Gaussian Process Single Index Models for Conditional Copulas
نویسندگان
چکیده
Parametric conditional copula models allow the copula parameters to vary with a set of covariates according to an unknown calibration function. In this paper we develop a flexible Bayesian method to estimate the calibration function of a bivariate conditional copula. We construct a prior distribution over the set of smooth calibration functions using a sparse Gaussian process (GP) prior for the single index model (SIM). The estimation of parameters from the marginal distributions and the calibration function is done jointly via a Markov Chain Monte Carlo algorithm that is used to sample from the full posterior distribution. We introduce a novel Conditional Cross Validated Pseudo-Marginal (CCVML) criterion that is used along with the Deviance Information Criterion (DIC), the Watanabe-Akaike Information criterion (WAIC) and the regular Cross-Validated Pseudo-Marginal Likelihood (CVML) criterion to perform copula selection and to compare the full model to one with constant calibration function. The performance of the estimation method and model selection criteria is studied via a series of simulations using correct and misspecified models with Clayton, Frank and Gaussian copulas and a real weather data example.
منابع مشابه
Bayesian inference for conditional copulas using Gaussian Process single index models
Parametric conditional copulamodels allow the copula parameters to vary with a set of covariates according to an unknown calibration function. Flexible Bayesian inference for the calibration function of a bivariate conditional copula is introduced. The prior distribution over the set of smooth calibration functions is built using a sparse Gaussian process (GP) prior for the single index model (...
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