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@stat.math.ethz.ch
[mailto:r-sig-finance-bounces@stat.math.ethz.ch] On Behalf Of Adrian
Trapletti
Sent: Thursday, November 08, 2007 3:37 AM
To: rory.winston@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
<http://www.google.ch/search?hl=en&q=%22realized+covariance%22&btnG=Search&m
eta=> &q=%22realized+covariance%22&btnG=Search&meta=

Best regards
Adrian




Message: 1

Date: Wed, 7 Nov 2007 18:31:16 +0000

From: "Rory Winston"  <mailto:rory.winston@gmail.com>
<rory.winston@gmail.com>

Subject: [R-SIG-Finance] Interpolating/comparing two irregular

	time/price	sequences?

To: r-sig-finance@stat.math.ethz.ch

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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@swissonline.ch

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