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The asymptotic behavior of the empirical copula constructed from residuals of stochastic volatility models is studied. It is shown that if the stochastic volatility matrix is diagonal, then the empirical copula process behaves like if the parameters were known, a remarkable property. However, this is not true in general. Applications for goodness-of-fit and detection of structural change in the copula of the innovations are discussed.doi:10.14288/1.0044032 fatcat:f4o6njyydjgmbos2a7kar4s2lu