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We consider several time series and for each of them, we fit an appropriate dynamic parametric model. This produces serially independent error terms for each time series. The dependence between these error terms is then modeled by a regime-switching copula. The EM algorithm is used for estimating the parameters and a sequential goodness-of- fit procedure based on Cramer-von Mises statistics is proposed to select the appropriate number of regimes. Numerical experiments are performed to assess the validity of the proposed methodology. As an example of application, we evaluate a European put-on-max option on the returns of two assets. In order to facilitate the use of our methodology, we have built a R package HMMcopula available on CRAN.

The goal of this paper is to introduce new families of multivariate copulas, extending the chi-square copulas, the Fisher copula, and squared copulas. The new families are constructed from existing copulas by first transforming their margins to standard Gaussian distributions, then transforming these variables into non-central chi-square variables with one degree of freedom, and finally by considering the copula associated with these new variables. It is shown that by varying the non-centrality parameters, one can model non-monotonic dependence, and when one or many non-centrality parameters are outside a given hyper-rectangle, then the copula is almost the same as the one when these parameters are infinite. For these new families, the tail behavior, the monotonicity of dependence measures such as Kendall’s tau and Spearman’s rho are investigated, and estimation is discussed. The R package NCSCopula ( Nasri, 2019 ) can be used to estimate the parameters for several copula families.

We consider several time series and for each of them, we fit an appropriate dynamic parametric model. This produces serially independent error terms for each time series. The dependence between these error terms is then modeled by a regime-switching copula. The EM algorithm is used for estimating the parameters and a sequential goodness-of- fit procedure based on Cramer-von Mises statistics is proposed to select the appropriate number of regimes. Numerical experiments are performed to assess the validity of the proposed methodology. As an example of application, we evaluate a European put-on-max option on the returns of two assets. In order to facilitate the use of our methodology, we have built a R package HMMcopula available on CRAN.

In this paper, we consider non-stationary response variables and covariates, where the marginal distributions and the associated copula may be time-dependent. We propose estimators for the unknown parameters and we establish the limiting distribution of the estimators of the copula and the conditional copula, together with a parametric bootstrap method for constructing confidence bands around the estimator and for testing the adequacy of the model. We also consider three examples of functionals of the copula-based model under non-stationarity: conditional quantiles, conditional mean, and conditional expected shortfall. The asymptotic distribution of the estimation errors is shown to be Gaussian, and bootstrapping methods are proposed to estimate their asymptotic variances. The finite sample performance of our estimators is investigated through Monte Carlo experiments, and we show three examples of implementation of the proposed methodology.

In this paper, we propose an intuitive way to couple several dynamic time series models by inducing dependence between the so-called generalized errors of each model. This extends previous work for modelling dependance between innovations of stochastic volatility models. We consider time-independent and time-dependent copula models and we study the asymptotic behavior of some empirical processes constructed from pseudo-observations, as well as the behavior of pseudo-maximum likelihood estimators of the associated copula parameters. The results show that even if the generalized errors depend on unknown parameters, the limiting behaviour of many processes of interest do not depend on the estimation errors. One can easily perform tests of change-point on the full distribution, and the margins or the copula, as if the generalized errors were observed. For some interesting parametric models of time-dependent copulas, the same behavior is observed: one can work with the pseudo-observations, as if we were observing the generalized errors. This interesting property makes it possible to construct consistent tests of specification for the dependence models, without having to consider the dynamic time series models. An example of application with financial data is given.

We consider several time series and for each of them, we fit an appropriate dynamic parametric model. This produces serially independent error terms for each time series. The dependence between these error terms is then modeled by a regime-switching copula. The EM algorithm is used for estimating the parameters and a sequential goodness-of-fit procedure based on Cramer-von Mises statistics is proposed to select the appropriate number of regimes. Numerical experiments are performed to assess the validity of the proposed methodology. As an example of application, we evaluate a European put-on-max option on the returns of two assets. In order to facilitate the use of our methodology, we have built a R package HMMcopula available on CRAN.