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Estimating Copulas for Innovations in Dependent Time Series

Article Quant Q&A · Author: Pierre
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Summary

The discussion concerns estimating the dependence structure between innovations from two time series. The question points to parametric and nonparametric approaches and asks what it means to filter time out before estimating a copula. The answer frames the task as modeling the joint distribution of a vector formed from the two series and notes that time-varying copulas are one relevant setting.

It recommends consulting methodological references that survey estimation choices and related literature, but does not provide a step-by-step procedure or resolve the filtering question. The main practical implication is that the method depends on whether a parametric or nonparametric copula is desired and whether dependence itself changes over time. The exchange is a pointer to further study rather than a worked estimation example, so implementation details and diagnostics remain unspecified.

Key ideas

  • A copula can model the joint dependence between innovations from two time series.
  • Copula estimation methods vary, including parametric and nonparametric approaches.
  • Time-varying copulas may be relevant when the dependence structure changes over time.
  • The discussion points to literature but does not explain how to filter time effects or implement an estimator.

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StatisticsMachine learningRisk management
Full text
# How to estimate a copula for time series


# How to estimate a copula for time series












I want to estimate a copula for the innovations of two dependent time series (A and B). I have found no reference with a step by step on how to do this. I have only found summarized papers from which I am not able to get the details.

Would you have a reference for this subject?

[EDIT]

Section 4 of Nonparametric Estimation Of Copulas For Time Series, by JD Fermanian, O Scaillet is an example.

Page 14 of Estimating copula densities through wavelets, by Genest, Masiello, Tribouley is another example. Here the author states that he estimates the copula "once the effect of time has been filtered out". And then he gets figure 9 c). But I do not understand what the author means with "filtering time out".

## Answer by A. G. (score 1)

https://quant.stackexchange.com/a/38083

It sounds like you wish to model the joint distribution of some random vector comprised of those 2 time series, so you are interested in time-varying copulas.

There are many ways of estimating copulas, depending on whether they are parametric, nonparametric, etc. Patton Section 2.3 cites a number of papers and textbooks that discuss different methods, so this should help you in your literature search.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.