Quotient correlation: A sample based alternative to Pearson's correlation

The quotient correlation is defined here as an alternative to Pearson's correlation that is more intuitive and flexible in cases where the tail behavior of data is important. It measures nonlinear dependence where the regular correlation coefficient is generally not applicable. One of its most useful features is a test statistic that has high power when testing nonlinear dependence in cases where the Fisher's $Z$-transformation test may fail to reach a right conclusion. Unlike most asymptotic test statistics, which are either normal or $\chi^2$, this test statistic has a limiting gamma distribution (henceforth, the gamma test statistic). More than the common usages of correlation, the quotient correlation can easily and intuitively be adjusted to values at tails. This adjustment generates two new concepts--the tail quotient correlation and the tail independence test statistics, which are also gamma statistics. Due to the fact that there is no analogue of the correlation coefficient in extreme value theory, and there does not exist an efficient tail independence test statistic, these two new concepts may open up a new field of study. In addition, an alternative to Spearman's rank correlation, a rank based quotient correlation, is also defined. The advantages of using these new concepts are illustrated with simulated data and a real data analysis of internet traffic.Comment: Published in at http://dx.doi.org/10.1214/009053607000000866 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

"Bayesian Estimation and Particle Filter for Max-Stable Processes"

Extreme values are often correlated over time, for example, in a financial time series, and these values carry various risks. Max-stable processes such as maxima of moving maxima (M3) processes have been recently considered in the literature to describe timedependent dynamics, which have been difficult to estimate. This paper first proposes a feasible and efficient Bayesian estimation method for nonlinear and non-Gaussian state space models based on these processes and describes a Markov chain Monte Carlo algorithm where the sampling efficiency is improved by the normal mixture sampler. Furthermore, a unique particle filter that adapts to extreme observations is proposed and shown to be highly accurate in comparison with other well-known filters. Our proposed algorithms were applied to daily minima of high-frequency stock return data, and a model comparison was conducted using marginal likelihoods to investigate the time-dependent dynamics in extreme stock returns for financial risk management.

Electrochemical Materials Design for Micro-Supercapacitors

Micro–supercapacitors (m–SC) arise from the demand of developing micro–power system for MEMS devices, attracting much research interest in recent years. As m–SC has to achieve high areal energy and power densities, the volumetric capacitance and the rate capability of the electrode materials have become the most important concern. This review compares the intrinsic electrochemical properties of the state–of–art electrode materials for m–SC, reporting the recent advances in the three types of electrode materials. For carbon electrode materials, two developing trends are identified: one is to enhance volumetric capacitance through a proper film fabrication process, while the other one is to further promote its fast response rate by making open–structured devices. For pseudocapacitive oxides, in order to achieve better rate capability and cyclability, the relationship between the electrochemical property and the structure is worth further exploration. As an example, the composition, microstructure, and morphology of the molybdenum oxide film were optimized to realize superior electrochemical performance as an electrode material for m–SC. Architecture design is another important factor for m–SC. In–plane interdigital architectures have proven its success to fabricate fast response devices. Further study on the interplay effect between such architecture and pseudocapacitive materials is in need

Study of the Tail Dependence Structure in Global Financial Markets Using Extreme Value Theory

Abstract: The presence of tail dependencies invalidates the multivariate normality assumptions in portfolio risk management. The identification of tail (in)dependencies has drawn major attention in empirical financial studies. Yet it is still a challenging issue both theoretically and practically. Previous studies based on either a restrictive model or the null hypothesis of tail (perfect) dependence does not well describe or interpret extreme co-movements in financial markets. This paper examines tail dependence structures underlying a broad range of financial asset classes employing the newly developed tail quotient correlation coefficients. In theory, the original tail quotient correlation coefficient proposed in (Zhang 2008) is adapted to incorporate cases with varying data driven random thresholds. Our empirical results demonstrate different tail dependence structures underlying various global financial markets. Either omission or unanimous treatment of the tail dependence structures for different financial markets will lead to erroneous conclusions or suboptimal investment choices. The multivariate extreme value theory framework in this study has the potential to serve as an useful tool in exploiting arbitrage opportunities, optimizing asset allocations, and building robust risk management strategies