Improving forecasting performance using covariate-dependent copula models

Copulas provide an attractive approach to the construction of multivariate distributions with flexible marginal distributions and different forms of dependences. Of particular importance in many areas is the possibility of forecasting the tail-dependences explicitly. Most of the available approaches are only able to estimate tail-dependences and correlations via nuisance parameters, and cannot be used for either interpretation or forecasting. We propose a general Bayesian approach for modeling and forecasting tail-dependences and correlations as explicit functions of covariates, with the aim of improving the copula forecasting performance. The proposed covariate-dependent copula model also allows for Bayesian variable selection from among the covariates of the marginal models, as well as the copula density. The copulas that we study include the Joe-Clayton copula, the Clayton copula, the Gumbel copula and the Student’s $t$-copula. Posterior inference is carried out using an efficient MCMC simulation method. Our approach is applied to both simulated data and the S&P 100 and S&P 600 stock indices. The forecasting performance of the proposed approach is compared with those of other modeling strategies based on log predictive scores. A value-at-risk evaluation is also performed for the model comparisons.     

Risk spillover between the US and the remaining G7 stock markets using time-varying copulas with Markov switching: Evidence from over a century of data

This paper analyses the risk spillover effect between the US stock market and the remaining G7 stock markets by measuring the conditional Value-at-Risk (CoVaR) using time-varying copula models with Markov switching and data that covers more than 100 years. The main results suggest that the dependence structure varies with time and has distinct high and low dependence regimes. Our findings verify the existence of risk spillover between the US stock market and the remaining G7 stock markets. Furthermore, the results imply the following: 1) abnormal spikes of dynamic CoVaR were induced by well-known historical economic shocks; 2) The value of upside risk spillover is significantly larger than the downside risk spillover and 3) The magnitudes of risk spillover from the remaining G7 countries to the US are significantly larger than that from the US to these countries.     

Contagion effects and risk transmission channels in the housing,stock, interest rate and currency markets: An Empirical Study in China and the U.S.

This paper aims to investigate the crisis linkage and transmission channels within the housing, stock, interest rate and the currency markets in the U.S. and China in the past decade since the 2008 Subprime Mortgage Crisis. Two hybrid models, namely the SWARCH-EVT-Copula and the Bivariate SWARCH-EVT models, are proposed and applied in order to take into account (A) the high/low volatility regimes, (B) the interdependence structure inherited from the joint tail behaviours, as well as, (C) the risk spillover dynamics among financial sectors during market turmoils. We empirically show that the housing and stock markets share the strongest linkage and play central roles in the spreading of shocks. With a highly integrated system, the American financial sectors are under greater exposure to risk contagion and systemic risk during crises than the Chinese markets. Nevertheless, the exchange rate risk of Renminbi remains at an intensive level since its “crawl-like arrangement” and leads to increasing co-movements in the stock and interest rate markets since 2014.     

Empirical evidence of extreme dependence and contagion risk between main cryptocurrencies

This study examines the dependence and contagion risk between Bitcoin (BTC), Litecoin (LTC) and Ripple (XRP) using non-parametric mixture copulas (developed by Zimmer, 2012) and recently proposed methods of full-range tail dependence copulas (advanced by Hua, 2017, Su and Hua, 2017), for the period from 04-08-2013 to 17-06-2018. The Chi-plots and Kendall plots results show heavy tail dependence between each pairs of the cryptocurrencies. Evidence from the mixture copula indicates that for the BTC-LTC pair the upper-tail dependence is both stronger and more prevalent, while for the other pairs of cryptocurrencies the lower-tail dependence is very strong and more prevalent. However, the results of the full-range tail dependence copulas reveal a strong and prevalent upper and lower-tail dependence of each pairs of cryptocurrencies. These results provide evidence of significant risk contagion among price returns of major cryptocurrencies, both in bull and bear markets.     

A TVM-Copula-MIDAS-GARCH model with applications to VaR-based portfolio selection

This paper develops a novel time-varying multivariate Copula-MIDAS-GARCH (TVM-Copula-MIDAS-GARCH) model with exogenous explanatory variables to model the joint distribution of returns. The model accounts for mixed frequency factors that affect the time-varying dependence structure of financial assets. Furthermore, we examine the effectiveness of the proposed model in VaR-based portfolio selection. We conduct an empirical analysis on estimating the 90%, 95%, 99% VaRs of the portfolio constituted of the Shanghai Composite Index, Shanghai SE Fund Index, and Shanghai SE Treasury Bond Index. The empirical results show that the proposed TVM-Copula-MIDAS-GARCH model is effective to investigate the nonlinear time-varying dependence among those three indices and performs better in portfolio selection.     

Spatio-temporal probabilistic forecasting of wind power for multiple farms: A copula-based hybrid model

Accurate probabilistic forecasting of wind power output is critical to maximizing network integration of this clean energy source. There is a large literature on temporal modeling of wind power forecasting, but considerably less work combining spatial dependence into the forecasting framework. Through the careful consideration of the temporal modeling component, complemented by support vector regression of the temporal model residuals, this work demonstrates that a DVINE copula model most accurately represents the residual spatial dependence. Additionally, this work proposes a complete set of validation mechanisms for multi-h-step forecasts that, when considered together, comprehensively evaluate accuracy. The model and validation mechanisms are demonstrated in two case studies, totaling ten wind farms in the Texas electric grid. The proposed method outperforms baseline and competitive models, with an average Continuous Ranked Probability Score of less than 0.15 for individual farms, and an average Energy Score of less than 0.35 for multiple farms, over the 24-hour-ahead horizon. Results show the model’s ability to replicate the power output dynamics through calibrated and sharp predictive densities.     

Examining dynamic currency linkages amongst South Asian economies: An empirical study

In this paper, we examine the currency market linkages of South Asian member countries using daily data from 6 January 2004 to 31st March 2016. Time invariant and varying Copula GARCH models show that South Asian countries, except for India and Nepal/Bhutan, have low levels of currency market linkages which can be ascribed to poor levels of intra-regional trade intensity and portfolio flows. We reconfirm the copula results through Diebold and Yilmaz methodology and document that currency market connectedness is very limited in the South Asian region. The trends of the fundamental determinants of currency co-movements for the South Asian member countries were compared with its neighbouring regional economic bloc in Asia which has a much longer history and a wider membership base i.e ASEAN + 6. From a comparative analysis, it was found that South Asia member states have to work on their governance parameters, improve on their trade linkages and trade tariffs and work towards greater degree of capital account convertibility with adequate safeguards to achieve higher levels of currency market linkages.     

Insurance ratemaking using a copula-based multivariate Tweedie model

The Tweedie distribution, featured with a mass probability at zero, is a convenient tool for insurance claims modeling and pure premium determination in general insurance. Motivated by the fact that an insurance policy typically provides multiple types of coverage, we propose a copula-based multivariate Tweedie regression for modeling the semi-continuous claims while accommodating the association among different types. The proposed approach also allows for dispersion modeling, resulting in a multivariate version of the double generalized linear model. We demonstrate the application in insurance ratemaking using a portfolio of policyholders of automobile insurance from the state of Massachusetts in the United States.     

担保债权凭证之评价——多因子模型和KMV模型之探讨

探讨担保债权凭证商品之评价，包含缩减式模型及结构式模型两种研究方法；前者以多因子相关性模型，而後者以KMV模型为方法探讨之主轴。多因子相关性模型中资产的违约分配函数分别假设为指数、韦伯及Burr分配；再分别结合Gauss Copula或t5 Copula函数，估计商品的信用价差。实证分析以台湾“玉山银行债券资产证券化特殊目的信托2005—1受益证券”为例。实证研究结果发现，指数分配之信用价差估计值偏大，Burr分配估计值最小；t5 Copula函数之信用价差估计值都较Gauss Copula函数之估计值大。此外，将数据作适当调整後应用KMV模型之信用价差估计值比多因子相关性模型之估计值大。     

Relationship between oil price and exchange rate by FDA and copula

This article investigates the relationship between daily crude oil prices and exchange rates. Functional data analysis is used to show the clustering pattern of exchange rates and oil prices over the time period through high dimensional visualizations. We select exchange rates for important currencies related to crude oil prices by using the objective Bayesian variable selection method. The selected sample data exhibits non-normal distribution with fat tails and skewness. Under the non-normality of the return series, we use copula functions that do not require to assume the bivariate normality to consider marginal distribution. In particular, our study applies the popular and powerful statistical methods such as Gaussian copula partial correlations and Gaussian copula marginal regression. We find evidence of significant dependence for all considered pairs, except for the Mexican peso-Brent. Our empirical results also show that the rise in the West Texas Intermediate (WTI) oil price returns is associated with a depreciation of the US dollar.