Copula-based Multivariate Models Research Articles

Dynamic high-frequency dependence structure of Chinese agricultural commodity futures based on the semi-parametric copula

This paper investigates the dynamic high-frequency dependence structure of Chinese four major agricultural commodity futures by utilizing a semi-parametric copula-based multivariate model with 5-minute high-frequency trading data. The empirical results show that the daily dependence between the agricultural commodity futures is time-varying and slightly asymmetric, and that this dependence and its asymmetry are more pronounced during the world food crisis (2007–2008) and the global financial crisis (2008–2011). Furthermore, the intraday dependence structure exhibits a lopsided inverted U-shaped pattern with relatively lower dependence level around the opening and closing time, and a peak around the mid-trading day.

An integrated clustering and copula-based model to assess the impact of intersection characteristics on violation-related collisions

The main goal of this study is to investigate the impact of a variety of factors on the frequency and the severity of pedestrian-vehicle collisions that involve pedestrian violations. To that end, the collision dataset of the City of Hamilton between 2010 and 2017 was reviewed to filter out pedestrian collisions that involved pedestrian violations. A Latent Class Analysis (LCA) method was applied to divide the dataset into a set of homogeneous clusters, based on traffic and intersection characteristics. A copula-based multivariate model was then developed for each cluster in order to study the impact of the different factors on collisions under the prevailing conditions of each cluster. The results showed that the number of bus stops within the intersection area is directly associated with the frequency and the severity of collisions involving pedestrian violations. A reduction in collisions was observed with the increase in the frequency of buses at intersections that are located along main transit routes. Moreover, the presence of schools near the intersection tends to increase the frequency of collisions involving pedestrian violations, especially at large intersections. The results also revealed that the presence of central refuge islands, despite their overall safety benefits, increases the likelihood of collisions involving pedestrian violations in large intersections. The results of this study provide valuable insights for a better understanding of the safety consequences of pedestrian violations. Such understanding assists engineers and planners to design intersections that reduce the frequency of pedestrian violations and mitigate their negative safety consequences.

On multivariate copula modeling of dependent degradation processes

Multivariate degradation processes have been observed in many engineering systems. Most existing multivariate degradation modeling techniques, such as multivariate general path models or multivariate Wiener process models, assume an underlying Gaussian dependence structure. Unfortunately, in reality, the dependencies among degradation processes are often nonlinear, asymmetric and greatly tail-skewed, and thus limit the usefulness of the conventional modeling techniques in practice. To overcome these limitations, in this paper, we develop a copula-based multivariate modeling framework. Three fundamental copula classes are applied to model the complex dependence structure among correlated degradation processes. Statistical inference and model selection techniques, including two graphical diagnostic tools, a test of independence and a goodness-of-fit test, are employed to identify the best model. The advantages of the proposed modeling framework are demonstrated through simulation studies. And we also discuss the effect of ignoring tail dependence on system failure probability assessment. Finally, the applications of the copula-based multivariate degradation models on both system reliability evaluation and remaining useful life prediction are provided. The proposed methodology is illustrated using a numerical example.

Investigating dependencies among oil price and tanker market variables by copula-based multivariate models

Crude oil price, bunker price, and tanker freight rate are very volatile in recent years. Uncertainties about the complicated relationships among these market variables could impose substantial business risks on investors, shipowners, ship operators, and charterers in oil transportation by tankers. A better understanding of the dependencies among these variables can help improve investment and operational decisions. This study aims to develop copula-based multivariate models for analyzing oil price and tanker market variables, and associated efficient approaches to reveal the time varying effects for the relationships. Given the volatilities in oil prices over the recent years, this study analyzes the impact that the changes in oil price has on bunker price and tanker freight rates. The West Texas Intermediate, Bloomberg Weighted Average Bunker Fuel Price, Baltic Handysize Index, Baltic Supramax Index and Baltic Panamax Index are analyzed using various selected copula models, from 2008 through 2015. Findings reveal that high oil price is a factor causing a weak dependence among the studied variables in the tanker market. The use of copula has more advantages over the conventional methods and can best characterize the relationships for the tanker market variables. The time varying effects in the dependences can be well identified in the copula modeling. The results could provide valuable information for the policy makers and participants in the maritime industry. The understanding of the dynamic relationships among the oil market could help the participants to foresee the potential risks and the policy makers to organize a more efficient market.

A novel statistical model for content-based stereo image retrieval in the complex wavelet domain

This paper presents a new stereo image (SI) retrieval method based on a statistical model of complex wavelet coefficients subbands. In this context, a Gaussian copula-based multivariate model is used to capture the dependence between complex wavelet coefficients of both left and right images, and a non-Gaussian univariate model is used to characterize the statistical behavior of the disparity map. Thanks to its flexibility, the copula tool allows us to choose several marginal densities while keeping the multivariate properties. Features are extracted by estimating parameters for both multivariate and univariate models. Finally, a weighted Jeffrey divergence (JD) is used as a similarity measurement between the underlying models. Experimental results on a stereo image database demonstrate the performance of the proposed method in terms of the retrieval rates as well as the computational time.

Gaussian Copula Multivariate Modeling for Texture Image Retrieval Using Wavelet Transforms

In the framework of texture image retrieval, a new family of stochastic multivariate modeling is proposed based on Gaussian Copula and wavelet decompositions. We take advantage of the copula paradigm, which makes it possible to separate dependence structure from marginal behavior. We introduce two new multivariate models using, respectively, generalized Gaussian and Weibull densities. These models capture both the subband marginal distributions and the correlation between wavelet coefficients. We derive, as a similarity measure, a closed form expression of the Jeffrey divergence between Gaussian copula-based multivariate models. Experimental results on well-known databases show significant improvements in retrieval rates using the proposed method compared with the best known state-of-the-art approaches.

A review of copula models for economic time series

This survey reviews the large and growing literature on copula-based models for economic and financial time series. Copula-based multivariate models allow the researcher to specify the models for the marginal distributions separately from the dependence structure that links these distributions to form a joint distribution. This allows for a much greater degree of flexibility in specifying and estimating the model, freeing the researcher from considering only existing multivariate distributions. The author surveys estimation and inference methods and goodness-of-fit tests for such models, as well as empirical applications of these copulas for economic and financial time series.

Dynamic Copula Processes

This paper presents a flexible new family of copula-based multivariate models designed for handling large numbers of variables (1) as random vectors in the static case or (2) as vector stochastic processes in the dynamic case. The family includes models with upper and lower tail dependence. Variables need not be exchangeable. To illustrate the model’s potential; three radically different examples have been constructed: a straight additive model, an additive conditional gamma model and a switching model. Archimedean copulas turn out to be a special case of the general model. Another advantage of these models it that it is easy to construct dynamic versions of the static copulas. Lastly, as these models are defined in a conditional independence framework, they are easy to simulate.

Copula-Based Multivariate Models with Applications to Risk Management and Insurance

The purpose of this paper consists in analysing the relevance of dependence concepts in finance, insurance and risk management, exploring how these concepts can be implemented in a statistical model via copula functions and pointing out some difficulties related to this methodology. In particular, we first review the statistical models currently used in the actuarial and financial fields when dealing with loss data; then we show, by means of two risk management applications, that copula-based models are very flexible but sometimes difficult to set up and to estimate; finally we study, by means of a simulation experiment, the properties of the maximum likelihood estimators of the Gaussian and Gumbel copula.