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In such a case we propose using a multi\u2010stage maximum likelihood estimator (MSMLE) based on all available data rather than the usual one\u2010stage maximum likelihood estimator (1SMLE) based only on the overlapping data. We provide conditions under which the MSMLE is<jats:italic>not less<\/jats:italic>asymptotically efficient than the 1SMLE, and we examine the small sample efficiency of the estimators via simulations. The analysis in this paper is motivated by a model of the joint distribution of daily Japanese yen\u2013US dollar and euro\u2013US dollar exchange rates. We find significant evidence of time variation in the conditional copula of these exchange rates, and evidence of greater dependence during extreme events than under the normal distribution. 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