A Multivariate GARCH Model with Time-Varying correlations

In this paper we propose a new multivariate GARCH model with time- varying correlations. We adopt the vech representation based on the conditional variances and the conditional correlations. While each conditional-variance term is assumed to follow a univariate GARCH formulation, the conditional-correlation matrix is postulated to follow an autoregressive moving average type of analogue. By imposing some suitable restrictions on the conditional-correlation-matrix equation, we construct a MGARCH model in which the conditional-correlation matrix is guaranteed to be positive definite during the optimisation. Thus, our new model retains the intuition and interpretation of the univariate GARCH model and yet satisfies the positive-definite condition as found in the constant-correlation and BEKK models. We report some Monte Carlo results on the finite-sample distributions of the MLE of the varying- correlation MGARCH model. The new model is applied to some real data sets. It is found that extending the constant-correlation model to allow for time-varying correlations provides some interesting time histories that are not available in a constant-correlation model.BEKK model, constant correlation, Monte Carlo method, multivariate GARCH model, maximum likelihood estimate, varying correlation

Thermodynamic Study of Excitations in a 3D Spin Liquid

In order to characterize thermal excitations in a frustrated spin liquid, we have examined the magnetothermodynamics of a model geometrically frustrated magnet. Our data demonstrate a crossover in the nature of the spin excitations between the spin liquid phase and the high-temperature paramagnetic state. The temperature dependence of both the specific heat and magnetization in the spin liquid phase can be fit within a simple model which assumes that the spin excitations have a gapped quadratic dispersion relation.Comment: 5 figure

Observation of pinning mode in Wigner solid of 1/3 fractional quantum Hall excitations

We report the observation of a resonance in the microwave spectra of the real diagonal conductivities of a two-dimensional electron system within a range of ~ +- .0.015 $from filling factor$\nu=1/3$. The resonance is remarkably similar to resonances previously observed near integer$\nu$, and is interpreted as the collective pinning mode of a disorder-pinned Wigner solid phase of$e/3$-charged carriers .Comment: version with edits for clarity, improved Figure 3 and added referenc

A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model with Time-Varying Correlations

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Fractional flux periodicity of a twisted planar square lattice

We present fractional flux periodicity in the ground state of planar systems made of a square lattice whose boundary is compacted into a torus. The ground-state energy shows a fractional period of the fundamental unit of magnetic flux depending on the twist around the torus axis.Comment: 4 pages, 2 figures, corrected typos (v3

Evidence for Two Different Solid Phases of Two Dimensional Electrons in High Magnetic Fields

We have performed RF spectroscopy on very high quality two dimensional electron systems in the high magnetic field insulating phase, usually associated with a Wigner solid (WS) pinned by disorder. We have found two different resonances in the frequency dependent real diagonal conductivity spectrum and we interpret them as coming from \textit{two} different pinned solid phases (labeled as "WS-A" and "WS-B"). The resonance of WS-A is observable for Landau level filling $\nu$$<$2/9 (but absent around the $\nu$=1/5 fractional quantum Hall effect (FQHE)); it then \textit{crosses over} for $\nu$$<$0.18 to the different WS-B resonance which dominates the spectrum at $\nu$$<$0.125. Moreover, WS-A resonance is found to show dispersion with respect to the size of transmission line, indicating that WS-A has a large correlation length (exceeding $\sim$100 $\mu$m); in contrast no such behavior is found for WS-B. We suggest that quantum correlations such as those responsible for FQHE may play an important role in giving rise to such different solids.Comment: 4 pages, 3 figure

Observation of pinning mode of stripe phases of 2D systems in high Landau levels

We study the radio-frequency diagonal conductivities of the anisotropic stripe phases of higher Landau levels near half integer fillings. In the hard direction, in which larger dc resistivity occurs, the spectrum exhibits a striking resonance, while in the orthogonal, easy direction, no resonance is discernable. The resonance is interpreted as a pinning mode of the stripe phase

Modeling the Conditional Heteroscedasticity and Leverage Effect in the Chinese Stock Markets

Abstract: The Chinese stock market has experienced an astonishing growth and unprecedented development since its inception in the early 1990s, emerged to be the world&apos;s second-largest by market value by the end of 2009. The Chinese stock market is also one of the most volatile markets, which has been called by many observers a &quot;casino&quot;. In the recent years there are several far-reaching events that have reshaped the Chinese stock markets. The most notable events include the &quot;dot-com bubble&quot; in 2000, China&apos;s non-tradable shares reform in 2005 and the global financial crisis in 2008. It is noted that the &quot;dot-com bubble&quot; has caused the Chinese stock markets a sharp oscillation since 2000. With a short-lived bull, the Chinese stock markets experienced a nearly five years long bear market until June 2005 when the reform of non-tradable shares was implemented, which increased the liquidity and brought the markets back to a long-term bull run. Since the US sub-prime mortgage crisis the Chinese stock markets have shown extreme instability and severe volatility, which has become the major concern to the policy-makers and investors. Many existing studies have revealed that the financial time series data exhibit linear dependence in volatility, which indicates the presence of heteroskedasticity, implying the existence of volatility clustering. Although direct generalizations from the univariate GARCH models are straightforward, their applications are limited by practical issues associated with cumbersome computation and strong restrictions on parameters to guarantee positive definiteness of variance matrixes. This study intends to examine the presence of heteroskedasticity and the leverage effect in the two Chinese stock markets, and to capture the dynamics of conditional correlation between returns of China&apos;s stock markets and those of the U.S. in a bivariate VC-MGARCH framework. The results show that that the leverage effect is significant in both Shanghai and Shenzhen markets during the sample period in [2000][2001][2002][2003][2004][2005][2006][2007][2008], and the conditional correlation between mainland China&apos;s and the U.S. stock markets is quite low and highly volatile. The results indicate that that uncertainty derived from time-varying relationship between Shanghai and the U.S. stock markets is more significant than that between Shenzhen and the U.S. stock markets. In addition, the Chinese stock markets are found to be highly regimes persistent, thereby reducing potential benefits induced by actively trading. These findings have important implication for investors seeking opportunity of portfolio diversification