The global financial crisis in 2007-2008 and the European sovereign debt crisis in 2010 have an impact on governments and investors. This has engendered new interest within the financial research community in the study of correlations as one of the central issues in asset allocation is that financial markets become more interdependent during a financial crisis, thus diminishing the positive effects of diversification when they are needed most. Intuitively, we often receive news from television, newspapers or networks that some big corporations seek bankruptcy protection, but hardly do we hear of message about profitable investment. These excessive downside movements are also known as asymmetric correlation. Obviously, the asymmetric correlation is caused by the asymmetric behavior of the asset prices, which is affected by the financial market environment and is a dynamic time-varying process.This paper studies the relationship between financial assets, In particular the relationship during the period of the recent financial crisis is included. Specifically, we expand our correlation studies from two-folds: first, the study of the correlation stylized facts is from the perspective of statistical tests, in particular asymmetry in correlation. To this end, we constructed a test statistic for these purposes using empirical likelihood method. Second, we take account for these finding in correlations when building correlation models. we expect to capture these facts and improve the performance in our empirical experiment. These correlation models include: the correlation of the contracts on the crude oil markets and their hedging effectiveness, modeling the correlation between the high-dimensional asset portfolio diversification, modeling the realized correlation using tick by tick data, and modeling the dependence between the crude oil markets and the stock market.The difference between the existing literatures, the main work and the conclusions of this paper are as follows:(1) With empirical likelihood method, we construct a model-free based statistic to test asymmetry in correlations. In theory, because the empirical likelihood statistic allowed non-equal weights, but GMM method is equally weighted, the empirical likelihood method is more robust than GMM method. Comparing with the relating literature Hong et al. [1], we find that if the real data shows moderate asymmetric. Under the same conditions, our test has a 10%- 20% higher power than Hong et al. [1]. It represents that the empirical likelihood statistic can better capture the information of asymmetry in some cases. Meanwhile, using the test statistic for China’s capital market, we found that there is an asymmetric phenomenon among small cap portfolio and the Shanghai Composite Index, while the mid-cap portfolio, the large-cap portfolio and the Shanghai Composite Index has no existence of asymmetric phenomenon.(2) Using a regime switching method to analyze the hedging efficiency. Meanwhile, we construct a regime switching asymmetric dynamic correlation(RS-ADCC)model, and distinguish between the two phenomena: exogenous macroeconomic factors lead to structure break, which depicted by regime switching mechanism; Meanwhile, there are asymmetric correlation phenomenon, it is commonly described by GJR model and multivariate ADCC model. Empirical experiment, we analyze the cross hedging, as there exists insufficient futures contracts in many countries. The results show that, Regime switching model have a better performance than other traditional multivariate GARCH models. For some cases, RS-ADCC model has a best performance, thus this model should be considered for cross hedging.(3) Extend the DECO model in order to capture the high-dimension data. Specially, we extend three folds: first, using the dynamic time warping technique for clustering rather than original industrial class, it lets the data speak. Second, build the mechanism linking the univariate and block; Third, adding a asymmetry into the dynamic correlation. In empirically, using the component of S&P 100 index form the portfolio, we find that under minimum-variance portfolio diversification, our proposed model has a better performance both in and out of sample than competing modes in the sense of some popular criteria.(4) based on tick by tick data, we have constructed a new RS-HAR model and RS-AR(1) model for realized correlation. This model take account for features of the high frequency data: long memory, which uses moving average of 5 and 22 depict,similar to model realized volatility with HAR structures; structural break, which uses the regime switching describes; heteroscedasticity feature, allows that the variance is different under different market conditions, is also captured by regime switching mechanism. An EM algorithm is proposed to estimate the parameters of RS-HAR model,the benefits of this approach is to avoid the initial value setting, which leads to local solution of the problem, while local solution is usually appear in maximum likelihood estimation. For forecasting ability comparison, in one-step ahead forecast, it shows that RS-HAR model and RS-AR(1) model in most measure criterion is dominant; in multisteps ahead forecasts, RS-HAR model and RS-AR(1) fully dominated other competing models.
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