Copula Processes

By Andrew Gordon Wilson, Zoubin Ghahramani. 2010

122 citations recorded by the source corpus.

We define a copula process which describes the dependencies between arbitrarily many random variables independently of their marginal distributions. As an example, we develop a stochastic volatility model, Gaussian Copula Process Volatility (GCPV), to predict the latent standard deviations of a sequence of random variables. To make predictions we use Bayesian inference, with the Laplace approximation, and with Markov chain Monte Carlo as an alternative. We find our model can outperform GARCH on simulated and financial data. And unlike GARCH, GCPV can easily handle missing data, incorporate covariates other than time, and model a rich class of covariance structures.

Subfields: Finance, Management Science and Operations Research

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Citations in the corpus

High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes (2019, methodology): “The challenge posed by this for estimating global models across time series has been noted in previous work [26, 37, 27].”
Autoregressive Convolutional Neural Networks for Asynchronous Time Series (2017, background): “Though still largely independent, researchers have started to “bring together the machine learning and econometrics communities" by building on top of their respective fundamental models yielding to, for example, the Gaussian Copula Process Volatility model Wilson & Ghahramani (2010).”
Gaussian Process Regression Networks (2011, methodology): “e t distributed, with minimal changes to the inference procedures; 3) we can transform the components of the product W(xi)f^(xi) so that the priors on the components of y(xi) become copula processes (Wilson and Ghahramani, 2010a) and have whatever marginals we desire. We can also do this without sig”
Gaussian Process Training with Input Noise (2011, background): “Recently Wilson and Ghahramani broadened the scope still further and proposed Copula and Wishart Process methods [7, 8].”
From Dependence to Causation (2016, methodology): “, 2011), clustering (Rey and Roth, 2012), Gaussian processes (Wilson and Ghahramani, 2010) and financial time series modeling (Hernández-Lobato et al.”
Copulas in Machine Learning (2013, methodology): “Wilson and Ghahramani, however, consider a more challenging application setting that requires further algorithmic innovation.”
Variational Heteroscedastic Gaussian Process Regression (2011, methodology): “Following (Wilson & Ghahramani, 2010), we use a rolling window of the previous 120 days of returns to Variational Heteroscedastic Gaussian Process Regression make 1, 7, and 30 day ahead volatility forecasts and retrain the model every 7 days.”
Dynamic Covariance Models for Multivariate Financial Time Series (2013, background): “This topic has recently received attention in the machine learning community, with the development of copula processes (Wilson & Ghahramani, 2010) and heteroskedastic Gaussian processes (L´azaro-Gredilla & Titsias, 2011).”
Learning Scalable Deep Kernels with Recurrent Structure (2016, background): “We remark that combinations of GPs with nonlinear functions have also been considered in the past in a slightly diﬀerent setting of warped regression targets (Snelson et al., 2003; Wilson and Ghahramani, 2010; Lázaro-Gredilla, 2012).”
Deep feature synthesis: Towards automating data science endeavors (2015, methodology): “in [5] through warping the output space.”