was the value of B at each time A
>>ticked:
>>
>>C
>>time tick
>>16:01 2.04 <--- constant interpolation from value of B @ 16:00
>>16:02 2.06
>>
>>Has anyone done anything like this before? I'm looking at the zoo
>>package to see if it can help me, but I havent quite figured out how
>>to do this kind of thing yet. Is this even a good way to checking
>>whether series B is very similar to series A at the discrete tick
>>intervals? Any better methods?(I guess another way might be to align
>>the two subsetted series exactly and just take differences).
>>
>>Thanks
>>Rory
>>
>>
>>
>>
>>
>>--
>>Adrian Trapletti
>>Wildsbergstrasse 31
>>8610 Uster
>>Switzerland
>>
>>Phone : +41 (0) 44 9945630
>>Mobile : +41 (0) 76 3705631
>>
>>Email : a.trapletti at swissonline.ch
>>
>>
>>    
>>
>
>  
>

-- 
Adrian Trapletti
Wildsbergstrasse 31
8610 Uster
Switzerland

Phone :   +41 (0) 44 9945630
Mobile :  +41 (0) 76 3705631

Email :   a.trapletti at swissonline.ch