In this paper, a new time-varying optimal copula model is proposed to precisely identify the optimal dependence structure of bivariate time series at every time point. In this model, half-rotated copulas, i.e. CR1G(u,v;θ)=v-COG(1-u,v;θ) and CR2G(u,v;θ)=u-COG(1-u,v;θ), are constructed to capture the asymmetric negative dependence, especially for the negative extreme dependence, i.e. lower-upper tail τLU(α)=Pr(X< FX-1(α)|Y >FY-1(1-α)) and upper-lower tail dependence τLU(α)=Pr(X >FX-1(1-α)|Y< FY-1(α)) for a small α, e.g. 0.05. Meanwhile, the distribution-free test for independence is introduced to verify the dependent relationship and reduce the computation time. At last, the time-varying optimal copula model is employed to analyse the dynamic dependence between energy markets, i.e. crude oil and natural gas markets, and exchange market. It is found that for Brent-USDX pair the dependence is significantly negative, the proportion of half-rotated Gumbel copula is larger than that of the original Gumbel or rotated Gumbel, the lower-upper or upper-lower tail dependence is obviously larger than the upper-upper or lower-lower tail dependence especially in the crisis period, and above empirical results for GAS-USDX pair are similar but not very remarkable. However, the dependence between Brent and GAS is positive and the upper-upper or lower-lower tail dependence is larger than lower-upper or upper-lower tail dependence. Meanwhile, the types of dependence structureacross markets vary over time and that emergencies are usually the major cause of sudden changes in the dependence structure. Resulas also show that the TVOC model captures the dynamic characteristics of the direction and intensity of the dependence as well as the dynamic characteristics of the types of dependence structure. In particular, the TVOC model canbe employed to predict the copula-dependence structure in a newway, which provides an analytical tool for market investors and risk managers to adjust their portfolio strategy, hedge the investment risk and guard against risk spillover and even a financial contagion.
JI Qiang, LIU Bing-yue, FAN Ying
. Dynamic Dependence Between International Oil, Natural Gas and Exchange Market Based on a New Time-varying Optimal Copula Model[J]. Chinese Journal of Management Science, 2016
, 24(10)
: 1
-9
.
DOI: 10.16381/j.cnki.issn1003-207x.2016.10.001
[1] Cherubini U,Luciano E,Vecchiato W.Copula methods in finance[M].New Jersey:John Wiley&Sons,2004.
[2] 韦艳华,张世英.金融市场的相关性分析——Copula-GARCH模型及其应用[J].系统工程,2004,22(4):7-12.
[3] Penzer J,Schmid F,Schmidt R.Measuring large comovements in financial markets[J].Quantitative Finance,2012,12(7):1037-1049.
[4] Wu C C,Lin Z Y.An economic evaluation of stock-bond return comovements with copula-based GARCH models[J].Quantitative Finance,2014,14(7):1283-1296.
[5] 亢娅丽,朱磊,范英.基于Copula函数的EU ETS和电力市场间相关性分析[J].中国管理科学,2014,22(S1):814-821.
[6] 吴振翔,陈敏,叶五一,等.基于Copula-GARCH的投资组合风险分析[J].系统工程理论与实践,2006,26(3):45-52.
[7] Kole E,Koedijk K,Verbeek M.Selecting copulas for risk management[J].Journal of Banking&Finance,2007,31(8):2405-2423.
[8] 韦艳华,张世英.多元Copula-GARCH模型及其在金融风险分析上的应用[J].数理统计与管理,2007,26(3):432-439.
[9] 叶五一,缪柏其.基于Copula变点检测的美国次级债金融危机传染分析[J].中国管理科学,2009,17(3):1-7.
[10] Ning C.Dependence structure between the equity market and the foreign exchange market-a copula approach[J].Journal of International Money and Finance,2010,29:743-759.
[11] 李建平,丰吉闯,宋浩,等.风险相关性下的信用风险、市场风险和操作风险集成度量[J].中国管理科学,2010,18(1):18-25.
[12] 吴吉林.基于机制转换Copula模型的股市量价尾部关系研究[J].中国管理科学,2012,20(5):16-23.
[13] 叶五一,李磊,缪柏其.高频连涨连跌收益率的相依结构以及CVaR分析[J].中国管理科学,2013,21(1):8-15.
[14] Hu Ling.Dependence patterns across financial markets:a mixed copula approach[J].Applied Financial Economics,2006,16(10):717-729.
[15] Patton AJ.Modelling asymmetric exchange rate dependence[J].International Economic Review,2006,47(2):527-556.
[16] Creal D,Koopman S J,Lucas A.A general framework for observation driven time-varying parameter models[R].Tinbergen Institute Discussion Paper,2008.
[17] Giacomini E,Härdle W,Spokoiny V.Inhomogeneous dependence modeling with time-varying copulae[J].Journal of Business&Economic Statistics,2009,27(2):224-234.
[18] Hafner C M,Reznikova O.Efficient estimation of a semiparametric dynamic copula model[J].Computational Statistics&Data Analysis,2010,54(11):2609-2627.
[19] Narayan P K,Narayan S,Prasad A.Understanding the oil price-exchange rate nexus for the Fiji islands[J].Energy Economics,2008,30(5):2686-2696.
[20] Ji Qiang.System analysis approach for the identification of factors driving crude oil prices[J].Computers&Industrial Engineering,2012,63(3):615-625.
[21] Ji Qiang,Fan Ying.How does oil price volatility affect non-energy commodity markets?[J].Applied Energy,2012,89(1):273-280.
[22] Patton A J.A review of copula models for economic time series[J].Journal of Multivariate Analysis,2012,110(5):4-18.
[23] Sklar A.Fonctions de répartitionàn dimensions et leurs marges[J].Publications de l'Institut Statistique de l'UniversitéParis,1959,8:229-231.
[24] Joe H.Multivariate models and dependence concepts[M].London:Chapman&Hall,1997.
[25] Nelsen R B.An introduction to copulas[M].New York:Springer,1999.
[26] Fermanian J D,Scaillet O.Some statistical pitfalls in copula modeling for financial applications[R].FAME Working Paper,2004.
[27] Kojadinovic I,Yan Jun,Holmes M.Fast large-sample goodness-of-fit tests for copulas[J].Statistica Sinica,2011,21(2):841-871.
[28] Guégan D,Zhang Jing.Change analysis of a dynamic copula for measuring dependence in multivariate financial data[J].Quantitative Finance,2010,10(4):421-430.
[29] Okimoto T.New evidence of asymmetric dependence structures in international equity markets[J].Journal of Financial and Quantitative Analysis,2008,43(3):781-815.
[30] Garcia R,Tsafack G.Dependence structure and extreme comovements in international equity and bond markets[J].Journal of Banking&Finance,2011,35(8):1954-1970.
[31] Hollander M,Wolfe D A.Nonparametric statistical methods[M].New York:John Wiley&Sons,1973.
[32] Swanson N R.Money and output viewed through a rolling window[J].Journal of Monetary Economics,1998,41(3):455-474.
[33] Fan Jianqing,Gu Juan.Semiparametric estimation of Value at Risk[J].The Econometrics Journal,2003,6(2):261-290.
[34] Hill J B.Efficient tests of long-run causation in trivariate VAR processes with a rolling window study of the money-income relationship[J].Journal of Applied Econometrics,2007,22:747-765.
[35] Aloui R,Hammoudeh S,Nguyen D K.A time-varying copula approach to oil and stock market dependence:The case of transition economies[J].Energy Economics,2013,39:208-221.
[36] Reboredo J C.Modelling oil price and exchange rate co-movements[J].Journal of Policy Modeling,2012,34(3):419-440.
[37] Wu C C,Chung H,Chang Y H.The economic value of co-movement between oil price and exchange rate using copula-based GARCH models[J].Energy Economics,2012,34(1):270-282.
[38] Aloui R,Aïssa M S B,Nguyen D K.Conditional dependence structure between oil prices and exchange rates:A copula-GARCH approach[J].Journal of International Money and Finance,2013,32:719-738.
