copula-GARCH Approach Research Articles

Development of decomposition-based model using Copula-GARCH approach to simulate instantaneous peak discharge

Estimation of instantaneous peak discharge is important in the design of hydraulic structures and reservoir management. In this study, a new approach called CEEMD-Copula-GARCH is presented for simulating instantaneous peak discharge in the Qale Shahrokh basin, upstream of Zayanderood Dam, Iran. In the developed method, the Complementary ensemble empirical mode decomposition (CEEMD) algorithm was used to analyze the observed values and generate the intrinsic mode function values and residual series. For this purpose, the intrinsic mode function values were simulated based on vine copula and its tree sequence (C-vine, D-vine, R-vine and their independent and Gaussian modes), and the residual series of the CEEMD algorithm were simulated by the GARCH model. The results of simulating instantaneous peak discharge values (m3/s) using the CEEMD-Copula-GARCH approach in the study area showed that the amount of simulation error based on the RMSE statistic compared to the CEEMD-Copula model and simulation without decomposition has improved by about 20 and 70%, respectively. The model’s efficiency was also estimated based on the Nash–Sutcliffe efficiency in the proposed approach of 0.99, and the certainty of the proposed approach was also confirmed based on the presented violin plot. According to the presented results, the proposed approach has high accuracy and efficiency in the simulation of instantaneous peak discharge (m3/s), which can be used in the flood control system design and flood management. Using the methodology proposed in this study, multivariable models can be used in simulating univariate series with high accuracy.

The application of the hybrid copula-GARCH approach in the simulation of extreme discharge values

Statistical analysis and simulation of annual maximum discharge values, while considering the corresponding maximum daily rainfall, provide a comprehensive view of flood management. This research presents the application of copula functions for simulating and modeling two variables of annual maximum discharge and corresponding precipitation. In this research, the performance of copula-based models and ARCH-based models including VAR-GARCH, copula, and copula-GARCH models was then evaluated to simulate the annual maximum discharge values. The simulation results of all three models were evaluated using NSE and NRMSE statistics. According to the 95% confidence intervals, the accuracy of all three models was confirmed. The correlation results of the studied pair variables confirmed the possibility of using copula-based models. The results of simulations revealed that a higher accuracy of the copula-GARCH approach compared with two models copula and VAR-GARCH. Considering 76% efficiency (NSE = 0.76) of the copula-GARCH approach, the results indicated 20 and 2.7% improvements in the performance of the proposed approach compared to both VAR-GARCH and copula models. The results also illustrated that by combining nonlinear ARCH models with copula-based simulations, the reliability of simulation results increased. The results obtained in this study suggest that the proposed method is very effective for increasing the certainty of frequency analysis of two variables. Because the copula-GARCH approach simulates the average values, the first and third quarters, as well as the amplitude of changes of 5 and 95% of the data better than the other two models.Graphical abstractViolin plot of AMD series in copula scale

Time-varying dependence of Bitcoin

This paper analyzes Bitcoin investment in terms of portfolio diversification. Over the period July 2011-April 2021, we use the copula-GARCH approach to test the time-varying dependence of Bitcoin in a portfolio composed of six stock markets (CAC40, DJIA, EUROSTOXX50, FTSE100, HANGSENG, and NIKKEI225). Our results reveal that volatility modeling provides better results with the Dynamic Conditional Correlation model. The performance of the portfolio is largely due to the high returns of Bitcoin which allows for better portfolio diversification. As a result, there is a mitigation of the extreme rates of return associated with crypto-currencies. Finally, while Bitcoin's contribution to the portfolio is more attributable to its risk than its return, it does play a role in stabilizing portfolio performance, for varying levels of risk.

Multivariate time-series modeling with generative neural networks

Generative moment matching networks (GMMNs) are introduced as dependence models for the joint innovation distribution of multivariate time series (MTS). Following the popular copula–GARCH approach for modeling dependent MTS data, a framework based on a GMMN–GARCH approach is presented. First, ARMA–GARCH models are utilized to capture the serial dependence within each univariate marginal time series. Second, if the number of marginal time series is large, principal component analysis (PCA) is used as a dimension-reduction step. Last, the remaining cross-sectional dependence is modeled via a GMMN, the main contribution of this work. GMMNs are highly flexible and easy to simulate from, which is a major advantage over the copula–GARCH approach. Applications involving yield curve modeling and the analysis of foreign exchange-rate returns demonstrate the utility of the GMMN–GARCH approach, especially in terms of producing better empirical predictive distributions and making better probabilistic forecasts.

Did The Global Financial Crisis Alter Cross-market Correlation? A Copula-GARCH Approach

This paper uses a wide variety of copulas to study the correlation between the US market and a sample composed of nine developed and emerging markets over a 13 years period, including the subprime crisis. We try to analyze the markets behavior during high volatility periods and assess if the financial crisis led to a significant and durable change in the cross-market correlation patterns. Results offer strong evidence in favor of a contagion effect. Developed markets are those who registered the most important increases in cross-market correlations during high volatility periods. This may be attributed to their high degree of financial integration. However, cross-market correlation is weak for the whole sample period and decreased during the post-crisis period, implying that international diversification still offers interesting opportunities for investors. Moreover, diversification opportunities are not restricted to emerging markets but also concern developed markets.

Modeling Co-Movement among Different Agricultural Commodity Markets: A Copula-GARCH Approach

The aim of this research is to explore the volatility contagion among different agricultural commodity markets. For this purpose, this research make use of the copula-GARCH (Generalized Autoregressive Conditional Heteroskedasticity) model for the daily spot prices of six major agriculture grain commodities including corn, wheat, soybeans, soya oil, cotton, and oat over the period from 2000 to 2019. Our results provide evidence that significant contagion effects and risk transmissions exist among different agricultural grain commodity markets, suggesting that potential speculation effects on one agricultural market could be contagious for another agricultural market and result an increase in volatility in agricultural product markets. Second, agricultural commodities appears to co-move symmetrically. We also find substantial extreme co-movements among agricultural commodity markets. This indicates that agricultural commodity markets tend to crash (boom) together during extreme events. Moreover, after the food crisis, contagion effects and risk transmissions among different agricultural commodity markets increased substantially. Fourth, we find that the strongest contagion effects and risk transmissions are between corn and soybeans, and the weakest contagion effects and risk transmissions are between soya oil cotton and between cotton and oat. Last, we document that the co-movement varies over time. Our findings hold important implications for modeling the co-movement by the copula-GARCH approach.

The extreme risk spillovers between the US and China’s agricultural commodity futures markets

In this study, we investigate the downside and upside risk spillover effects between the same kind of agricultural futures in the Chinese and US markets, taking the value-at-risk (VaR) and conditional value-at-risk (CVaR) as a risk measure, characterized and computed using copula-GARCH approach. We find evidence of a significant positive dependence between the US and Chinese agricultural commodity futures markets. And the empirical results also show that the existence of downside and upside risk spillover effects between variables, especially significant during financial turmoil periods. Market regulators and traders of agricultural futures will benefit by identifying tail dependence and extreme risk spillovers.

Integrated measurement of liquidity risk and market risk of company bonds based on the optimal Copula model

The bond market is an important part of the capital market, reflecting the debtor-creditor relationship. Correspondingly, the P2P network lending platform, which plays a vital role in emerging Internet Finance, represents the same relationship. In both markets, the risks in investment and financing channels are complex and diverse, including liquidity risk, market risk, tax risk and so on. All the risks do not exist alone, performed as an integrated risk. This paper establishes an index for measuring corporate bonds’ liquidity, by using a Copula-GARCH approach and generating empirical distribution to integrate the liquidity risk and market risk of corporate bonds. Particularly, according to the Likelihood function test results, t-Copula is the optimum Copula function. The model can also be applied to measure the integrated risk of the P2P network lending platform after improvement.

Interdependence of oil prices and exchange rates: Evidence from copula-based GARCH model

This paper aims to investigate the conditional dependence structure between crude oil prices and three US dollar exchange rates (China, India and South Korea) from a new perspective using a copula-GARCH approach. Various kinds of copulas both time-invariant and time-varying dependence dynamics are fitted. Over the 2008–2018 period, the findings provide evidence of significant dependence in terms of symmetric structure between the oil prices and the exchange rate returns. Further, the tail dependence and dynamic dependence between two variables add a supplement to the explanatory ability of the model. Empirical results indicate the intercorrelation between crude oil and exchange rate movements, and provide benefits in risk diversification and inflation targeting. The findings also have significant implications for risk management, monetary policies to determine the behavior of fiscal policy in oil-exporting countries.

An analysis of dependence between oil price and stock market with Copula-Garch approach: An empirical analysis from Istanbul stock exchange

This paper examines the dependence structure between National 100, National 50, and National 30 Indices of Istanbul Stock Exchange and international Brent oil price by using copula-GARCH method. Linear correlation has a serious deficiency. Whereas copula method is not invariant under non-linear strictly increasing transformation. Meanwhile the dependence measures derived from copulas can overcome this shortcoming and have broader applications. Furthermore, copulas can be used to describe more complex multivariate dependence structures, such as non-linear and tail dependence. In this study, we covered the period from March 14, 2001 to March 23, 2018 by using daily prices. Our findings suggest that there is a weak dependence structure between Istanbul Stock Exchange and Brent oil prices which may have significant implications for policymakers, investors and risk managers in terms of the relationship between oil prices and the stock market.

A copula-GARCH approach for analyzing dynamic conditional dependency structure between liquefied petroleum gas freight rate, product price arbitrage and crude oil price

Global liquefied petroleum gas (LPG) trade shows an increasing trend but is under-researched. This paper focuses on the LPG market and aims to model the dependence dynamics among LPG freight rates, crude oil price and propane location arbitrage. Conditional copula-GARCH model is applied to estimate dependencies. Different types of copulas with both time-invariant and time-varying dependence structures are fitted and their suitability has been compared. The findings suggest that firstly, Baltic LPG (BLPG) freight rate and the arbitrage between propane Far East and Middle East prices have conditional time-varying dependence and the dependence is higher in market downturns. Furthermore, BLPG and the arbitrage between Far East and US propane prices, have symmetric dependence and such a relationship has strengthened since 2013. Secondly, Middle East propane price is found to have the strongest correlation with crude oil prices compared to Far East and US propane prices, indicating higher sensitivity to crude oil price changes. Last but not least, the relationship between crude oil and BLPG is relatively weak and mostly positive.

An empirical study of inbound tourism demand in China: a copula-GARCH approach

ABSTRACTThis paper proposes new models for analyzing the volatility and dependence of monthly tourist arrivals to China applying a copula-GARCH approach. A desegregation of the top six origins of China inbound tourists from the period January 1994 to December 2013 is used in this study. The empirical results show that there is a strong seasonal effect in all cases and ​​​​​​ some habit persistence on monthly tourist arrival growth rate for South Korea, Russia, the United States (US), and Malaysia. Second, the volatilities of arrival growth rates to China are impacted significantly by their own short- and long-run effects, except for Russia and South Korea. Only short-run shock affects Russian arrivals while only long-run shocks are affecting South Korea arrivals. Third, the conditional dependence among different source countries is found to be positive and significant, but the conditional dependence for all considered pairs is low. Moreover, there is extreme co-movement (tail dependence) between the six major tourism source countries, suggesting the pairwise of international tourist arrivals shows a related increasing or decreasing pattern during extreme events. Implications are discussed and recommendations provided.

Dependence between stock market and foreign exchange market in South Asia: A Copula-Garch approach

The paper studies the dependence pattern between stock market and foreign exchange market of three South Asian countries; namely Bangladesh, India and Sri Lanka by using five copula functions, to reveal asymmetric dependence structure. This paper focuses South Asia because of its promise as portfolio investment destination. The dependence structure between stock market and foreign exchange market assists MNCs, private equity firms, international portfolio managers and policy makers in international investment decision making. The paper also studies tail dependence (upper and lower). Markets crash together rather boom together, which can be traced by tail dependence parameter. Correlation, Kendall’s tau and Spearman’s rho reveal linear dependence. However, Copulas reveal non-linear dependence between non-normal distributions. In this paper, Copula functions are applied between marginal distributions of stationary uni-variate return series. Using daily return series for the period of July 31, 2009 to July 31, 2013, ARMA-GARCH type model are applied to obtain marginal distributions of return series. The results from marginal models indicate that volatility dies immediately after a crisis; meanwhile positive news creates more volatility than negatives. The results from copula models indicate existence of asymmetric dependence, with upper tail dependence for all pairs, implying dependence increases in bull market situation (price increase in financial instruments). Both Bangladeshi and Indian pairs provide some diversification possibility, against no diversification for investing in Sri Lankan market. Moreover, Bangladesh and India demonstrated as promising investment destination in terms of risk –return criteria. Foreign investors are recommended to employ proper risk and investment management strategy in order to earn capital gain, by following diversification strategy. Conversely, investment recipient countries are recommended to establish a stable, well regulated stock market, with high stock market capitalization to GDP. Besides, monetary policy should stabilize the exchange rate of currency to attract foreign investors. Copula based dependence measures assist foreign investors and investment recipient countries to change their related strategies and policies; subsequently they will be able to maximize their utility functions.

A Method for Systemic Risk Estimation Based on CDS Indices

Abstract The copula-GARCH approach provides a flexible and versatile method for modeling multivariate time series. In this study we focus on describing the credit risk dependence pattern between real and financial sectors as it is described by two representative iTraxx indices. Multi-stage estimation is used for parametric ARMA-GARCH-copula models. We derive critical values for the parameter estimates using asymptotic, bootstrap and copula sampling methods. The results obtained indicate a positive symmetric dependence structure with statistically significant tail dependence coefficients. Goodness-of-Fit tests indicate which model provides the best fit to data.

The Conditional Dependence Structure between Precious Metals: A Copula-GARCH Approach

The aim of the paper is to analyse the conditional dependence structure between precious metal returns using a copula-DCC-GARCH approach. Conditional correlation matrices are used to identify the states of the precious metals market by assuming that a given state of the market corresponds to a typical pattern of the conditional dependence structure. Cluster analysis allows for pointing at transition points between the market states, that is the points of drastic change in the conditional dependence structure. The application of the methodology described above to the period between 1997 and 2013 indicates three market states of four major precious metals (gold, silver, platinum and palladium). The results obtained reveal a sudden increase in dependencies between precious metals at the turn of April and May 2004.

The conditional dependence structure of insurance sector credit default swap indices

This study assesses the dependence structure of insurance sector credit default swap indices, using a copula-GARCH approach. We use daily data of the US, EU, and UK insurance sectors, covering the period from January 2004 to June 2013. We find substantial increases in dependence during the financial crisis periods. Prior to the crises, various copulas are found to best fit each pair; specifically, asymmetric tail dependence is found for the UK–US pair, suggesting the possibility of large simultaneous losses. However, during the crisis periods, the Frank copula fits best, with no significant tail dependence detected, implying low systemic risks.

Dependence and extreme dependence of crude oil and natural gas prices with applications to risk management

In this article, we show how the copula-GARCH approach can be appropriately used to investigate the conditional dependence structure between the crude oil and natural gas markets as well as to derive implications for portfolio risk management in extreme economic conditions. Using daily price data from January 1997 to October 2011, our in-sample results show evidence of asymmetric dependence between the two markets. The crude oil and gas markets tend to comove closely together during bullish periods, but not at all during bearish periods. Moreover, taking the extreme comovement into account leads to an improvement in the accuracy of the out-of-sample Value-at-Risk forecasts.

Conditional dependence structure between oil prices and exchange rates: A copula-GARCH approach

We study the conditional dependence structure between crude oil prices and U.S. dollar exchange rates using a copula-GARCH approach. Various copula functions of the elliptical, Archimedean and quadratic families are used to model the underlying dependence structure in both bearish and bullish market phases. Over the 2000–2011 period, we find evidence of significant and symmetric dependence for almost all the oil-exchange rate pairs considered. The rise in the price of oil is found to be associated with the depreciation of the dollar. Moreover, we show that Student-t copulas best capture the extreme dependence, and that taking the extreme comovement into account leads to improve the accuracy of VaR forecasts. Our main results remain unchanged when considering alternative GARCH-type specifications and the crisis period, but are sensitive to the use of raw returns.

Modeling the Dependence Structure between Bonds and Stocks: A Multivariate Copula Approach

We apply a copula-GARCH approach to modeling the joint distribution of excess returns of four major assets: one year and ten year Treasury bonds and S&P 500 and Nasdaq indices. Three approaches are attempted in building the multivariate copula for the dependence structure of multiple assets: (1) n-dimensional normal copula and n-dimensional Student's t copula, (2) hierarchical Archimedean copula and (3) mixed copula. To ensure better convergence in estimation, we adopt a two-stage estimation procedure where marginal distributions are estimated separately in the first stage and then the copula is estimated in the second. Our results show that normal copula and Student's t copula yield higher log-likelihoods while hierarchical Archimedean copula and mixed copula yield lower log-likelihoods. We plot overall and rolling correlation, exceedance correlation and tail dependence of the data and find significant time-varying features with correlations between stocks and bonds, and with asymmetric exceedance correlation among all assets. With a time-varying dependence structure, our Student's t copula yields the highest log-likelihood and generates the most consistent dependence patterns with the data.