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Estimation of Copula-Based Semiparametric Time Series Models

  • Xiaohong Chen


    (Department of Economics, New York University)

  • Yanqin Fan


    (Department of Economics, Vanderbilt University)

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    This paper studies the estimation of a class of copula-based semiparametric stationary Markov models. These models are characterized by nonparametric invariant (or marginal) distributions and parametric copula functions that capture the temporal dependence of the processes; the implied transition distributions are all semiparametric, and a member in this class can be expressed as a generalized semiparametric regression transformation model. One advantage of this copula approach is to separate out the temporal dependence (such as clustering, tail dependence) from the marginal behavior (such as asymmetry, fat tails) of a time series. We present conditions under which processes generated by models in this class are beta-mixing; naturally, these conditions depend only on the copula specification. Simple estimators of the marginal distribution and the copula parameter are provided, and their asymptotic properties are established under easily verifiable conditions. These results allow us to easily obtain the root-n consistent and asymptotically normal estimators of important features of the transition distribution such as the (nonlinear) conditional moments and conditional quantiles. In addition, the semiparametric conditional quantile estimators are automatically monotonic across quantiles, which is attractive for portfolio conditional value-at-risk calculation.

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    File Function: Revised version, 2004
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    Paper provided by Vanderbilt University Department of Economics in its series Vanderbilt University Department of Economics Working Papers with number 0226.

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    Date of creation: Oct 2002
    Date of revision: Oct 2004
    Handle: RePEc:van:wpaper:0226
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