Statistical properties of the yuan exchange rate index

We choice the yuan exchange rate index based on a basket of currencies as the effective exchange rate of the yuan and investigate the statistical properties of the yuan exchange rate index after China’s exchange rate system reform on the 21st July 2005. After dividing the time series into two parts according to the change in the yuan exchange rate regime in July 2008, we compare the statistical properties of the yuan exchange rate index during these two periods. We find that the distribution of the two return series has the exponential form. We also perform the detrending moving average analysis (DMA) and the multifractal detrending moving average analysis (MFDMA). The two periods possess different degrees of long-range correlations, and the multifractal nature is also unveiled in these two time series. Significant difference is found in the scaling exponents τ(q)$\tau \left(q\right)$ and singularity spectra f(α)$f\left(\alpha \right)$ of the two periods obtained from the MFDMA analysis. Besides, in order to detect the sources of multifractality, shuffling and phase randomization procedures are applied to destroy the long-range temporal correlation and fat-tailed distribution of the yuan exchange rate index respectively. We find that the fat-tailedness plays a critical role in the sources of multifractality in the first period, while the long memory is the major cause in the second period. The results suggest that the change in China’s exchange rate regime in July 2008 gives rise to the different multifractal properties of the yuan exchange rate index in these two periods, and thus has an effect on the effective exchange rate of the yuan after the exchange rate reform on the 21st July 2005.     

Long range order in the ground state of quantum interacting rotors in two dimensions

It has been rigorously proved that the ground state of interacting quantum rotors in two dimensions exhibits the magnetic long-range order in the ferromagnetic case. The assumptions are that the interaction is between nearest neighbors and it is strong enough, and that rotors are sufficiently heavy. The proof is based on the Reflection Positivity technique.     

Modeling teletraffic arrivals by a Poisson cluster process

In this paper we consider a Poisson cluster process N as a generating process for the arrivals of packets to a server. This process generalizes in a more realistic way the infinite source Poisson model which has been used for modeling teletraffic for a long time. At each Poisson point Γ _j , a flow of packets is initiated which is modeled as a partial iid sum process , with a random limit K _j which is independent of (X _ji ) and the underlying Poisson points (Γ _j ). We study the covariance structure of the increment process of N. In particular, the covariance function of the increment process is not summable if the right tail P(K _j > x) is regularly varying with index α∊ (1, 2), the distribution of the X _ji ’s being irrelevant. This means that the increment process exhibits long-range dependence. If var(K _j ) < ∞ long-range dependence is excluded. We study the asymptotic behavior of the process (N(t)) _{t≥ 0} and give conditions on the distribution of K _j and X _ji under which the random sums have a regularly varying tail. Using the form of the distribution of the interarrival times of the process N under the Palm distribution, we also conduct an exploratory statistical analysis of simulated data and of Internet packet arrivals to a server. We illustrate how the theoretical results can be used to detect distribution al characteristics of K _j , X _ji , and of the Poisson process. AMS Subject Classifications Primary—60K30; Secondary—60K25 A large part of this research was done with support of Institut Mittag-Leffler of the Royal Swedish Academy of Sciences when the authors participated in the Fall 2004 program on Queuing Theory and Teletraffic Theory. Mikosch’s research is also partially supported by MaPhySto, the Danish research network for mathematical physics and stochastics and the Danish Research Council (SNF) Grant No 21-04-0400. Samorodnitsky’s research is also partially supported by NSF grant DMS-0303493 and NSA grant MSPF-02G-183 at Cornell University. González-Arévalo’s research is partially supported by BoRSF grant LEQSF(2004-2007)-RD-A-31 at the University of Louisiana at Lafayette.     

Multifractal spectrum analysis of nonlinear dynamical mechanisms in China’s agricultural futures markets

Based on Partition Function and Multifractal Spectrum Analysis, we investigated the nonlinear dynamical mechanisms in China’s agricultural futures markets, namely, Dalian Commodity Exchange (DCE for short) and Zhengzhou Commodity Exchange (ZCE for short), where nearly all agricultural futures contracts are traded in the two markets. Firstly, we found nontrivial multifractal spectra, which are the empirical evidence of the existence of multifractal features, in 4 representative futures markets in China, that is, Hard Winter wheat (HW for short) and Strong Gluten wheat (SG for short) futures markets from ZCE and Soy Meal (SM for short) futures and Soy Bean No.1 (SB for short) futures markets from DCE. Secondly, by shuffling the original time series, we destroyed the underlying nonlinear temporal correlation; thus, we identified that long-range correlation mechanism constitutes major contributions in the formation in the multifractals of the markets. Thirdly, by tracking the evolution of left- and right-half spectra, we found that there exist critical points, between which there are different behaviors, in the left-half spectra for large price fluctuations; but for the right-hand spectra for small price fluctuations, the width of those increases slowly as the delay t increases in the long run. Finally, the dynamics of large fluctuations is significantly different from that of the small ones, which implies that there exist different underlying mechanisms in the formation of multifractality in the markets. Our main contributions focus on that we not only provided empirical evidence of the existence of multifractal features in China agricultural commodity futures markets; but also we pioneered in investigating the sources of the multifractality in China’s agricultural futures markets in current literature; furthermore, we investigated the nonlinear dynamical mechanisms based on spectrum analysis, which offers us insights into the underlying dynamical mechanisms in China’s agricultural futures markets.     

Synchronization time in a hyperbolic dynamical system with long-range interactions

We show that the threshold of complete synchronization in a lattice of coupled non-smooth chaotic maps is determined by linear stability along the directions transversal to the synchronization subspace. We examine carefully the synchronization time and show that an inadequate observation of the system evolution leads to wrong results. We present both careful numerical experiments and a rigorous mathematical explanation confirming this fact, allowing for a generalization involving hyperbolic coupled map lattices.     

聚对苯乙炔的能带结构和关联能计算

在考虑电子-电子相互作用情况下,对基态非简并聚合物聚对苯乙炔（PPV）的长程关联能进行了理论计算,并用长程关联能对带隙进行修正,最后讨论了长程关联能对带隙的影响。在对PPV链的计算中发现,长程关联能先会随着链长N的增加而减小,但当链长大于10后长程关联能会达到饱和。在链长为20个单元的PPV计算中,长程关联能的修正会降低由Hartree-Fock(HF)方法所得的能隙宽度。修正后的能隙宽度能很好的接近实验结果。     

Heat Kernel Estimates for Strongly Recurrent Random Walk on Random Media

We establish general estimates for simple random walk on an arbitrary infinite random graph, assuming suitable bounds on volume and effective resistance for the graph. These are generalizations of the results in Barlow et al. (Commun. Math. Phys. 278:385–431, 2008, Sects. 1, 2) and in particular imply the spectral dimension of the random graph. We will also give an application of the results to random walk on a long-range percolation cluster. J. Misumi research partially supported by the 21 century COE program at Graduate School of Mathematical Sciences, the University of Tokyo.     

On the Truncation of Systems with Non-Summable Interactions

In this note we consider long-range q-states Potts models on Z ^d , d≥ 2. For various families of non-summable ferromagnetic pair potentials φ(x)≥ 0, we show that there exists, for all inverse temperature β > 0, an integer N such that the truncated model, in which all interactions between spins at distance larger than N are suppressed, has at least q distinct infinite-volume Gibbs states. This holds, in particular, for all potentials whose asymptotic behaviour is of the type φ(x)∼ ‖x‖^−α, 0≤α≤ d. These results are obtained using simple percolation arguments. Work supported by Swiss National Foundation for Science, Conselho Nacional de Desenvolvimento Cientìfico e Tecnològico, and Programa de Auxìlio para Recèm Doutores PRPq-UFMG.     

Models of structure and properties of H-bonded molecular mixtures

Results on the modeling of molecular interactions, supramolecular organization and physicochemical properties of binary mixtures of organic solvents are presented. The mixtures, both with negative deviation from ideality, such as propanone–trichloromethane, dimethylsulfoxide–trichloromethane, and with positive deviation, such as 1,4-dioxane–methanol, 1,4-dioxane–ethanol, trichloromethane–methanol, trichloromethane–ethanol, have been studied. Models for the aggregation in mixtures due to specific intermolecular interactions are proposed. Integral and differential parameters of the supramolecular organization were obtained. Thermodynamic characteristics of aggregation (equilibrium constants, Gibbs energy, enthalpy and entropy) and structural parameters of the aggregates have been determined. Long-range molecular correlations and cooperativity of H-bonds have been established. The manifestations of the supramolecular ordering in the physicochemical properties of the mixtures are discussed.     

Sensitivity of the Hermite rank

The Hermite rank appears in limit theorems involving long memory. We show that a Hermite rank higher than one is unstable when the data is slightly perturbed by transformations such as shift and scaling. We carry out a “near higher order rank analysis” to illustrate how the limit theorems are affected by a shift perturbation that is decreasing in size. We also consider the case where the deterministic shift is replaced by centering with respect to the sample mean. The paper is a companion of Bai and Taqqu (2017) which discusses the instability of the Hermite rank in the statistical context.