Modeling high‐dimensional time‐varying dependence using dynamic D‐vine models

Abstract

We consider the problem of modeling the dependence among many time series. We build high-dimensional time-varying copula models by combining pair-copula constructions with stochastic autoregressive copula and generalized autoregressive score models to capture dependence that changes over time. We show how the estimation of this highly complex model can be broken down into the estimation of a sequence of bivariate models, which can be achieved by using the method of maximum likelihood. Further, by restricting the conditional dependence parameter on higher cascades of the pair copula construction to be constant, we can greatly reduce the number of parameters to be estimated without losing much flexibility. Applications to five MSCI stock market indices and to a large dataset of daily stock returns of all constituents of the Dax 30 illustrate the usefulness of the proposed model class in-sample and for density forecasting.

Modeling Dependence in High Dimensions With Factor Copulas

“…The copula of the latent variables X, denoted C (θ) , is used as the model for the copula of the observable variables Y. 4 An important point about the above construction is that the marginal distributions of X i may be different from those of the original variables Y i , so F i G i in general; we use the structure for the vector X only for its copula, and completely discard the resulting marginal distributions. This is motivated by our desire to use the dimension-reduction technique of imposing a factor structure only in the component of the joint distribution that is difficult to estimate in high dimensions, namely the copula.…”

Large portfolio risk management and optimal portfolio allocation with dynamic elliptical copulas

“…Latent factor copula models, see [13] and [42] for example, are particularly attractive for relatively high dimensional applications to the factor structure, but factor copula models do not generally have a closed-form likelihood, making maximum likelihood estimation di cult. Vine copulas are constructed by sequentially applying bivariate copulas to build up a larger-dimension copula, see, e.g., [2] and [10]. However, as shown by [1], vine copulas are almost invariably based on an assumption that is hard to interpret and to test.…”

“…The assumption that the portfolio returns come from a univariate conditional t-distribution, with portfolio variance computed from conditional covariance matrix with DCC or DECO, does recover some of the fat tails, but at the sacri ce of the upper quantiles. (2) Neglecting dynamic dependence alone in the copula can cause over-aggressive risk management. The proportion of excessive losses can be seriously underestimated when real dependence is changing, for example, in the post high-tech bubble period.…”

Modeling and forecasting intraday VaR of an exchange rate portfolio

“…For example, Palaro and Hotta (2006) applied bivariate copula models to forecast the VaR of a foreign exchange portfolio, and Almeida et al (2016) proposed a dynamic D-vine copula for forecasting the dependence among a large dataset of daily returns. For example, Palaro and Hotta (2006) applied bivariate copula models to forecast the VaR of a foreign exchange portfolio, and Almeida et al (2016) proposed a dynamic D-vine copula for forecasting the dependence among a large dataset of daily returns.…”