A Time-Varying Multivariate Noncentral Contaminated Normal Copula Model and Its Application to the Visualized Dependence Analysis of Hong Kong Stock Markets

Zhenyu Xiao,Teng Yuan Cheng,Kuiran Shi,Jie Wang,Dehua Shen

doi:10.1155/2020/9673623

Zhenyu Xiao, Teng Yuan Cheng + Show 3 more

Open Access

https://doi.org/10.1155/2020/9673623

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Abstract

Financial data usually have the features of complexity and interdependence structure, such as asymmetric, tail, and time-varying dependence. This study constructs a new multivariate skewed fat-tailed copula, namely, noncentral contaminated normal (NCCN) copula, to analyze the dependent structure of financial market data. The dynamic conditional correlation (DCC) model is also incorporated into constructing the time-varying NCCN copula model. This study comprehensively examines the effects of the DCC-NCCN copula and related models on fitting dependence structures of Hong Kong stock markets. The results show that the DCC-NCCN copula model can better depict the dependence structures of returns. Considering the flexibility and complexity, the DCC-NCCN copula model is a relatively ideal, time-varying, multivariate skewed fat-tailed copula model.

Highlights

After suffering from loss in the stock market, Isaac Newton ever said that “I can calculate the motions of the heavenly bodies, but not the madness of people.” is reflects the complexity of financial markets
The financial asset return series have relatively complex interdependence structural features, such as asymmetric dependence, tail dependence, and time-varying dependence. According to whether it can depict asymmetric dependence and fat-tailed dependence, copula can be divided into four categories: symmetric thin-tailed copula, symmetric fat-tailed copula, skewed thin-tailed copula, and skewed fat-tailed copula. e examples above are normal copula, t-copula, skew-normal copula, and skew-t-copula. e multivariate skew-normal copula is the copula of the multivariate skew-normal distribution, such as Wei et al [1] proposed the copula of the multivariate skew-normal distribution of Azzalini and Valle [2]. e multivariate skew-t-copula is the copula of the multivariate skew-t distribution, such as Demarta and McNeil [3] proposed the copula of the multivariate generalized hyperbolic skew-t (GHST) distribution of Barndorff-Nielsen [4]
These multivariate skew-t copulas are very flexible, they are highly complex and challenging to apply. Considering both flexibility and complexity, these multivariate skew-t copulas may not be very ideal. is study constructs a new multivariate skewed fat-tailed distribution, namely, the multivariate noncentral contaminated normal (NCCN) distribution. e multivariate NCCN distribution can be interpreted as a multivariate noncentral normal scale mixture distribution, which is similar to the multivariate normal variance-mean mixture distribution and multivariate skew-normal scale mixture distribution. e multivariate NCCN distribution can be interpreted as a simplified mixture of two multivariate normal distributions

Summary

Introduction

After suffering from loss in the stock market, Isaac Newton ever said that “I can calculate the motions of the heavenly bodies, but not the madness of people.” is reflects the complexity of financial markets. The financial asset return series have relatively complex interdependence structural features, such as asymmetric dependence, tail dependence, and time-varying dependence. The flexibility of the NCCN copula is similar to that of skew-t copulas, but the complexity of the NCCN copula is significantly lower than that of skew-t copulas According to whether it can delineate the time-varying dependence, the copula can be divided into two classes: static copula and dynamic one. E advantages of the DCC model and TVC model are as follows: dimension is unlimited, the dynamic structure is simple, and the interpretation meaning of the dynamic structure is clear; the disadvantage is to limit the type of time-varying parameters to the linear correlation matrix. The copula of the multivariate NCCN distribution, namely, multivariate NCCN copula, is proposed. ird, we adopt the DCC model to construct a new time-varying copula model, namely, DCC-NCCN copula model. e last, employing the Hang Seng Index (HSI), Hang Seng China Enterprises Index (CEI), and Hang Seng China-Affiliated Corporations Index (CCI) as our sample data, we compare the fitting effects of the DCC-NCCN copula model with some other copula models and perform the visualized dependence analysis of Hong Kong stock markets

Model Development

Multivariate NCCN Distribution and Multivariate NCCN

Empirical Results