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covariance with tick data
Posted: December 7th, 2005, 3:02 pm
by nikol
problem:I have two series of tick data with varying trade frequency. How to calculate the covariance in this case?Do you have any idea/solution?thanks.
covariance with tick data
Posted: December 7th, 2005, 3:35 pm
by madmax
check Yacine Ait-Sahalia website in Princeton for papers dealing with related issues.
covariance with tick data
Posted: December 7th, 2005, 4:05 pm
by nikol
thanks. I think, i got easier solution. It seems to work OK in my quick test with synchronized MC-data. Will check tomorrow with asyncronous one.The idea, briefly is:Calculate at each step EWMAverage and calculate at every tick the EW-COVariance, but also give additional weight due to time-distance between ticks:Suppose, x-tick has arrived and the last y-tick arrived N-seconds ago, so I have estimations:* <x>_(k-1) and <y>_(k-1) and cov(x,y)_(k-1), and * due to time distance between x_(k-1) and y_(k-1), I have additional weight W = exp(-alfa*N)I know, there is normalisation problem (due to W) - I will try to account for that (maybe someone has any idea how?)What do you think?
covariance with tick data
Posted: December 7th, 2005, 6:44 pm
by crowlogic
You might try the variogram. It is used commonly in geostatistics apparantly but I don't know much about it.
http://globec.whoi.edu/software/kriging ... lish.htmlI am also trying to find correlation between irregularly spaced series.. I've just been using an EWMA on both series and using last-point interpolation to make the 2 series spaced on the same data points ( but still irregular), and this seems to work, but I might be missing something here..--StephenQuoteOriginally posted by: nikolproblem:I have two series of tick data with varying trade frequency. How to calculate the covariance in this case?Do you have any thanks.
covariance with tick data
Posted: December 7th, 2005, 9:20 pm
by nikol
the main point to get correct covariance matrix is to have correct normalization and to preserve unity of the corr-matrix...in principle one try to get estimation E[ x * y ], where x and y are mean-shifted and the space how you weight depends on your taste. if you do all correct, then |Corr(x,y)|=1thanks for paper.
covariance with tick data
Posted: October 5th, 2006, 1:43 pm
by soulman
hi nikol,i have tried your suggestion but cannot get the mean shifted series to have a correlation of 1. how do you choose your alfa in your weighting?regards
covariance with tick data
Posted: October 5th, 2006, 1:43 pm
by soulman
hi nikol,i have tried your suggestion but cannot get the mean shifted series to have a correlation of 1. how do you choose your alfa in your weighting?regards
covariance with tick data
Posted: October 19th, 2006, 12:33 am
by frontofficequant
Here is an interesting approach to that problem in the context of multivariable Brownian motion and more generally diffusions.
http://www.stats.uwaterloo.ca/stats_nav ... 006-12.pdf