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I am trying to analyze the lead-lag between time series of two stock prices. In regular time series analysis, we can do Cross Correlaton, VECM (Granger Causality). However how does one handle the same in irregularly spaced time series.

The hypothesis is that one of the instruments leads the other.

I have data for both symbols to the microseconds.

I have looked at RTAQ package and also tried applying VECM. RTAQ is more on a univariate time series while VECM is not significant on these timescales.

> dput(STOCKS[,]))
structure(c(29979, 29980, 29980, 29980, 29981, 29981, 29991, 
29992, 29993, 29991, 29990, 29992), .Dim = c(6L, 2L), .Dimnames = list(NULL, c("Pair_Bid", "Calc_Bid" )), index = structure(c(1340686178.55163, 1340686181.40801, 1340686187.2642, 
1340686187.52668, 1340686187.78777, 1340686189.36693), class = c("POSIXct", "POSIXt"), tzone = ""), class = "zoo")
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  • $\begingroup$ you need to use a reproducible set of data $\endgroup$ – John Jun 26 '12 at 9:53
  • $\begingroup$ Not really sure why you say so? Can you elaborate? $\endgroup$ – shoonya Jun 26 '12 at 9:56
  • $\begingroup$ @John means (I think) that you are more likely to get a useful answer if you provide data that can easily be used by answerers to test and illustrate their methods (see tinyurl.com/reproducible-000 ). I would guess that parametric models for the cross-correlations/cross-spectra would be necessary ... $\endgroup$ – Ben Bolker Jun 26 '12 at 9:59
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    $\begingroup$ this should really go on CrossValidated $\endgroup$ – nico Jun 26 '12 at 10:17
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    $\begingroup$ because the question is probably sufficiently challenging that there isn't an obvious standard methodology. Rather than "I want to use well-known statistical procedure X, is it implemented in R/how do I go about using it?", this is more along the lines of "is there a good statistical procedure for solving problem Y"? Alternately, it might be worth checking out r-sig-finance (I think there is such a mailing list ...) $\endgroup$ – Ben Bolker Jun 26 '12 at 10:27
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I know of one possible solution, but it is sufficiently complicated that I'm going to take the easy option and link you to the relevant academic paper (a critically under-rated paper in my opinion):

Frank de Jong, Theo Nijman (1997) "High Frequency Analysis of Lead-Lag Relationships Between Financial Markets"

I'm sure more work must have been done on this problem since then. A good way to find it is to use the "citations" page on ideas.repec. A link to the relevant page for the above-mentioned paper is here. A few titles look quite relevant.

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