Scaling and memory in the return intervals of realized volatility

We perform return interval analysis of 1-min realized volatility defined by the sum of absolute high-frequency intraday returns for the Shanghai Stock Exchange Composite Index (SSEC) and 22 constituent stocks of SSEC. The scaling behavior and memory effect of the return intervals between successive realized volatilities above a certain threshold q are carefully investigated. In comparison with the volatility defined by the closest tick prices to the minute marks, the return interval distribution for the realized volatility shows a better scaling behavior since 20 stocks (out of 22 stocks) and the SSEC pass the Kolmogorov-Smirnov (KS) test and exhibit scaling behaviors, among which the scaling function for 8 stocks could be approximated well by a stretched exponential distribution revealed by the KS goodness-of-fit test under the significance level of 5%. The improved scaling behavior is further confirmed by the relation between the fitted exponent γ and the threshold q. In addition, the similarity of the return interval distributions for different stocks is also observed for the realized volatility. The investigation of the conditional probability distribution and the detrended fluctuation analysis (DFA) show that both short-term and long-term memory exists in the return intervals of realized volatility.     

A long-range memory stochastic model of the return in financial markets

We present a nonlinear stochastic differential equation (SDE) which mimics the probability density function (PDF) of the return and the power spectrum of the absolute return in financial markets. Absolute return as a measure of market volatility is considered in the proposed model as a long-range memory stochastic variable. The SDE is obtained from the analogy with an earlier proposed model of trading activity in the financial markets and generalized within the nonextensive statistical mechanics framework. The proposed stochastic model generates time series of the return with two power law statistics, i.e., the PDF and the power spectral density, reproducing the empirical data for the one-minute trading return in the NYSE.     

Return to equilibrium

The problem of return to equilibrium is phrased in terms of aC*-algebraU, and two one-parameter groups of automorphisms , ^P corresponding to the unperturbed and locally perturbed evolutions. The asymptotic evolution, under , of ^P -invariant, and ^P -K.M.S., states is considered. This study is a generalization of scattering theory and results concerning the existence of limit states are obtained by techniques similar to those used to prove the existence, and intertwining properties, of wave-operators. Conditions of asymptotic abelianness provide the necessary dispersive properties for the return to equilibrium. It is demonstrated that the ^P -equilibrium states and their limit states are coupled by automorphisms with a quasi-local property; they are not necessarily normal with respect to one another. An application to theX–Y model is given which extends previously known results and other applications, and examples, are given for the Fermi gas.     

Scaling and memory effect in volatility return interval of the Chinese stock market

We investigate the probability distribution of the volatility return intervals τ for the Chinese stock market. We rescale both the probability distribution P_q(τ) and the volatility return intervals τ as to obtain a uniform scaling curve for different threshold value q. The scaling curve can be well fitted by the stretched exponential function , which suggests memory exists in τ. To demonstrate the memory effect, we investigate the conditional probability distribution P_q(τ|τ₀), the mean conditional interval 〈τ|τ₀〉 and the cumulative probability distribution of the cluster size of τ. The results show clear clustering effect. We further investigate the persistence probability distribution P_±(t) and find that P₋(t) decays by a power law with the exponent far different from the value 0.5 for the random walk, which further confirms long memory exists in τ. The scaling and long memory effect of τ for the Chinese stock market are similar to those obtained from the United States and the Japanese financial markets.     

Monotonic return to steady nonequilibrium

We propose and analyze a new candidate Lyapunov function for relaxation towards general nonequilibrium steady states. The proposed functional is obtained from the large time asymptotics of time-symmetric fluctuations. For driven Markov jump or diffusion processes it measures an excess in dynamical activity rates. We present numerical evidence and we report on a rigorous argument for its monotonic time dependence close to the steady nonequilibrium or in general after a long enough time. This is in contrast with the behavior of approximate Lyapunov functions based on entropy production that when driven far from equilibrium often keep exhibiting temporal oscillations even close to stationarity.     

No return to classical reality

At a fundamental level, the classical picture of the world is dead, and has been dead now for almost a century. Pinning down exactly which quantum phenomena are responsible for this has proved to be a tricky and controversial question, but a lot of progress has been made in the past few decades. We now have a range of precise statements showing that whatever the ultimate laws of nature are, they cannot be classical. In this article, we review results on the fundamental phenomena of quantum theory that cannot be understood in classical terms. We proceed by first granting quite a broad notion of classicality, describe a range of quantum phenomena (such as randomness, discreteness, the indistinguishability of states, measurement-uncertainty, measurement-disturbance, complementarity, non-commutativity, interference, the no-cloning theorem and the collapse of the wave-packet) that do fall under its liberal scope, and then finally describe some aspects of quantum physics that can never admit a classical understanding – the intrinsically quantum mechanical aspects of nature. The most famous of these is Bell’s theorem, but we also review two more recent results in this area. Firstly, Hardy’s theorem shows that even a finite-dimensional quantum system must contain an infinite amount of information, and secondly, the Pusey–Barrett–Rudolph theorem shows that the wave function must be an objective property of an individual quantum system. Besides being of foundational interest, results of this sort now find surprising practical applications in areas such as quantum information science and the simulation of quantum systems.     

Long memory properties in return and volatility: Evidence from the Korean stock market

In this paper, we study the dual long memory property of the Korean stock market. For this purpose, the ARFIMA-FIGARCH model is applied to two daily Korean stock price indices (KOSPI and KOSDAQ). Our empirical results indicate that long memory dynamics in the returns and volatility can be adequately estimated by the joint ARFIMA-FIGARCH model. We also found that the assumption of a skewed Student-t distribution is better for incorporating the tendency of asymmetric leptokurtosis in a return distribution.     

Microwave Doppler spectra of sea return at small incidence angles: specular point scattering contribution

It is well known that the sea return echo contains contributions from at least two scattering mechanisms. In addition to the resonant Bragg scattering, the specular point scattering plays an important role as the incidence angle becomes smaller (≤20o). Here, in combination with the Kirchhoff integral equation of scattering field and the stationary phase approximation, analytical expressions for Doppler shift and spectral bandwidth of specular point scattering, which are insensitive to the polarization state, are derived theoretically. For comparison, the simulated results related to the two-scale method (TSM) and the method of moment (MOM) are also presented. It is found that the Doppler shift and the spectral bandwidth given by TSM are insufficient at small incidence angles. However, a comparison between the analytical results and the numerical simulations by MOM in the backscatter configuration shows that our proposed formulas are valid for the specular point scattering case. In this work, the dependences of the predicted results on incidence angle, radar frequency, and wind speed are also discussed. The obtained conclusions seem promising for a better understanding of the Doppler spectra of the specular point scattering fields from time-varying sea surfaces.     

Multiple phases and return to equilibrium

This paper considers the problem of return to equilibrium for perturbations of the dynamics of the one-sided and two-sidedXY-models with external field. We find that, in the presence of multiple ground states, return to equilibrium fails for certain perturbations while still holding wen there is a unique ground state.     

Return to foundations of wave optics

The Huygens-Fresnel wave principle is found to extend far beyond its traditional use. Using only elementary mathematical means, it is shown in particular that this principle suffices to provide the exact solution of Sommerfeld's problem of plane wave diffraction by a perfectly conducting half-plane. A more exact formulation of the wave principle itself is proposed.     

Return to equilibrium in theXY model

We prove that the locally perturbedXY model returns to equilibrium under the unperturbed evolution but the unperturbed model does not necessarily approach equilibrium under the perturbed evolution. In fact this latter property is false for perturbation by a local magnetization. The failure is directly attributable to the formation of bound states. If the perturbation is quadratic these problems are reduced to spectral analysis of the one-particle Hamiltonian. We demonstrate that the perturbed Hamiltonian has a finite set of eigenvalues of finite multiplicity together with some absolutely continuous spectrum. Eigenvalues can occur in the continuum if, and only if, the perturbation dislocates the system. Singular continuous spectrum cannot occur.     

清新淡雅 回归本质—2009年山东省高考物理试题分析

1 综合评价 2009年高考理科综合能力测试试题山东卷物理部分,突出对物理核心思维方法和重要的处理问题方法的考查,适当注意联系考生生活实践和社会实际,不刻意求新,题目提供信息简捷明确,没有设置冗长的无关信息,减少审题时间,注重思维层次和品质考查.试题模型注重推陈出新,在看似熟悉的物理模型上巧妙设问.统观全卷,给人以"浑然一体,清新淡雅,回归物理本质"的感觉,符合当今物理教学发展的趋势.     

The aspect experiment and the return to reality

It is argued that the results of atomic cascade photon correlation experiments of the static type may be given a natural interpretation in the framework of at least one objective local theory, namely stochastic electrodynamics. It follows that the Aspect experiment is more likely than the Clauser-Horne experiment to be crucial in deciding between objective local theories and quantum mechanics.     

Stock market return distributions: From past to present

We show that recent stock market fluctuations are characterized by the cumulative distributions whose tails on short, minute time scales exhibit power scaling with the scaling index α>3 and this index tends to increase quickly with decreasing sampling frequency. Our study is based on high-frequency recordings of the S&P500, DAX and WIG20 indices over the interval May 2004-May 2006. Our findings suggest that dynamics of the contemporary market may differ from the one observed in the past. This effect indicates a constantly increasing efficiency of world markets.     

Microwave sea return at moderate to high incidence angles

Abstract

Bragg scattering is widely recognized as the dominant mechanism by which the ocean surface backscatters microwave radiation, but efforts to identify other, non-Bragg sources of this scattering have been pursued for many years. Non-Bragg backscattering from the sea surface is known to occur at incidence angles close to 0° and 90°. In this paper Bragg scattering is shown to explain most features of sea surface backscatter for incidence angles between about 20° and 80°, except when it predicts very small mean cross sections. The often-quoted evidence for non-Bragg scattering in this incidence angle range is that σ _o (HH) is occasionally found to be larger than or equal to σ _o (VV) for short integration times. We show that because of fading this is not evidence of non-Bragg scattering. For incidence angles up to about 50°, standard Bragg/composite surface scattering theory yields probabilities of finding σ _o (HH)>σ _o (VV) that are only slightly smaller than those found experimentally. As the incidence angle increases, greater differences between theoretical and experimental probabilities are found. The addition of Bragg scattering from bound, tilted waves brings theory into excellent agreement with experiment at incidence angles near 45° but still cannot account adequately for the probability of σ _o (HH)>σ _o (VV) or observed σ _o (HH) cross sections at higher incidence angles. We show that the addition of a small, non-Bragg cross section that is independent of the incidence angle and polarization, brings simulated cross sections and probability distributions into good agreement with data. A possible source of this small, non-Bragg sea return is sea spray just above the air/sea interface.     

Polarized (letter ‘8’) memory in CdSe point contact diodes

Polarized memory, i.e., the memory in which switching between ON and OFF states depends on the polarity of bias voltage has been found in point contact diodes on single crystals of CdSe, CdS, CdTe, GaAs and GaP. The detailed features of switching characteristics depend on the choice of metals for the point contact electrode, on the sharpness of the contact and also on the resistance of the current limiter in the circuit. Observation of the transients between ON and OFF has also been performed.     

物理教学应该回归原始物理问题——浅谈物理核心素养的培养

针对目前物理教学中的问题以及物理学科核心素养的构建意义,提出了物理教学应该回归原始物理问题,从课堂设计和课外活动两个方面举例说明如何在教学中落实原始物理问题.     

Analytical solution to LIDAR return signals from clouds with regard to multiple scattering

An analytical approach to LIDAR return signal calculation with regard to multiple scattering is suggested. Two versions of the method are developed. The first one is completely analytical and undispensible for qualitative studies. The second semianalytical approach provides a sufficient accuracy up to a sounding optical depth about 5. Being somewhat more tedious than the proposed analytical solution, the second approach appears to be time saving in comparison with known methods.