Time-varying Copula Research Articles

The development of a novel nonstationary meteorological and hydrological drought index using the climatic and anthropogenic indices as covariates

Hydrometeorological variables such as precipitation and runoff are not necessarily stationary under change environment due to anthropogenic influences and climate change. Therefore, the assumption of stationary of standardized drought indices cannot necessarily be applied in the future. The novelty of this study is to develop a nonstationary multivariate standardized drought index, entitled the Nonstationary Meteorological and Hydrological Drought Index (NMHDI), as an improvement of the Meteorological and Hydrological Drought Index (MHDI). The method used consisted of three parts: (1) simulation of the nonstationary marginal distribution of precipitation data using climatic indices as covariates; (2) the nonstationary probability model fitted to runoff data using the climatic and anthropogenic indices as covariates and; (3) using the time-varying copula model to describe the temporal dependence structure of precipitation and runoff, following which the NMHDI was calculated. The performances of the NMHDI and MHDI was compared at the Huaxian station in Weihe River Basin, western China for the period 1961–2010 to illustrate the capabilities of the NMHDI. Moreover, bivariate frequency analysis was conducted using the two indices. The results indicated that the nonstationary model showed better performance in reproducing the variations in precipitation and runoff data and their dependence structure over time as compared with stationary one. The NMHDI identified more frequent extreme droughts. The improved performance of the NMHDI was attributed to its ability to respond to the continuously changing environment. In addition, the MHDI and NMHDI estimated significantly different recurrence periods. The proposed NMHDI provides a novel approach to comprehensive drought monitoring, and can provide valuable information for drought management policymaking under a changing environment.

Determining the optimal window length of the time-varying copula parameter: a simulation study

A time-varying copula is a multivariate cumulative distribution function that can accommodate the temporal dependence of random variables. To capture the temporal dependence of random variables using a copula, we can form a time variation on copula parameters. Some studies reported that a function of a latent variable following an autoregressive process defines time-varying copula parameters. The process consists of an autoregressive coefficient describing the influence of the parameters in previous times and a forcing variable representing the relationship between the marginal variables which utilize previous information over a certain number of window lengths of the observations. Previous studies reported that ARMA(1,10) defines time-varying copula parameters. However, the optimal parameters of time-varying copulas do not always require ten last observations. Therefore, we determine the optimal window length of the time-varying copula parameter by conducting a numerical simulation on four types of copula with different strengths and directions of dependence. The window length is defined as a new parameter and the optimal parameters can be obtained by finding the values producing the smallest AIC. We also provide a numerical simulation on how to improve the accuracy of the predicted series by changing the mean and standard deviation of the residual pairs.

Re-examination of international bond market dependence: Evidence from a pair copula approach

The finance literature provides substantial evidence on the dependence between international bond markets across developed and emerging countries. Early works in this area were based on linear models and multivariate GARCH models. However, based on the limitations of these models this paper re-examines the non-linearity, multivariate and tail dependence structure between government bond markets of the US, UK, Japan, Germany, Canada, France, Italy, Australia and the Eurozone, from January 1970 to February 2019 using ARMA-GARCH based pair- copula models. We find that the bond markets in our sample tend to have both upper tail dependence in terms of positive shocks and lower tail dependence in terms of negative shocks. The estimated C-vine shows Eurozone has the highest average dependency. The D-vine, with optimal chain dependency structure shows the best order of connectedness to be the UK, the USA, Italy, Japan, Eurozone, France, Canada, Germany and Australia. The R-vine copula results underline the complex dynamics of bond market relations existing between the selected economies. The estimated R-vine shows Eurozone, Germany and Australia are the most inter-connected nodes. The multivariate distribution structure (interdependency) of bond markets for all countries were modelled with the C-vine, D-vine and R-vine copulas. In this application, the R-vine copula allows for detailed modelling of all bond markets and hence provides a more accurate goodness of fit and mean square error for the interdependency between all markets. In light of the changing volatility in bond markets, we conduct additional tests using time-varying copulas and find that the dependence structure among the bond markets examined is time-varying with the dynamic dependence parameter plots revealing that the nature of the dependence structure is intense during crisis periods.

Measuring dynamic dependency using time-varying copulas with extended parameters: Evidence from exchange rates data

This study proposes a novel approach that investigates the dynamic dependency among exchange rates by extending time-varying copulas' parameters following an autoregressive moving average (ARMA) process. The process consists of an autoregressive part that explains the effect of the previous parameters and a forcing variable that measures the dependence structure between marginal variables. We apply this model to the daily data of the exchange rates of five Asian countries with the strongest economies before and during the 2020 pandemic, namely CNY/USD, IDR/USD, INR/USD, JPY/USD, and KRW/USD. The ARIMA-GARCH model was used to model the exchange rates data and estimate the dynamic dependence using time-varying copulas with the extended parameters. The dynamic dependencies between Chinas and the four countries' exchange rates before and during the 2020 pandemic was evidenced. Moreover, India is the country whose exchange rate has been most strongly affected by the pandemic. Some of the highlights of the proposed approach are:•This paper provides two algorithms to investigate the dynamic dependencies among exchange rates data during a crisis and forecast the data using time-varying copulas with the extended parameters.•There are four extended time-varying copulas' parameters which can measure the dynamic dependencies between variables.•The computation procedure is easy to implement.

Analysis of dependence structure among investor sentiment, policy uncertainty and international oil prices

The behavioural aspect of finance and economics has an embedded importance in the literature. This paper provides an evidence of the interrelationship of international oil prices with economic policy uncertainty, consumer sentiments and US investor sentiment proxies. To test the underlying dependence structure, we employ time invariant and time-varying copula methods due to dynamic return patterns of our sampled indices. Our analysis reveals an underlying relationship of investor sentiments and economic policy uncertainty with international oil prices not only during normal periods but also in the periods of financial turmoil. Results of our nonlinear causality highlight potential of bidirectional spillover between oil prices and investor sentiment indices across all quantiles. This helps in understanding that a volatile international oil market may have significant impact on investor sentiments and economic policy uncertainty and vice versa. [Received: December 20, 2019; Accepted: June 17, 2020]

Analysis of dependence structure among investor sentiment, policy uncertainty and international oil prices

The behavioural aspect of finance and economics has an embedded importance in the literature. This paper provides an evidence of the interrelationship of international oil prices with economic policy uncertainty, consumer sentiments and US investor sentiment proxies. To test the underlying dependence structure, we employ time invariant and time-varying copula methods due to dynamic return patterns of our sampled indices. Our analysis reveals an underlying relationship of investor sentiments and economic policy uncertainty with international oil prices not only during normal periods but also in the periods of financial turmoil. Results of our nonlinear causality highlight potential of bidirectional spillover between oil prices and investor sentiment indices across all quantiles. This helps in understanding that a volatile international oil market may have significant impact on investor sentiments and economic policy uncertainty and vice versa. [Received: December 20, 2019; Accepted: June 17, 2020]

Joint Planning of Transmission and Distribution Network Considering Wind-solar Complementarity

The temporal and spatial distribution characteristics of wind power and photovoltaic output are complementary to a certain extent, which can stabilize the volatility of single new energy power generation to a certain extent and improve the ability of the grid to absorb new energy. This paper aims to study the joint planning method of power transmission and distribution network considering the complementary characteristics of wind-solar time and space. First, a wind-solar joint distribution model based on the time-varying Copula theory is established, and a wind-solar output simulation method considering the complementary characteristics of time and space is proposed. Then, taking the system investment and new energy consumption capacity as the optimization goals, and taking the system power balance, line transmission capacity, conventional generator set output and climbing capacity as constraints, the joint planning model of transmission and distribution network is established. At last, the analysis of calculation examples proves that the joint planning model of transmission and distribution network considering the complementary characteristics of wind-solar time and space can significantly improve the capacity of the grid to absorb new energy.

Variable structure Copula model and its Comparison with static and time-varying Copula models

Copula model has been increasingly used in reliability modeling of correlation systems. In this paper, the static copula model, time-varying copula model and variable structure copula model are compared. Firstly, variable structure copula model is introduced. Secondly, the procedures of Bayes diagnosis method which is used to diagnose the variable structure points are introduced. Finally, the correctness of Bayes diagnosis method for finding variable structure points is verified by a simple numerical example. The comparison results illustrate that the staged correlation parameter estimated by variable structure Copula model is better than the constant correlation parameter estimated by static Copula model, and also it has a consistent trend with correlation parameter estimated by time-varying Copula model.

Asymmetric Dependence between Oil Prices and Maritime Freight Rates: A Time-Varying Copula Approach

Changes in crude oil price affect the shipping freight market via three different channels. This study explores the dependence structure between oil prices and maritime freight rates to identify the effective channel. Therefore, it investigates the relationship between oil prices and three major maritime freight rates; the Baltic Dry Index (BDI), the Baltic Dirty Tanker Index (BDTI), and the Baltic Clean Tanker Index (BCTI). We employ the decomposition method, not studied in the existing literature, and the copula approach which can identify the time-varying effects and asymmetry in the tail dependence structure between oil prices and freight rates. The main results of this analysis are as follows: the decomposed components display different conditional dependence patterns, and asymmetry is revealed in the upper and lower tail dependence. In the long-run, we find more dependence in extreme periods like the financial crises. In short-run fluctuations, we find the dependence increases in an economic boom. The implications of the results suggest that dependence can vary over time and may change depending on extreme events, implying that the complementary strategies should be different the long-run and short-run.

Climate and nomadic migration in a nonlinear world: evidence of the historical China

This paper deals with climate change and nomadic migration relationships at a long term and wide geographical scale using a statistical approach in the vein of Bai and Kung (2011). More precisely, it presents a reassessment of these relationships in a nonlinear world using threshold regressions, time varying-copula and nonlinear causality tests. The large amount of historical records in China enables us to re-interpret the link between climate and historical social dynamics (Hsiang et al., 2013) through different regimes of temperatures and precipitations.

Temperature gradient modeling of a steel box-girder suspension bridge using Copulas probabilistic method and field monitoring

A novel copula-based probabilistic model is proposed to establish the temperature difference analysis model for a long-span suspension bridge’s steel box girder. The key idea is to express a two-dimensional function of the temperature difference in flat steel box girder by using copulas. The maximum and minimum values of daily temperature difference model was developed using long-terms structural health monitoring data. Then, the correlation between adjacent temperature differences is investigated using five types of copulas. Akaike information criterion (AIC) is used to select an optimal model from five types of copulas, and the optimal joint function (two-dimensional function) for steel box girder’s temperature difference is established. Finally, the structure’s temperature gradient model is extrapolated for the service life of the structure by using Monte Carlo method. Moreover, this paper discusses the temperature gradient models using five types of common copulas and four types of time-varying copulas. The result shows that the t-copula is the optimal function to build the two-dimensional functions for steel box girder’s temperature difference, and the temperature model along the transverse direction can offer useful information that is not available in the design codes.

Extreme linkages between foreign exchange and general financial markets

This study investigates the dynamic linkages between foreign exchange and general financial markets using asymmetric time-varying copula models for the developed markets of G7 countries. We also examine the extreme spillover effects from foreign exchange markets to general financial markets by the copula-based CoVaR approach. The copula estimations reveal asymmetric tail dependence and a positive (negative) dependence between currency and stock markets in Canada (Japan and the United States); a positive (negative) dependence between currency and bond markets in Japan (Canada and the United States). Furthermore, this study observes both the downside and upside spillovers in most of the G7 countries; the evidence of downside spillover is more prevalent than the upside spillover, especially for the stock market. The results indicate that these spillovers are generally asymmetric, namely, the downside spillovers are significantly greater than the upside spillovers. These findings are relevant for international investors and policy makers.

Application Research on Reliability Modeling of Multi-failure Modes Correlation System Based on Time Varying Copula Model

The reliability modeling of dynamic correlation system with multi-failure modes is studied in this paper. Firstly, Patton model, one of the time-varying copula models, is introduced. Secondly, multi-dimensional time-varying copula function of multi-failure modes correlation system is transformed into two-dimensional time-varying copula functions based on vine Copula function, and then reliability modeling and solution procedure of multi-failure modes correlation system is presented based on time-varying copula model. Finally, the above reliability modeling and solution procedures are demonstrated through a vehicle suspension system engineering case, and their correctness are proved by the results obtained in engineering case.

Modeling dynamic dependence between crude oil and natural gas return rates: A time-varying geometric copula approach

The widely used models associated with copulas usually fall in the time-invariant framework where the parameters in copulas do not change through time. Recently, time-varying copulas whose parameters are driven by lagged variables and past observations have attracted considerable attention. This paper examines the dynamic dependence between crude oil and natural gas return rates by time-varying copulas including geometric copulas. West Texas Intermediate (WTI) crude oil and New York Harbor (NYH) natural gas daily prices over the period January 3, 2006 to December 30, 2016 is analyzed. The marginal models are specified as AR(p)-GJR-GARCH(P,Q)-skewed-t models. The performance of time-varying copulas and time-invariant copulas is demonstrated. According to Bayesian Information Criterion, time-varying rotated geometric Gumbel copula performs the best.

The dependence structure between equity and foreign exchange markets and tail risk forecasts of foreign investments

Motivated by the importance of the dependence structure between equity and foreign exchange rates in international financial markets, we investigate whether modelling the dependence structure can help forecast the tail risk of foreign investments. We propose a new time-varying asymmetric copula for modelling the dependence structure and forecasting the tail risk. We conduct backtesting on our tail risk forecasts for 12 major developed and emerging markets. We find that modelling the dependence structure can improve the tail risk forecast and make risk management of foreign investments more robust.

Do Tense Geopolitical Factors Drive Crude Oil Prices?

Geopolitical factors are considered a crucial factor that makes a difference in crude oil prices. Over the last three decades, many political events occurred frequently, causing short-term fluctuations in crude oil prices. This paper aims to examine the dynamic correlation and causal link between geopolitical factors and crude oil prices based on data from June 1987 to February 2020. By using a time-varying copula approach, it is shown that the correlation between geopolitical factors and crude oil prices is strong during periods of political tensions. The GPA (geopolitical acts) index, as the real factor, drives the rise in prices of crude oil. Moreover, the dynamic correlation between geopolitical factors and crude oil prices shows strong volatility over time during periods of political tensions. We also found unidirectional causality running from geopolitical factors to crude oil prices by using the Granger causality test.

Geopolitical risk and renewable energy stock markets: An insight from multiscale dynamic risk spillover

This paper investigates the risk spillovers from geopolitical risk to five renewable energy stock markets by measuring four types of (normalized) delta conditional Value-at-Risk incorporating the variational mode decomposition and time-varying copula approaches, and further tests the possible asymmetries of risk spillovers. The empirical results manifest that, there are significant risk spillovers from geopolitical risk to renewable energy stock markets and the risk spillovers do not exhibit as clear positive or negative pattern. Next, the asymmetries of risk spillovers widely exist on the following three facets. First, the risk spillovers from stock and oil market uncertainties are obviously higher than that from geopolitical risk in most cases, whereas geopolitical risk manifests similar short-run effects on China’s renewable energy stock market as the other two uncertainties. Second, the downside risks of renewable energy stock markets are more sensitive to the variations of stock and oil market uncertainties, while the risk spillovers from geopolitical risk are more symmetric during bull and bear market periods. Finally, there are significantly greater long-run risk spillovers to China’s renewable energy stock market. Conversely, the other four markets are more heavily shocked in the short-run.

Dependence and risk spillovers between green bonds and clean energy markets

In this study, we first examine the dynamic dependence structure between green bonds (GBs) and several global and sectoral clean energy (CE) markets by using several time-invariant and time-varying copula approaches over the period from 5 July 2011 to 24 February 2020. We then apply conditional value-at-risk (CoVaR) and delta CoVaR to capture downside and upside risk spillovers from CE to GB, and vice versa. Our empirical analysis shows that there is positive time-varying average and tail dependence between GBs and CE stock markets. Moreover, extreme downward or upward movements in the CE stock market have a spillover effect on the GB market, and vice versa. Furthermore, the risk spillover between these markets is asymmetric. These results make an important contribution to policymakers and environmentally friendly investors with GB positions by adding unexpected tail losses. It is critical for the GB investors to invest their capital effectively in economic activities that are consistent with a low-carbon economy.

Studying the properties of the Bitcoin as a diversifying and hedging asset through a copula analysis: Constant and time-varying

In this study, we analyze the properties of Bitcoin as a diversifier asset and hedge asset against the movement of international market stock indices: S&P500 (US), STOXX50 (EU), NIKKEI (Japan), CSI300 (Shanghai), and HSI (Hong Kong). For this, we use several copula models: Gaussian, Student-t, Clayton, Gumbel, and Frank. The analysis period runs from August 18, 2011 to June 31, 2019. We found that the Gaussian and Student-t copulas are best at fitting the structure dependence between markets. Also, these copulas suggest that under normal market conditions, Bitcoin might act as a hedge asset against the stock price movements of all international markets analyzed. However, the dependence on the Shanghai and Hong Kong markets was somewhat higher. Also, under extreme market conditions, the role of Bitcoin might change from hedge to diversifier. In a time-varying copula analysis, given by the Student-t copula, we found that even under normal market conditions, for some markets, the role of Bitcoin as a hedge asset might fail on a high number of days.

Household margin insurance of agricultural sector in Indonesia using a farmer exchange rate index

PurposeFarmer exchange rate (FER) is the ratio between a farmer's income and expenditure and is also an indicator of farmers’ welfare. There is little research regarding its use in risk modeling in crop insurance. This study seeks to propose a design for a household margin insurance scheme of the agricultural sector based on FER.Design/methodology/approachThis research employs various risk modeling concepts, i.e. value at risk, loss models and premium calculation, to construct the proposed model. The standard linear, static and time-varying copula models are used to identify the dependency between variables involved in calculating FER.FindingsFirst, FER can be considered as the primary variable for risk modeling in agricultural household margin insurance because it demonstrates farmers’ financial ability. Second, temporal dependence estimated using the time-varying copula can minimize errors, reduce the premium rate and result in a tighter guarantee's level of security.Originality/valueThis research extends the previous similar studies related to the use of index ratio in margin insurance loss modeling. Its authenticity is in the use of FER, which represents the farmers' trading capability. FER determines farmers’ losses by considering two aspects: the farmers’ income rate and their ability to fulfill their life and farming needs. Also, originality exists in the use of the time-varying copulas in identifying the dependence of the indices involved in calculating FER.