Estimation and Model Selection of Copulas with an Application to Exchange Rates

Copulas are the part of a multivariate distribution function that fully captures the cross sectional dependence between the variables of interest and they have become a very popular tool to model dependencies different from the linear correlation of elliptical distributions. We review the theory of copula functions, present a number of examples and describe how to sample random data from these. Different techniques for estimation and model selection are discussed and compared in an extensive Monte Carlo study. We find that a test not considered in the literature, namely the Jarque-Bera test applied on transformed data from the conditional copula, has the best properties of the presented tests, but that the most reliable criterion for selecting the best fitting copula is the Akaike information criterion. We model exchange rate returns of Latin American currencies against the euro with copulas and we find evidence of symmetric dependence, excess upper tail dependence and excess lower tail dependence.econometrics;

Tails of correlation mixtures of elliptical copulas

Correlation mixtures of elliptical copulas arise when the correlation parameter is driven itself by a latent random process. For such copulas, both penultimate and asymptotic tail dependence are much larger than for ordinary elliptical copulas with the same unconditional correlation. Furthermore, for Gaussian and Student t-copulas, tail dependence at sub-asymptotic levels is generally larger than in the limit, which can have serious consequences for estimation and evaluation of extreme risk. Finally, although correlation mixtures of Gaussian copulas inherit the property of asymptotic independence, at the same time they fall in the newly defined category of near asymptotic dependence. The consequences of these findings for modeling are assessed by means of a simulation study and a case study involving financial time series.Comment: 21 pages, 3 figure

Testing for Asset Market Linkages: A new Approach based on Time-Varying Copulas

This paper proposes a new approach based on time-varying copulas to test for the presence of increases in stock market interdependence after financial crises, also known as shift-contagion process. We show that the previous approaches that take into account changes in volatility regimes are biased when the DGP is either copula based or when there is a break in variance significantly different from the one in correlation. A sequential algorithm is then elaborated to remove this bias. Applied to the recent 1997 Asian crisis, it confirms that breaks in variances always precede those in conditional correlation. It also turns out that this financial turmoil has been characterized by shift-contagion.financial economics and financial management ;

On the causes of car accidents on German Autobahn connectors

The work at hand tries to identify factors that explain accidents on German Autobahn connectors. To find these factors the empirical study makes use of count data models. The findings are based on a set of 197 ramps, which we classified into three distinct types of ramps. For these ramps accident data was available for a period of 3 years (January 2003 until December 2005). The Negative Binomial model proved to be an appropriate model for our cross-sectional setting in detecting factors that cause accidents. The heterogeneity in our dataset forced us to investigate the three different types of ramps separately. By comparing results of the aggregated model and results of the ramp-specific models ramp-type-independent as well as ramp-type-specific factors were identified. The most significant variable in all models was a measure of the average daily traffic. For geometric variables not only continuous effects were found to be significant but also threshold effects. --highway connectors,German Autobahn,accident causes,Poisson regression,Negative Binomial regression

Forecasting international stock market correlations: does anything beat a CCC?

It is well known that the correlation between financial series varies over time. Here, the forecasting performance of different time-varying correlation models is compared for cross-country correlations of weekly G5 and daily European stock market indices. In contrast to previous studies only the correlation and not the entire covariance matrix is forecasted and multi-step forecasts are considered. The forecast comparison is done by considering statistical and economic criteria. The results suggest that under a statistical criterion time-varying correlation models perform quite well for weekly data, but cannot outperform the constant correlation model for daily data. Considering economic criteria it is hard to beat a constant correlation model. --dynamic conditional correlation,regime switching,stochastic correlation,smooth correlations,indirect model comparison,portfolio construction

Dynamic stochastic copula models: Estimation, inference and applications

We propose a new dynamic copula model where the parameter characterizing dependence follows an autoregressive process. As this model class includes the Gaussian copula with stochastic correlation process, it can be viewed as a generalization of multivariate stochastic volatility models. Despite the complexity of the model, the decoupling of marginals and dependence parameters facilitates estimation. We propose estimation in two steps, where first the parameters of the marginal distributions are estimated, and then those of the copula. Parameters of the latent processes (volatilities and dependence) are estimated using efficient importance sampling (EIS). We discuss goodness-of-fit tests and ways to forecast the dependence parameter. For two bivariate stock index series, we show that theproposed model outperforms standard competing models.econometrics;

Order Invariant Evaluation of Multivariate Density Forecasts

We derive new tests for proper calibration of multivariate density forecasts based on Rosenblatt probability integral transforms. These tests have the advantage that they i) do not depend on the ordering of variables in the forecasting model, ii) are applicable to densities of arbitrary dimensions, and iii) have superior power relative to existing approaches. We furthermore develop adjusted tests that allow for estimated parameters and, consequently, can be used as in-sample specification tests. We demonstrate the problems of existing tests and how our new approaches can overcome those using Monte Carlo Simulation as well as two applications based on multivariate GARCH-based models for stock market returns and on a macroeconomic Bayesian vectorautoregressive model

Oxidized Phospholipids Inhibit the Formation of Cholesterol-Dependent Plasma Membrane Nanoplatforms

We previously developed a single-molecule microscopy method termed TOCCSL (thinning out clusters while conserving stoichiometry of labeling), which allows for direct imaging of stable nanoscopic platforms with raft-like properties diffusing in the plasma membrane. As a consensus raft marker, we chose monomeric GFP linked via a glycosylphosphatidylinositol (GPI) anchor to the cell membrane (mGFP-GPI). With this probe, we previously observed cholesterol-dependent homo-association to nanoplatforms diffusing in the plasma membrane of live CHO cells. Here, we report the release of this homo-association upon addition of 1-palmitoyl-2-(5-oxovaleroyl)-sn-glycero-3-phosphocholine (POVPC) or 1-palmitoyl-2-glutaroyl-sn-glycero-3-phosphocholine, two oxidized phospholipids (oxPLs) that are typically present in oxidatively modified low-density lipoprotein. We found a dose-response relationship for mGFP-GPI nanoplatform disintegration upon addition of POVPC, correlating with the signal of the apoptosis marker Annexin V-Cy3. Similar concentrations of lysolipid showed no effect, indicating that the observed phenomena were not linked to properties of the lipid bilayer itself. Inhibition of acid sphingomyelinase by NB-19 before addition of POVPC completely abolished nanoplatform disintegration by oxPLs. In conclusion, we were able to determine how oxidized lipid species disrupt mGFP-GPI nanoplatforms in the plasma membrane. Our results favor an indirect mechanism involving acid sphingomyelinase activity rather than a direct interaction of oxPLs with nanoplatform constituents. © 2016 Biophysical Society