Stationarity Considerations for Copula Estimation on Time Series

Summary

The document asks whether initial nonstationarity in a simulated VAR series matters when estimating a copula with kernels. It describes an experiment in a cited paper using repeated series of length 1,024 and asks whether every observation, including early values, can be included. It then extends the question to dependence estimation from historical prices of two assets.

The text provides no answer or empirical comparison. Its main research issue is whether the data used for copula estimation should come from a stationary process, and whether raw price levels meet that requirement. It does not specify the VAR parameters, kernel procedure, dependence measure, or how the simulated series are initialized. The cited paper is identified, but no findings from it are summarized. Readers should treat this as an open methodological question rather than guidance that raw prices or the full simulated sample are appropriate inputs.

Key ideas

• The document raises whether early, potentially nonstationary observations affect kernel-based copula estimation.
• It describes a cited VAR experiment with simulated time series of length 1,024.
• It asks whether all observations can be used when constructing the copula.
• It also questions whether historical asset price levels are suitable inputs for dependence modeling.
• The document offers no conclusion or evidence resolving these questions.

Tags

# Is non-stationarity an issue during copula estimation?


# Is non-stationarity an issue during copula estimation?












In this paper (1), on page 14 (section 4), the author presents an empirical experiment on the computation of a copula through the use of kernels. To do so, he uses the following stochastic process (VAR):

$$ Y_t = A +BY_{t-1}+ \nu_t$$

I understood that he simulated 5000 times a time series of length 1024 ($Y_0 ...Y_{1023}$). Then, he used each of these time series (cotaining 1024 values of $Y$ each) to build a copula, using kernels.

My question is: do I have to care about the fact that at the beginning (small values of $t$) the time series is not stationary? Or I can simply consider all the values of $Y$ (from 0 to 1023) into the copula building process?

I am asking this because I need to know if I can use raw market data (historical prices of two different assets that share some dependence structure) or if I need to care if the price time series is already on stationary state, as a pre-requisite to use these time series as input in the copula building process.

(1): Scaillet , O. and Fermanian, Jean-David, Nonparametric Estimation of Copulas for Time Series. Revised February 2003 (November 2002).

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