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In this paper the conditional dependence of stock market in Mexico and the United States is studied. Symmetric Joe-Clayton copula is used and conditional probabilities of increases (decreases) in Mexico stock index when there are increases (decreases) in the U.S. stock index are estimated. For the marginal distributions, AR-TGARCH and AR-EGARCH models with a standardized Student's t distribution for innovations are proposed. Empirical results suggest that there is a high degree of conditional dependence in the tails, presenting higher volatility on the upper (right) tail throughout the period. [ABSTRACT FROM AUTHOR]