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.     

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.     

Empirical regularities of opening call auction in Chinese stock market

We study the statistical regularities of an opening call auction using the ultra-high-frequency data of 22 liquid stocks traded on the Shenzhen Stock Exchange in 2003. The distribution of the relative price, defined as the relative difference between the order price in the opening call auction and the closing price on the last trading day, is asymmetric and that the distribution displays a sharp peak at the zero relative price and a relatively wide peak at the negative relative price. The detrended fluctuation analysis (DFA) method is adopted to investigate the long-term memory of relative order prices. We further study the statistical regularities of order sizes in the opening call auction, and observe a phenomenon of number preference, known as order size clustering. The probability density function (PDF) of order sizes could be well fitted by a q-Gamma function, and the long-term memory also exists in order sizes. In addition, both the average volume and the average number of orders decrease exponentially with the price level away from the best bid or ask price level in the limit-order book (LOB) established immediately after the opening call auction, and a price clustering phenomenon is observed.     

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.     

Price forecast in the competitive electricity market by support vector machine

The electricity market has been widely introduced in many countries all over the world and the study on electricity price forecast technology has drawn a lot of attention. In this paper, with different parameter C_i and ε_i assigned to each training data, the flexible C_i Support Vector Regression (SVR) model is developed in terms of the particularity of the price forecast in electricity market. For Day Ahead Market (DAM) price forecast, the load, time of use index and index of day type are taken as the major factors to characterize the market price, therefore, they are selected as the inputs for the flexible SVR forecast model. For the long-term price forecast, we take the reserve margin R^m, HHI and the fuel price index as the inputs, since they are the major factors that drive the market price variation in long run. For short-term price forecast, besides the detailed analysis with the young Italian electricity market, the new model is tested on the experimental stage of the Spanish market, the New York market and the New England market. The long-term forecast with the SVR model presented is justified by the forecast with the data from the Long Run Market Simulator (LREMS).     

The risks and returns of stock investment in a financial market

The risks and returns of stock investment are discussed via numerically simulating the mean escape time and the probability density function of stock price returns in the modified Heston model with time delay. Through analyzing the effects of delay time and initial position on the risks and returns of stock investment, the results indicate that: (i) There is an optimal delay time matching minimal risks of stock investment, maximal average stock price returns and strongest stability of stock price returns for strong elasticity of demand of stocks (EDS), but the opposite results for weak EDS; (ii) The increment of initial position recedes the risks of stock investment, strengthens the average stock price returns and enhances stability of stock price returns. Finally, the probability density function of stock price returns and the probability density function of volatility and the correlation function of stock price returns are compared with other literatures. In addition, good agreements are found between them.     

Inter-relationship between optical dielectric constant and interatomic separation of mixed crystals in ionic and covalent binary compound families

An ion dependent dielectric model is developed for mixed binary crystals. The interatomic separation (R) and optical dielectric constant (ε_∞) of the mixed crystals are computed from the measured values of R and ε_∞ of pure crystals. An empirical relation between ε_∞ and R is therefore found for mixed crystals by using the computed values. It is found that the dielectric behaviour of ionic mixed crystals is cation dependent while that of covalent mixed crystals is anion dependent. The prescribed theory can therefore be used to form different mixed crystals with particular values of ε_∞ required in any specific opto-electronic devices.     

Optimization of VI/II pressure ratio in ZnTe growth on GaAs(0 0 1) by molecular beam epitaxy

ZnTe epilayers were grown on GaAs(0 0 1) substrates by molecular beam epitaxy (MBE) at different VI/II beam equivalent pressure (BEP) ratios (R_VI/II) in a wide range of 0.96-11 with constant Zn flux. Based on in situ reflection high-energy electron diffraction (RHEED) observation, two-dimensional (2D) growth mode can be formed by increasing the R_VI/II to 2.8. The Te/Zn pressure ratios lower than 4.0 correspond to Zn-rich growth state, while the ratios over 6.4 correspond to Te-rich one. The Zn sticking coefficient at various VI/II ratios are derived by the growth rate measurement. The ZnTe epilayer grown at a R_VI/II of 6.4 displays the narrowest full-width at half-maximum (FWHM) of double-crystal X-ray rocking curve (DCXRC) for (0 0 4) reflection. Atomic force microscopy (AFM) characterization shows that the grain size enlarges drastically with the R_VI/II. The surface root-mean-square (RMS) roughness decreases firstly, attains a minimum of 1.14 nm at a R_VI/II of 4.0 and then increases at higher ratios. It is suggested that the most suitable R_VI/II be controlled between 4.0 and 6.4 in order to grow high-quality ZnTe epitaxial thin films.     

Numerical irreversibility in self-gravitating small N-body systems, II: Influence of instability affected by softening parameters

We investigate the fundamental characteristics of numerical irreversibility appearing in self-gravitating small N-body systems by means of a molecular dynamics method from the viewpoint of time-reversible dynamics. We reconsider a closed spherical system consisting of 250 point-particles interacting through the Plummer softened potential. To investigate the characteristics of numerical irreversibility, we examine the influence of the instability affected by the softening parameter for the softened potential (the instability considered here is the instability of a dynamical system in chaos theory, e.g., a separation rate of the distance between two nearby trajectories in phase space or speed space). To this end, under the restriction of constant initial energy, the softening parameter for the Plummer softened potential is varied from 0.005R to 0.050R, where R is the radius of the spherical container. We first confirm that the size of the softening parameter, i.e., the deviation of the potential from a pure gravitational potential, influences the virial ratio, the density, the pressure on the spherical container, etc., during an early stage of the relaxation process. Through a time-reversible simulation based on a velocity inversion technique, we demonstrate that numerical irreversibility due to round-off errors appears more rapidly with decreasing softening parameter. This means that the higher the instability of the system or the higher the separation rate of the distance between two nearby trajectories, the earlier the memory of the initial conditions is lost. We show that the memory loss time , when the simulated trajectory completely forgets its initial conditions, increases approximately linearly with the timescale of the chaotic system, i.e., the Lyapunov time t_λ. In a small self-gravitating system, propagation of numerical irreversibility or loss of reversibility depends on both the energy state of the system and the instability affected by the softening parameter.     

Magneto-transport properties of [Co/Bi]n wire structures

The present study examines the artificial control of grain-boundary resistance and its contribution to the magneto-transport properties of [Co(1 nm)/Bi(2.5 nm)]_n (n=10 or 20) line structures on the Si(0 0 1)/SiN_x substrate. Conventional patterning and deposition processes are applied for the fabrication of a device that consists of five-line structures with a line width of 2 μm. A ΔR/R=80% ratio was observed in the five-line structure of [Co(1 nm)/Bi(2.5 nm)]₁₀ multilayers at 10 K. Our measurements indicate that grain-boundary effects can be associated with the large ΔR/R ratio of transverse magnetoresistance.     

Volatility return intervals analysis of the Japanese market

We investigate scaling and memory effects in return intervals between price volatilities above a certain threshold q for the Japanese stock market using daily and intraday data sets. We find that the distribution of return intervals can be approximated by a scaling function that depends only on the ratio between the return interval τ and its mean 〈τ〉. We also find memory effects such that a large (or small) return interval follows a large (or small) interval by investigating the conditional distribution and mean return interval. The results are similar to previous studies of other markets and indicate that similar statistical features appear in different financial markets. We also compare our results between the period before and after the big crash at the end of 1989. We find that scaling and memory effects of the return intervals show similar features although the statistical properties of the returns are different.     

Pricing European options with a log Student’s t-distribution: A Gosset formula

The distributions of returns for stocks are not well described by a normal probability density function (pdf). Student’s t-distributions, which have fat tails, are known to fit the distributions of the returns. We present pricing of European call or put options using a log Student’s t-distribution, which we call a Gosset approach in honour of W.S. Gosset, the author behind the nom de plume Student. The approach that we present can be used to price European options using other distributions and yields the Black-Scholes formula for returns described by a normal pdf.     

Combinatorial study of phase transformation characteristics of a Ti-Ni-Pd shape memory thin film composition spread in view of microactuator applications

Phase transformation characteristics of a Ti-Ni-Pd shape memory thin film composition spread have been investigated. The thin film composition spread was fabricated from elemental targets using an ultra-high vacuum combinatorial magnetron sputter-deposition system and subsequent annealing at 500 °C for 1 h in situ. Automated temperature-dependent resistance measurements (R(T)), energy dispersive X-ray analysis (EDX) and X-ray diffraction measurements (XRD) have been applied for the high-throughput characterization of the composition spread. Reversible phase transformations within the measurement range of −40 to 250 °C within the Ti-Ni-Pd system were observed for compositions with Ti content between 50 and ∼59 at.%. For Ti-richer films, Ti₂Ni and Ti₂Pd precipitates are inhibiting reversible phase transformations. The transformation temperatures and the thermal hysteresis were determined from R(T) measurements. Rising transformation temperatures with increasing Pd content and significantly lower thermal hysteresis for the B2-B19, compared to the B2-R-B19′ transformations were found in good agreement with published data. For low Pd contents (<7-12 at.%, depending on the Ti content) two-stage B2-R-B19′ transformations were observed. Compositions with higher Pd contents showed a single-stage B2-B19 transformation. Increasing Ti content within the B2-B19 transformation region results in a linear increase of the thermal hysteresis and decreasing transformation temperatures.     

Tick size and stock returns

Tick size is an important aspect of the micro-structural level organization of financial markets. It is the smallest institutionally allowed price increment, has a direct bearing on the bid-ask spread, influences the strategy of trading order placement in electronic markets, affects the price formation mechanism, and appears to be related to the long-term memory of volatility clustering. In this paper we investigate the impact of tick size on stock returns. We start with a simple simulation to demonstrate how continuous returns become distorted after confining the price to a discrete grid governed by the tick size. We then move on to a novel experimental set-up that combines decimalization pilot programs and cross-listed stocks in New York and Toronto. This allows us to observe a set of stocks traded simultaneously under two different ticks while holding all security-specific characteristics fixed. We then study the normality of the return distributions and carry out fits to the chosen distribution models. Our empirical findings are somewhat mixed and in some cases appear to challenge the simulation results.     

Multifractal properties of the Indian financial market

We investigate the multifractal properties of the logarithmic returns of the Indian financial indices (BSE & NSE) by applying the multifractal detrended fluctuation analysis. The results are compared with that of the US S&P 500 index. Numerically we find that qth-order generalized Hurst exponents h(q) and τ(q) change with the moments q. The nonlinear dependence of these scaling exponents and the singularity spectrum f(α) show that the returns possess multifractality. By comparing the MF-DFA results of the original series to those for the shuffled series, we find that the multifractality is due to the contributions of long-range correlations as well as the broad probability density function. The financial markets studied here are compared with the Binomial Multifractal Model (BMFM) and have a smaller multifractal strength than the BMFM.     

On the probability distribution of stock returns in the Mike-Farmer model

Recently, Mike and Farmer have constructed a very powerful and realistic behavioral model to mimick the dynamic process of stock price formation based on the empirical regularities of order placement and cancelation in a purely order-driven market, which can successfully reproduce the whole distribution of returns, not only the well-known power-law tails, together with several other important stylized facts. There are three key ingredients in the Mike-Farmer (MF) model: the long memory of order signs characterized by the Hurst index H_s, the distribution of relative order prices x in reference to the same best price described by a Student distribution (or Tsallis’ q-Gaussian), and the dynamics of order cancelation. They showed that different values of the Hurst index H_s and the freedom degree α_x of the Student distribution can always produce power-law tails in the return distribution f_r(r) with different tail exponent α_r. In this paper, we study the origin of the power-law tails of the return distribution f_r(r) in the MF model, based on extensive simulations with different combinations of the left part L(x) for x < 0 and the right part R(x) for x > 0 of f_x(x). We find that power-law tails appear only when L(x) has a power-law tail, no matter R(x) has a power-law tail or not. In addition, we find that the distributions of returns in the MF model at different timescales can be well modeled by the Student distributions, whose tail exponents are close to the well-known cubic law and increase with the timescale.     

A self-adapting herding model: The agent judge-abilities influence the dynamic behaviors

We propose a self-adapting herding model, in which the financial markets consist of agent clusters with different sizes and market desires. The ratio of successful exchange and merger depends on the volatility of the market and the market desires of the agent clusters. The desires are assigned in term of the wealth of the agent clusters when they merge. After an exchange, the beneficial cluster’s desire keeps on the same, the losing one’s desire is altered which is correlative with the agent judge-ability. A parameter R is given to all agents to denote the judge-ability. The numerical calculation shows that the dynamic behaviors of the market are influenced distinctly by R, which includes the exponential magnitudes of the probability distribution of sizes of the agent clusters and the volatility autocorrelation of the returns, the intensity and frequency of the volatility.     

Andronov-Hopf bifurcations in planar, piecewise-smooth, continuous flows

An equilibrium of a planar, piecewise-C¹, continuous system of differential equations that crosses a curve of discontinuity of the Jacobian of its vector field can undergo a number of discontinuous or border-crossing bifurcations. Here we prove that if the eigenvalues of the Jacobian limit to λL±iωL on one side of the discontinuity and −λR±iωR on the other, with λL,λR>0, and the quantity Λ=λL/ωL−λR/ωR is nonzero, then a periodic orbit is created or destroyed as the equilibrium crosses the discontinuity. This bifurcation is analogous to the classical Andronov-Hopf bifurcation, and is supercritical if Λ<0 and subcritical if Λ>0.     

Crystal structure of the quaternary compound CuTa2InTe4 from X-ray powder diffraction

The crystal structure of the new quaternary compound CuTa₂InTe₄ was studied using X-ray powder diffraction data. The powder pattern refined by the Rietveld method indicates that this material crystallizes in the tetragonal system with space group I-4¯2m (No. 121), Z=2, and unit cell parameters a=6.1963(2) Å, c=12.4164(4) Å, c/a=2.00 and V=476.72(3) Å³. The structural and instrumental refinement of 28 parameters led to R_p=10.4%, R_wp=11.1%, R_exp=6.8% and χ²=2.7 for 96 independent reflections.     

Tunneling magnetoresistance in exchange-biased CoFeB/AlOx/Co/IrMn junctions

A series of exchange-biased magnetic tunneling junctions (MTJs) were made in an in-plane deposition field (h) = 500 Oe. The deposition sequence was Si(1 0 0)/Ta(30 Å)/CoFeB(75 Å)/AlO_x(d Å)/Co(75 Å)/IrMn(90 Å)/Ta(100 Å), where d was varied from 12 Å to 30 Å. The MTJ was formed by the cross-strip method with a junction area of 0.0225 mm². The tunneling magnetoresistance (ΔR/R) of each MTJ was measured. The high-resolution cross-sectional transmission electron microscopic (HR X-TEM) image shows the very smooth interface and clear microstructure. X-ray diffraction (XRD) demonstrates that the IrMn layer of the MTJ exhibits a (1 1 1) texture. From the results (ΔR/R) increases from 17% to 50%, as d increases from 12 Å to 30 Å. The tunneling resistance (R_o) of these junctions ranges from 150 Ω to 250 Ω. The exchange-biasing field (H_ex) of the MTJ is 50-95 Oe. Finally, the saturation resistance (R_s) was measured as a function of the angle (α) of rotation, where α is the angle between h and the in-plane saturation field (H_s) = 1.1 kOe. The following figure presents the dependence of R_s on α, instead of originally expected independence, the curve actually varies with a period of π.