On Gaussian Comparison Inequality and Its Application to Spectral Analysis of Large Random Matrices

Recently, Chernozhukov, Chetverikov, and Kato [Ann. Statist. 42 (2014) 1564--1597] developed a new Gaussian comparison inequality for approximating the suprema of empirical processes. This paper exploits this technique to devise sharp inference on spectra of large random matrices. In particular, we show that two long-standing problems in random matrix theory can be solved: (i) simple bootstrap inference on sample eigenvalues when true eigenvalues are tied; (ii) conducting two-sample Roy's covariance test in high dimensions. To establish the asymptotic results, a generalized $\epsilon$-net argument regarding the matrix rescaled spectral norm and several new empirical process bounds are developed and of independent interest.Comment: to appear in Bernoull

Kinetic Ballooning Mode Under Steep Gradient: High Order Eigenstates and Mode Structure Parity Transition

The existence of kinetic ballooning mode (KBM) high order (non-ground) eigenstates for tokamak plasmas with steep gradient is demonstrated via gyrokinetic electromagnetic eigenvalue solutions, which reveals that eigenmode parity transition is an intrinsic property of electromagnetic plasmas. The eigenstates with quantum number $l=0$ for ground state and $l=1,2,3\ldots$ for non-ground states are found to coexist and the most unstable one can be the high order states ($l\neq0$). The conventional KBM is the $l=0$ state. It is shown that the $l=1$ KBM has the same mode structure parity as the micro-tearing mode (MTM). In contrast to the MTM, the $l=1$ KBM can be driven by pressure gradient even without collisions and electron temperature gradient. The relevance between various eigenstates of KBM under steep gradient and edge plasma physics is discussed.Comment: 6 pages, 6 figure

Transmission of information across international stock markets

This thesis aims to contribute to the existing literature about return and volatility spillovers. First, this study examines the direct transmission of information contained in returns, volatility and trading volume across the world’s eight biggest stock markets by market capitalisation using the ARCH-type models. The empirical results highlight the complexity of the information transmission mechanisms via different channels. Second, this study investigates the transmission of information in stock market index returns after considering the interactive effect between trading volume and returns. A new approach to analyse this joint-dynamic relation has been proposed and the findings are interpreted in the light of economic theory. The obtained results provide evidence that liquidity-based price movements, which are normally related to high trading volume, can also be transmitted across borders and have a global impact on market performance in other countries. Last but not least, this study explores the economic significance of international information spillovers and presents evidence showing that active investment strategies which apply trading rules based on the signals from the forecasts of the meteor shower models are profitable even after considering transaction costs. In addition, the information about the interactive relation between trading volume and returns is found to be an exploitable phenomenon which investors can use to trade profitably