It isn't clear to me how to calculate cointegration with irregular time series (ideally using the Johansen test with VECM). My initial thought would be to regularize the series and interpolate missing values, although that may bias the estimation.

Is there any literature on this subject?

  • $\begingroup$ Can you clarify what you mean by irregular? I had initially taken it to mean that you had two series of different discrete time intervals. $\endgroup$
    – Andy W
    Aug 30, 2010 at 12:42
  • 1
    $\begingroup$ Yes, I mean two time series with different random arrival times (not regularly sampled). $\endgroup$
    – Shane
    Aug 30, 2010 at 12:56

2 Answers 2


You could start with the following references:

  • Comte (1999) "Discrete and continuous time cointegration", Journal of Econometrics.
  • Ferstl (2009) "Cointegration in discrete and continuous time". Thesis.

Citations of Comte may also be useful.

  • $\begingroup$ "Citations of Comte may also be useful." link is dead now, what citation it was ? $\endgroup$
    – Qbik
    Jan 12, 2014 at 23:23

Although it may only be of little help, the problem you present to me is synonymous with the "Change of Support" problem encountered when using areal units. Although this work just presents a framework for what you describe as "reglarize and interpolate" using a method referred to as "kriging". I don't think any of this work will help answer your question of whether estimating your missing values in the series in such a manner will bias error correction estimates, although if some of your samples are in clustered time intervals for both series you may be able to check for yourself. You may also be interested in the technique of "co-kriging" from this field, which uses information from one source to estimate the value for another (if your interested I would suggest you check out the work being done by Pierre Goovaerts).

Again I'm not sure how helpful this will be though. It may be substantially simpler to just use current time-series forecasting techniques to estimate your missing data. It won't help you decide what to estimate either.

Good luck, and keep the thread updated if you find any pertinent material. I would be interested, and you would think with the proliferation of data sources online this would become an pertinent issue for at least some research projects.

  • 2
    $\begingroup$ The connection with kriging is good, but it should be mentioned that only certain kinds of irregular time series could be viewed as having variable support. In this context, the "support" of a value is the duration that the value represents. E.g., if the time series consists of eight-hour total readings of particular matter in air sampling stations, obtained daily during weekdays only, then the supports are constant, equal to eight hours. Thus the change-of-support (or variable support) issue is different from the irregular spacing of the supports themselves. $\endgroup$
    – whuber
    Aug 8, 2012 at 15:02

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