On the large-sample behavior of two estimators of the conditional copula under serially dependent data.

The conditional copula of a random pair (Y 1 , Y 2) given the value taken by some covariate X ∈ R is the function C x : [ 0 , 1 ] 2 → [ 0 , 1 ] such that P (Y 1 ≤ y 1 , Y 2 ≤ y 2 | X = x) = C x { P (Y 1 ≤ y 1 | X = x) , P (Y 2 ≤ y 2 | X = x) } . In this note, the weak convergence of the two estimators of C x proposed by Gijbels et al. (Comput Stat Data Anal 55(5):1919–1932, 2011) is established under α -mixing. It is shown that under appropriate conditions on the weight functions and on the mixing coefficients, the limiting processes are the same as those obtained by Veraverbeke et al. (Scand J Stat 38(4):766–780, 2011) under the i.i.d. setting. The performance of these estimators in small sample sizes is investigated with simulations. [ABSTRACT FROM AUTHOR]