Analysis of dependencies in low frequency financial data sets

This empirical study proposes a dependency analysis of monthly financial time series. We use the overlapping technique and non-parametric correlation in order to increase both accuracy and consistency. Copulas are used to test extreme co-movements between financial securities. Our results indicate that even in a low-frequency framework, the common practice of assuming independence over time should be taken with caution due to the presence of GARCH effects. In addition, extreme co-movements are observed across securities, especially for interest rates.dependencies; low-frequency; monthly; copula; GARCH

A weak bifucation theory for discrete time stochastic dynamical systems

This article presents a bifurcation theory of smooth stochastic dynamical systems that are governed by everywhere positive transition densities. The local dependence structure of the unique strictly stationary evolution of such a system can be expressed by the ratio of joint and marginal probability densities; this ‘dependence ratio’ is a geometric invariant of the system. By introducing a weak equivalence notion of these dependence ratios, we arrive at a bifurcation theory for which in the compact case, the set of stable (nonbifurcating) systems is open and dense. The theory is illustrated with some simple examples

Bayesian forecasting and scalable multivariate volatility analysis using simultaneous graphical dynamic models

The recently introduced class of simultaneous graphical dynamic linear models (SGDLMs) defines an ability to scale on-line Bayesian analysis and forecasting to higher-dimensional time series. This paper advances the methodology of SGDLMs, developing and embedding a novel, adaptive method of simultaneous predictor selection in forward filtering for on-line learning and forecasting. The advances include developments in Bayesian computation for scalability, and a case study in exploring the resulting potential for improved short-term forecasting of large-scale volatility matrices. A case study concerns financial forecasting and portfolio optimization with a 400-dimensional series of daily stock prices. Analysis shows that the SGDLM forecasts volatilities and co-volatilities well, making it ideally suited to contributing to quantitative investment strategies to improve portfolio returns. We also identify performance metrics linked to the sequential Bayesian filtering analysis that turn out to define a leading indicator of increased financial market stresses, comparable to but leading the standard St. Louis Fed Financial Stress Index (STLFSI) measure. Parallel computation using GPU implementations substantially advance the ability to fit and use these models.Comment: 28 pages, 9 figures, 7 table

Dependence Structures in Chinese and U.S. Financial Markets -- A Time-varying Conditional Copula Approach

In this paper, we use a Time-Varying Conditional Copula approach (TVCC) to model Chinese and U.S. stock markets‚ dependence structures with other financial markets. The AR-GARCH-t model is used to examine the marginals, while Normal and Generalized Joe-Clayton copula models are employed to analyze the joint distributions. In this pairwise analysis, both constant and time-varying conditional dependence parameters are estimated by a two-step maximum likelihood method. A comparative analysis of dependence structures in Chinese versus U.S. stock markets is also provided. There are three main findings: First, the time-varying-dependence model does not always perform better than constant-dependence model. This result has not previously been reported in the literature. Second, although previous research extensively reports that the lower tail dependence between stock markets tends to be higher than the upper tail dependence, we find a counterexample where the upper tail dependence is much higher than the lower tail dependence in some short periods. Last, Chinese financial market is relatively separate from other international financial markets in contrast to the U.S. market. The tail dependence with other financial markets is much lower in China than in the U.S.AR-GARCH-t model; Time-varying conditional copula; Dependence structure; Stock market

A copula-based clustering algorithm to analyse EU country diets

The aim of the paper is to suggest a novel clustering technique to explore the changes of the food diet in 40 European countries in accordance with common European policies and guidelines on healthy diets and lifestyles. The proposed clustering algorithm is based on copulas and it is called Co- Clust. The CoClust algorithm is able to find clusters according to the mul- tivariate dependence structure of the data generating process. The database analysed contains information on the proportions of calories from 16 food aggregates in 40 European countries observed over 40 years by the Food and Agriculture Organization of the United Nations (FAO). The findings suggest that European country diets are changing, individually or as a group, but not in a unique direction. Central and Eastern European countries are becoming unhealthier, while the tendency followed by the majority of the remaining countries is to integrate the common European guidelines on healthy, bal- anced, and diversified diets in their national policies

Analyzing Asymetric Dependence in Exchange Rates using Copula

In this paper I aimed to analyze the use of copulas in financial application, namely to investigate the assumption of asymmetric dependence and to compute some measures of risk. For this purpose I used a portfolio consisting in four currencies from Central and Eastern Europe. Due to some stylized facts observed in exchange rate series I filter the data with an ARMA GJR model. The marginal distributions of filtered residuals are fitted with a semi-parametric CDF, using a Gaussian kernel for the interior of distribution and Generalized Pareto Distribution for tails. To obtain a better view of the dependence among the four currencies I proposed a decomposition of large portfolio in other three bivariate sub-portfolios. For each of them I compute Value-at-Risk and Conditional Value-at-Risk and then backtest the results.Value-at-Risk, copula, Generalized Pareto Distribution

ANALYSIS OF THE TIME EVOLUTION OF NON-LINEAR FINANCIAL NETWORKS

We treat financial markets as complex networks. It is commonplace to create a filtered graph (usually a Minimally Spanning Tree) based on an empirical correlation matrix. In our previous studies we have extended this standard methodology by exchanging Pearson’s correlation coefficient with information—theoretic measures of mutual information and mutual information rate, which allow for the inclusion of non-linear relationships. In this study we investigate the time evolution of financial networks, by applying a running window approach. Since information—theoretic measures are slow to converge, we base our analysis on the Hirschfeld-Gebelein-Rényi Maximum Correlation Coefficient, estimated by the Randomized Dependence Coefficient (RDC). It is defined in terms of canonical correlation analysis of random non-linear copula projections. On this basis we create Minimally Spanning Trees for each window moving along the studied time series, and analyse the time evolution of various network characteristics, and their market significance. We apply this procedure to a dataset describing logarithmic stock returns from Warsaw Stock Exchange for the years between 2006 and 2013, and comment on the findings, their applicability and significance

Dependence Structures in Chinese and U.S. Financial Markets -- A Time-varying Conditional Copula Approach

In this paper, we use a Time-Varying Conditional Copula approach (TVCC) to model Chinese and U.S. stock markets‚ dependence structures with other financial markets. The AR-GARCH-t model is used to examine the marginals, while Normal and Generalized Joe-Clayton copula models are employed to analyze the joint distributions. In this pairwise analysis, both constant and time-varying conditional dependence parameters are estimated by a two-step maximum likelihood method. A comparative analysis of dependence structures in Chinese versus U.S. stock markets is also provided. There are three main findings: First, the time-varying-dependence model does not always perform better than constant-dependence model. This result has not previously been reported in the literature. Second, although previous research extensively reports that the lower tail dependence between stock markets tends to be higher than the upper tail dependence, we find a counterexample where the upper tail dependence is much higher than the lower tail dependence in some short periods. Last, Chinese financial market is relatively separate from other international financial markets in contrast to the U.S. market. The tail dependence with other financial markets is much lower in China than in the U.S