Forecasting Time Series with Multivariate Copulas

Forecasting, 2021

A novel forecasting method based on copula functions is proposed. It consists of an iterative algorithm in which a dependent variable is decomposed as a sum of error terms, where each one of them is estimated identifying the input variable which best “copulate” with it. The method has been tested over popular reference datasets, achieving competitive results in comparison with other well-known machine learning techniques.

Journal of Multivariate Analysis

This paper is concerned with modeling the dependence structure of two (or more) time-series in the presence of a (possibly multivariate) covariate which may include past values of the time series. We assume that the covariate influences only the conditional mean and the conditional variance of each of the time series but the distribution of the standardized innovations is not influenced by the covariate and is stable in time. The joint distribution of the time series is then determined by the conditional means, the conditional variances and the marginal distributions of the innovations, which we estimate nonparametrically, and the copula of the innovations, which represents the dependency structure. We consider a nonparametric as well as a semiparametric estimator based on the estimated residuals. We show that under suitable assumptions these copula estimators are asymptotically equivalent to estimators that would be based on the unobserved innovations. The theoretical results are illustrated by simulations and a real data example.

Journal of Multivariate Analysis, 2012

The authors extend to multivariate contexts the copula-based univariate time series modeling approach of Chen & Fan [X. Chen, Y. Fan, Estimation of copula-based semiparametric time series models, J. Econometrics 130 (2006) 307-335; X. Chen, Y. Fan, Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification, J. Econometrics 135 (2006) 125-154]. In so doing, they tackle simultaneously serial dependence and interdependence between time series. Their technique differs from the usual approach to time series copula modeling in which the series are first modeled individually and copulas are used to model the dependence between their innovations. The authors discuss parameter estimation and goodness-of-fit testing for their model, with emphasis on meta-elliptical and Archimedean copulas. The method is illustrated with data on the Canadian/US exchange rate and the value of oil futures over a ten-year period.

Journal of Multivariate Analysis

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SSRN Electronic Journal, 2013

This paper develops a testing framework for comparing the predictive accuracy of copula-based multivariate density forecasts, focusing on a specific part of the joint distribution. The test is framed in the context of the Kullback-Leibler Information Criterion, but using (out-of-sample) conditional likelihood and censored likelihood in order to focus the evaluation on the region of interest. Monte Carlo simulations document that the resulting test statistics have satisfactory size and power properties in small samples. In an empirical application to daily exchange rate returns we find evidence that the dependence structure varies with the sign and magnitude of returns, such that different parametric copula models achieve superior forecasting performance in different regions of the support. Our analysis highlights the importance of allowing for lower and upper tail dependence for accurate forecasting of common extreme appreciation and depreciation of different currencies.

SSRN Electronic Journal, 2000

This paper introduces multivariate dynamic copula models to account for the timevarying dependence structure in asset portfolios. We firstly enhance the flexibility of this structure by modeling regimes with multivariate mixture copulas. In our second approach, we derive dynamic elliptical copulas by applying the dynamic conditional correlation model (DCC) to multivariate elliptical copulas. The best-ranked copulas according to both in-sample fit and out-of-sample forecast performance indicate the importance of accounting for time-variation. The superiority of multivariate dynamic Clayton and Student-t models further highlight that tail dependence as well as the capability of capturing asymmetries in the dependence structure are crucial features of a well-fitting model for an equity portfolio.

Journal of Economic Dynamics and Control, 2010

We introduce a statistical test for comparing the predictive accuracy of competing copula specifications in multivariate density forecasts, based on the Kullback-Leibler Information Criterion (KLIC). The test is valid under general conditions: in particular it allows for parameter estimation uncertainty and for the copulas to be nested or nonnested. Monte Carlo simulations demonstrate that the proposed test has satisfactory size and power properties in finite samples. Applying the test to daily exchange rate returns of several major currencies against the US dollar we find that the Student's t copula is favored over Gaussian, Gumbel and Clayton copulas. This suggests that these exchange rate returns are characterized by symmetric tail dependence.

Communications in Statistics - Simulation and Computation, 2009

2007

Copulas provide convenient tool for describing dependencebetween variables.Applications in Finance, Insurance, Risk Management, EVT.Software: SPlus( S+FinMetrics), R, MatLab, Mathematicaetc.Copula: multivariate distribution whose marginal distributionsare uniform on (0,1).Copulas allow to model marginal distributions and dependencestruture of multivariate distribution separately.Some critical remarks (Mikosch, 2005):

Journal of Econometrics, 2022

Multivariate time series exhibit two types of dependence: across variables and across time points. Vine copulas are graphical models for the dependence and can conveniently capture both types of dependence in the same model. We derive the maximal class of graph structures that guarantee stationarity under a natural and verifiable condition called translation invariance. We propose computationally efficient methods for estimation, simulation, prediction, and uncertainty quantification and show their validity by asymptotic results and simulations. The theoretical results allow for misspecified models and, even when specialized to the iid case, go beyond what is available in the literature. The new model class is illustrated by an application to forecasting returns of a portfolio of 20 stocks, where they show excellent forecast performance. The paper is accompanied by an open source software implementation.