Measuring the self-similarity exponent in Lévy stable processes of financial time series

Geometric method-based procedures, which will be called GM algorithms herein, were introduced in [M.A. Sánchez Granero, J.E. Trinidad Segovia, J. García Pérez, Some comments on Hurst exponent and the long memory processes on capital markets, Phys. A 387 (2008) 5543-5551], to efficiently calculate the self-similarity exponent of a time series. In that paper, the authors showed empirically that these algorithms, based on a geometrical approach, are more accurate than the classical algorithms, especially with short length time series. The authors checked that GM algorithms are good when working with (fractional) Brownian motions. Moreover, in [J.E. Trinidad Segovia, M. Fernández-Martínez, M.A. Sánchez-Granero, A note on geometric method-based procedures to calculate the Hurst exponent, Phys. A 391 (2012) 2209-2214], a mathematical background for the validity of such procedures to estimate the self-similarity index of any random process with stationary and self-affine increments was provided. In particular, they proved theoretically that GM algorithms are also valid to explore long-memory in (fractional) Lévy stable motions.     

A note on geometric method-based procedures to calculate the Hurst exponent

Geometric method-based procedures, which we will call GM algorithms hereafter, were introduced in M.A. Sánchez-Granero, J.E. Trinidad Segovia, J. García Pérez, Some comments on Hurst exponent and the long memory processes on capital markets, Phys. A 387 (2008) 5543-5551, to calculate the Hurst exponent of a time series. The authors proved that GM algorithms, based on a geometrical approach, are more accurate than classical algorithms, especially with short length time series. The main contribution of this paper is to provide a mathematical background for the validity of these two algorithms to calculate the Hurst exponent H of random processes with stationary and self-affine increments. In particular, we show that these procedures are valid not only for exploring long memory in classical processes such as (fractional) Brownian motions, but also for estimating the Hurst exponent of (fractional) Lévy stable motions.     

Reinvestigation of crystal growth of thiosemicarbazide potassium chloride and thiosemicarbazide lithium chloride

Reinvestigation of the growth of thiosemicarbazide potassium chloride crystal (1) (Chandrasekaran et al. [1]) and thiosemicarbazide lithium chloride crystal (2) (Maadeswaran et al. [2]), unambiguously confirms that compounds 1 and 2 are pure thiosemicarbazide and do not contain any alkali metal or chloride ions. In this paper we demonstrate the use of classical halide test, flame test, as well as infrared (IR) spectra for correct product characterization.     

Estimation of the nuclear distortion in the Coulomb breakup of 6Li into α + d in the field of 208Pb ion

In this article the results of the evaluation of the contribution of nuclear disintegration, based on the basis of diffraction theory in the ²⁰⁸Pb(⁶Li, αd)²⁰⁸Pb Coulomb breakup at an energy of 156 MeV is presented. Comparison of the results of the calculation with the experimental data of Kiener et al. [Phys. Rev. C 44, 2195 (1991)] gives evidence for the dominance of the Coulomb dissociation mechanism and contribution of nuclear distortion, but essentially smaller than the value reported byHammache et al. [Phys. Rev. C 82, 065803 (2010)] and Sümmerer [Prog. Part. Nucl. Phys. 66, 298 (2011)].     

Characterization of electrodeposited nickel film surfaces using atomic force microscopy

Microstructures of nickel surfaces electrodeposited on indium tin oxides coated glasses are investigated using atomic force microscopy. The fractal dimension D and Hurst exponent H of the nickel surface images are determined from a frequency analysis method proposed by Aguilar et al. [J. Microsc. 172 (1993) 233] and from Hurst rescaled range analysis. The two methods are found to give the same value of the fractal dimension D∼2.0. The roughness exponent α and growth exponent β that characterize scaling behaviors of the surface growth in electrodeposition are calculated using the height-difference correlation function and interface width in Fourier space. The exponents of α∼1.0 and β∼0.8 show that the surface growth does not belong to the universality classes theoretically predicted by statistical growth models.     

On Hurst exponent estimation under heavy-tailed distributions

In this paper, we show how the sampling properties of the Hurst exponent methods of estimation change with the presence of heavy tails. We run extensive Monte Carlo simulations to find out how rescaled range analysis (R/S), multifractal detrended fluctuation analysis (MF-DFA), detrending moving average (DMA) and generalized Hurst exponent approach (GHE) estimate Hurst exponent on independent series with different heavy tails. For this purpose, we generate independent random series from stable distribution with stability exponent α changing from 1.1 (heaviest tails) to 2 (Gaussian normal distribution) and we estimate the Hurst exponent using the different methods. R/S and GHE prove to be robust to heavy tails in the underlying process. GHE provides the lowest variance and bias in comparison to the other methods regardless the presence of heavy tails in data and sample size. Utilizing this result, we apply a novel approach of the intraday time-dependent Hurst exponent and we estimate the Hurst exponent on high frequency data for each trading day separately. We obtain Hurst exponents for S&P500 index for the period beginning with year 1983 and ending by November 2009 and we discuss the surprising result which uncovers how the market’s behavior changed over this long period.     

Fluctuations in a lévy flight gas

We consider the density fluctuations of an ideal Brownian gas of particles performing Lévy flìghts characterized by the indexf. We find that the fluctuations scale as N(t) t^H, where the Hurst exponentH locks onto the universal value 1/4 for Lévy flights with a finite root-mean-square range (f>2). For Lévy flights with a finite mean range but infinite root-mean-square range (1相似文献   

Excited states of donors bound toXvalleys in GaAs–AlAs type II structures

We calculate the binding energies of 2s donor states bound tovalleys in type II GaAs–AlAs quantum well structures using an anisotropic variational method which enables us to take into account the effective mass anisotropy and quantum confinement. For a comparative study, we use two sets of effective masses obtained from different measurements [B. Rheinländeret al., Phys. Stat. Sol. (b)49, K167 (1972) and M. Goiranet al., Physica B177, 465 (1992)].     

Testing of Multifractional Brownian Motion

Fractional Brownian motion (FBM) is a generalization of the classical Brownian motion. Most of its statistical properties are characterized by the self-similarity (Hurst) index 0<H<1. In nature one often observes changes in the dynamics of a system over time. For example, this is true in single-particle tracking experiments where a transient behavior is revealed. The stationarity of increments of FBM restricts substantially its applicability to model such phenomena. Several generalizations of FBM have been proposed in the literature. One of these is called multifractional Brownian motion (MFBM) where the Hurst index becomes a function of time. In this paper, we introduce a rigorous statistical test on MFBM based on its covariance function. We consider three examples of the functions of the Hurst parameter: linear, logistic, and periodic. We study the power of the test for alternatives being MFBMs with different linear, logistic, and periodic Hurst exponent functions by utilizing Monte Carlo simulations. We also analyze mean-squared displacement (MSD) for the three cases of MFBM by comparing the ensemble average MSD and ensemble average time average MSD, which is related to the notion of ergodicity breaking. We believe that the presented results will be helpful in the analysis of various anomalous diffusion phenomena.     

Physics of novel site controlled InGaAs quantum dots on (1 1 1) oriented substrates

Recent work has shown that site-controlled dots (QD) grown on (1 1 1)B GaAs substrates, pre-patterned with tetrahedral pyramidal recesses (Baier et al., 2006) [1], (Pelucchi et al., 2007) [2], (Zhu et al., 2007) [3] are suitable for the generation of single and entangled photons (Young et al., 2009) [4]. We recently introduced InGaAs/GaAs site controlled QD structures which demonstrated record breaking spectral purity, and we showed that increasing the indium concentration of the active region allows easy tunability of the emission wavelength (Mereni et al., 2009) [5], [6]. We present here the first theoretical analysis of the emission energies and optical properties of this system as a function of QD height and In concentration. We model the dots using an 8 band k.p theory chosen to provide the best convergence and performance for structures oriented specifically along the (1 1 1) crystallographic direction.     

A note on scaled variance ratio estimation of the Hurst exponent with application to agricultural commodity prices

The measure of long-term memory is important for the study of economic and financial time series. This paper estimates the Hurst exponent from a Scaled Variance Ratio model for 17 commodity price series under the efficient market null H₀:H=0.5. The distribution about the estimates of H are obtained from 90%, 95% and 99% confidence intervals generated from 20,000 Monte Carlo replications of a geometric Brownian motion. The results show that the scaled variance ratio provides a very good and stable estimate of the Hurst exponent, but the estimates can be quite different from the measure obtained from rescaled range or R–S analysis. In general commodity prices are consistent with the underlying assumption of a geometric Brownian motion.     

Linear and non-linear features of the Taylor–Green dynamo

The Taylor–Green flow is a model flow sharing many properties with the von Kármán flow, in which experimental turbulent dynamo action has recently been achieved. We present here recent numerical results on the Taylor–Green dynamo instability, both in the linear and non-linear regime. Various properties are considered, such as the influence of turbulence, the energy transfer between different scales, the spatial structure of the neutral mode, the nature of the bifurcation and the saturation mechanisms. We also discuss the role of the velocity fluctuations on the dynamo onset. To cite this article: Y. Ponty et al., C. R. Physique 9 (2008).     

Scaling behavior of earthquakes’ inter-events time series

In this paper, we investigate the statistical and scaling properties of the California earthquakes’ inter-events over a period of the recent 40 years. To detect long-term correlations behavior, we apply detrended fluctuation analysis (DFA), which can systematically detect and overcome nonstationarities in the data set at all time scales. We calculate for various earthquakes with magnitudes larger than a given M. The results indicate that the Hurst exponent decreases with increasing M; characterized by a Hurst exponent, which is given by, H = 0:34 + 1:53/M, indicating that for events with very large magnitudes M, the Hurst exponent decreases to 0:50, which is for independent events.      

Damage spreading and critical exponents for “model A” Ising dynamics

Using damage spreading and heat bath dynamics, we study the Ising model in 2 and 3 dimensions with non-conservative dynamics. Our algorithm differs in some important points from previous ones, which makes it rather efficient. We give estimates for the exponent z which seem to be the most precise published so far (2.172 ± 0.006 for d = 2, 2.032 ± 0.004 for d = 3). We also give precise estimates of the exponent θ′ introduced by Janssen et al. (Z. Phys. B 73 (1989) 539) and of analogous but in principle independent exponents. We find surprisingly that some of the latter agree with θ′, and give an explanation for this.     

Precise determination of the Doppler width of a rovibrational absorption line using a comb-locked diode laser

We had reported in a previous paper the precision measurement of line profiles of a transition of ¹³C acetylene in the near-infrared region, employing a tunable diode-laser spectrometer, the frequency of which is locked to an optical-comb signal [K.M.T. Yamada et al., J. Mol. Spectrosc. 249 (2008) 95–99]. In the present article we review the methodology for the experiment and the analysis in determining the Boltzmann constant from the Doppler width of a rovibrational transition on the basis of our experiences. Problems to be surmounted for further improvement in accuracy are discussed. To cite this article: K.M.T. Yamada et al., C. R. Physique 10 (2009).     

Ab initio absorption spectra of 3-tert-butylcyclohexene

We present an ab initio investigation of the optical properties of 3-tert-butylcyclohexene in both its conformers. The optical spectra, here the photoabsorption cross section, have been obtained within density-functional theory at the independent-particle level, and within time-dependent density-functional theory. The optical spectra of the two conformers show small but visible differences, hence suggesting that optical absorption experiments can discriminate among the two molecular geometries. To cite this article: K. Gaál-Nagy et al., C. R. Physique 10 (2009).     

Hurst exponent determination for digital speckle patterns in roughness control of metallic surfaces

In this paper, we present a study of metallic surface roughness using the Hurst exponent calculated from speckle pattern. A set of samples was prepared using polishing techniques and the roughness was directly measured by means of an optical profilometer. To study the H exponent, an experiment was performed by illuminating the samples using an expanded laser beam and the surface image was captured by a CCD camera. We applied techniques of the Hurst exponent calculation, traditionally calculated from surface profile, in the digitalized speckle patterns generated by the rough surfaces. We showed a clear dependence of the H exponent on roughness of the samples. We demonstrated that this tool is very sensitive to defects in the surfaces and can be used for roughness control.     

Characterizing bid–ask prices in the Brazilian equity market

This paper presents evidence of long-range dependence in bid–ask prices for individual equity prices in the Brazilian stock market. Moreover, using the Hurst exponent calculated by the Local Whittle method as a measure of long-range dependence, we find evidence supporting that bid–ask prices shows a stronger long-range dependence than the one usually found in closing and opening prices. Finally, we show that bid–ask prices may be characterized by a distribution that decays as a power law reinforcing the results of Plerou et al. [Quantifying fluctuations in market liquidity: analysis of the bid–ask spread, Phys. Rev. E 71 (2005) 046131].     

pH Dependence of the Au-CN Species Adsorbed onto Activated Carbon — Reply to Comments

Several aspects of a recent paper [McGrath, A. C. et al., Hyp. Interact. 139/40 (2002), 471] have been criticised by Klauber [Klauber, C., Hyp. Interact. 155 (2004), 65]. Although some of the points in Klauber [Klauber, C., Hyp. Interact. 155 (2004), 65] are shown to be incorrect, we show that a further analysis of the data in McGrath et al. [McGrath, A. C. et al., Hyp. Interact. 139/40 (2002), 471] does lend support to Klauber's tetramer model for the AuCN species on activated carbon, but not necessarily for its method of bonding.     

Angle-of-arrival variance’s dependence on the aperture size for indoor convective turbulence

We analyze the angle-of-arrival variance of an expanded and collimated laser beam once it has traveled through an indoor convective turbulence. A continuous position detector is set at the focus of a lens collecting the laser beam. The effect of the different turbulent scales, between the inner and the outer scales, is studied by changing the diameter of a circular pupil before the collector lens. The experimental optical setup follows the design introduced by Masciadri and Vernin [Appl. Opt., 36(6) (1997) 1320]. Tilt data measurements are studied using the fractional Brownian motion model for the turbulent wave-front phase introduced in a previous paper [Pérez et al., J. Opt. Soc. Am. A 21(10) (2004) 1962]. The Hurst exponents associated to different strengths of turbulence are obtained from the here proposed D^2H−2 dependence.