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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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