Gaussian Process Conditional Copulas with Applications to Financial Time Series
The estimation of dependencies between multiple variables is a central problem in the analysis of financial time series. A common approach is to express these dependencies in terms of a copula function. Typically the copula function is assumed to be constant but this may be inaccurate when there are covariates that could have a large influence on the dependence structure of the data. To account for this, a Bayesian framework for the estimation of conditional copulas is proposed. In this framework the parameters of a copula are non-linearly related to some arbitrary conditioning variables. We evaluate the ability of our method to predict time-varying dependencies on several equities and currencies and observe consistent performance gains compared to static copula models and other timevarying copula methods.
Paper summary: The authors propose a Bayesian 
      inference procedure for conditional bivariate copula models, where the 
      copula models can have multiple parameters. The copula parameters are 
      related to conditioning variables by a composition of parameter mapping 
      functions and arbitrary latent functions with Gaussian process priors. The 
      inference procedure for this model is based on expectation propagation. 
      The method is evaluated on synthetic data and on financial time series 
      data and compared to alternative copula-based models. The paper also 
      includes an overview of related methods. Quality: The 
      proposed method is sound. The authors include a description of related 
      methods and list strengths and weaknesses of their method. 
      Clarity: The paper is written clearly and concisely. 
      It makes a very mature impression. I could not find any inconsistencies or 
      typos. The figures and tables complement the text seamlessly, equations 
      are clear and well explained and the text is flawless. 
      Originality: The model and its inference procedure is 
      an extension of a similar conditional copula model that was restricted to 
      copulas with only one parameter. The present work generalizes this 
      approach to allow more than one copula parameter. To my knowledge, this 
      extension is novel. Significance: The flexibility of 
      copula families with only one parameter is limited and the applicability 
      of more flexible families is a huge advantage. Performance gains compared 
      to the alternative methods are remarkable. This result is very promising.