基于相空间重构技术的原油价格的时序混沌判据和混沌特征量

通过相空间重构技术,对Brent和WTI原油价格增长率的时间序列分别进行相空间重构,将若干固定时间延迟点上的数据作为新维处理,形成相点,应用Wolf方法得出了最大的Lyapunov指数,从而给出了系统混沌存在的证据;利用关联函数求出了关联维度和Kolmogorov熵,从而给出了对系统的混沌程度的估计和对Brent和WTI原油价格进行有效性预测的时间尺度.     

A probe into the chaotic nature of daily streamflow time series by correlation dimension and largest Lyapunov methods

Two chaotic indicators namely the correlation dimension and the Lyapunov exponent methods are investigated for the daily river flow of Kizilirmak River. A delay time of 60 days used for the reconstruction is chosen after examining the first minimum of the average mutual information of the data. The sufficient embedding dimension is estimated using the false nearest neighbor algorithm, which has a value of 11. Based on these embedding parameters the correlation dimension of the resulting attractor is calculated, as well as the average divergence rate of nearby orbits given by the largest Lyapunov exponent. The presence of chaos in the examined river flow time series is evident with the low correlation dimension (2.4) and the positive value of the largest Lyapunov exponent (0.0061).     

原油期货价格的混沌识别研究

系统复杂性的研究是系统工程的一个热点研究领域。在虚假邻域概念基础上,给出了合适的嵌入参数的确定方法。讨论了分形维与最大Lyapunov指数的计算方法。纽约市场国际原油期货收盘价格时间序列数据的计算表明:这些数据来源于一最大Lyapunov指数值为0.038的混沌吸引子,混沌吸引子分形维为3.625,需用4个变量描述其所在系统的运动规律。此结论为进一步利用混沌理论研究原油期货价格的运动规律、进行相关的投资决策提供了重要信息。     

基于时间序列分析方法的伊犁州GDP的预测研究

基于时间序列理论,以伊犁州1978年至2014年来生产总值为基础数据,利用Eviewes8.0软件对数据进行处理分析,并对模型进行显著性检验,综合各种条件确定最终时间序列回归模型,对伊犁州未来三年的生产总值做出预测,为伊犁州党委、政府制定相关经济政策和发展战略提供科学依据.     

Chaos in fractional-order Genesio-Tesi system and its synchronization

In this paper we study the chaotic dynamics of fractional-order Genesio-Tesi system. Theoretically, a necessary condition for occurrence of chaos is obtained. Numerical investigations on the dynamics of this system have been carried out and properties of the system have been analyzed by means of Lyapunov exponents. It is shown that in case of commensurate system the lowest order of fractional-order Genesio-Tesi system to yield chaos is 2.79. Further, chaos synchronization of fractional-order Genesio-Tesi system is investigated via two different control strategies. Active control and sliding mode control are proposed and the stability of the controllers are studied. Numerical simulations have been carried out to verify the effectiveness of controllers.     

V^2C控制buck变换器的动力学分析及混沌控制研究

利用改进的最大李雅普诺夫指数分析了V^2C控制buck变换器中的动力学行为,通过分析切换面两侧子系统的几何关系,给出了不可微点处雅克比矩阵的补偿方法,显著提高了切换系统中动力学行为的分析精度.基于增加系统状态变量之间关联性能够削弱混沌的原则,在系统中加入了关联强度参数,并利用粒子群算法寻优出使系统稳态和瞬态性能最佳的参数,达到了消除混沌的目的.最后,通过仿真和实验验证了上述方法的可行性.     

Chaos and complexity in mine grade distribution series detected by nonlinear approaches

In this article, the underlying dynamics of treating grade distribution is interpreted as a chaotic system instead of a stochastic system for a better understanding. Here, we study the behavior of grade distribution spatial series acquired at the Chadormalu mine in Bafgh city of Iran to distinguish the possible existence of low‐dimensional deterministic chaos. This work applies a variety of nonlinear techniques for detecting the chaotic nature of the grade distribution spatial series and adopts a nonlinear prediction method for predicting the future of the grade distributions. First, the delay time dimension is computed using auto mutual information function to reconstruct the strange attractors. Then, the dimensionality of the trajectories is obtained using Cao's method and, correspondingly, the correlation dimension method is adopted to quantify the embedding dimension. The low embedding dimensions achieved from these methods show the existence of low dimensional chaos in the mining data. Next, the high sensitivity to initial conditions is evaluated using the maximal Lyapunov exponent criterion. Positive Lyapunov exponents obtained demonstrate the exponential divergence of the trajectories and hence the unpredictability of the data. Afterward, the nonlinear surrogate data test is done to further verify the nonlinear structure of the grade distribution series. This analysis provides considerable evidence for the being of low‐dimensional chaotic dynamics underlying the mining spatial series. Lastly, a nonlinear prediction scheme is carried out to predict the grade distribution series. Some computer simulations are presented to illustrate the efficiency of the applied nonlinear tools. © 2016 Wiley Periodicals, Inc. Complexity 21: 355–369, 2016     

Pre-operational forecasting of sea level height for the Río de la Plata

This paper presents the implementation and calibration of a pre-operational numerical model for the Río de la Plata river. This model is capable of predicting sea level variations in the Río de la Plata, and therefore constitutes a numerical tool of great value for the fluvial–maritime navigation and regional environmental management. A two-dimensional model (MOHID) with nested domains was used to simulate the hydrodynamics. This model was forced with a meso-scale atmospheric model (WRF) and a global tidal model (FES2004). The results obtained include astronomic and meteorological sea level variations in the Río de la Plata. Comparisons of modeled water levels with data have shown very good qualitative and quantitative agreement. The pre-operational test presented in this paper, a 4-day hydrodynamic forecast, was conducted in approximately 18 h.     

Information processing,memories, and synchronization in chaotic neural network with the time delay

Information processing and two types of memory in an analog neural network model with time delay that produces chaos similar to the human and animal EEGs are considered. There are two levels of information processing in this neural network: the level of individual neurons and the level of the neural network. Similar to the state of brain, the state of chaotic neural network is defined. It is characterized by two types of memories (memory I and memory II) and correlation structure between the neurons. In normal (unperturbed) state, the neural network generates chaotic patterns of averaged neuronal activities (memory I) and patterns of oscillation amplitudes (memory II). In the presence of external stimulation, the activity patterns change, showing changes in both types of memory. As in experiments on stimulation of the brain, the neural network model shows synchronization of neuronal activities due to stimulus measured by Pearson's correlation coefficient. An increase in neural network asymmetry (increase of the neural network excitability) leads to the phenomenon similar to the epilepsy. Modeling of brain injury, Parkinson's disease, and dementia is performed by removing and weakening interneuron connections. In all cases, the chaotic neural network shows a decrease of the degree of chaos and changes in both types of memory similar to those observed in experiments with healthy human subjects and patients with Parkinson's disease and dementia. © 2005 Wiley Periodicals, Inc. Complexity 11:39–52, 2005     

Densities of lattices corresponding to spaces of positive, negative, and variational dimension, and their application to time series

We prove a general theorem concerning a distribution of Bose-Einstein type. Using this theorem, we apply the notions of lattice dimension and lattice density to oscillatory time series.     

Multifractal and Multi-Multifractal of One-Dimensional Expanding Markov Maps

In measure theory, one is interested in local behaviours, for example in local dimensions, local entropies or local Lyapunov exponents. It has been relevant to study dynamical systems where one can develop further the study of multifractal and multi-multifractal, particularly when there exist strange attractors or repellers. Multifractal and multi-multifractal refer to a notion of size, which emphasizes the local variations of different values coming from the theory of dynamical systems and generated by the dimension theory of invariant measures. This paper gives some part of the literature in this field. Many results are already known, but the large deviations approach allows us to reprove these results and to obtain quite easily results concerning extremal points and extremal measures.     

我国外汇储备变动的时间序列建模预测

本文通过对我国最近十三年来的外汇储备月度数据进行分析,利用不同的建模思想建立了三次趋势模型、Holter-Winter非季节模型和AR IMA模型来分析短期内我国外汇储备的变动趋势。这三种模型对原始数据都能够较好的拟合,而且用于预测时的结果也相差不大,可以为短期内预测管理我国外汇储备提供有效参考。     

中国证券市场的高维混沌现象分析

将高维混沌理论应用到中国证券市场的分析之中,指出了当前许多文献中计算中国证券市场混沌特征指数出现较大差异的原因.通过比较上证综合指数与英国M organ S tan ley C ap ita l In ternationa l指数后指出,中国证券市场较复杂,且存在较多的高维(接近四维)混沌成分.     

Extended and Unscented Kalman filtering based feedforward neural networks for time series prediction

With the ability to deal with high non-linearity, artificial neural networks (ANNs) and support vector machines (SVMs) have been widely studied and successfully applied to time series prediction. However, good fitting results of ANNs and SVMs to nonlinear models do not guarantee an equally good prediction performance. One main reason is that their dynamics and properties are changing with time, and another key problem is the inherent noise of the fitting data. Nonlinear filtering methods have some advantages such as handling additive noises and following the movement of a system when the underlying model is evolving through time. The present paper investigates time series prediction algorithms by using a combination of nonlinear filtering approaches and the feedforward neural network (FNN). The nonlinear filtering model is established by using the FNN’s weights to present state equation and the FNN’s output to present the observation equation, and the input vector to the FNN is composed of the predicted signal with given length, then the extended Kalman filtering (EKF) and Unscented Kalman filtering (UKF) are used to online train the FNN. Time series prediction results are presented by the predicted observation value of nonlinear filtering approaches. To evaluate the proposed methods, the developed techniques are applied to the predictions of one simulated Mackey-Glass chaotic time series and one real monthly mean water levels time series. Generally, the prediction accuracy of the UKF-based FNN is better than the EKF-based FNN when the model is highly nonlinear. However, comparing from prediction accuracy and computational effort based on the prediction model proposed in our study, we draw the conclusion that the EKF-based FNN is superior to the UKF-based FNN for the theoretical Mackey-Glass time series prediction and the real monthly mean water levels time series prediction.     

Short-term prediction of wind power using EMD and chaotic theory

Due to the strong non-linear, complexity and non-stationary characteristics of wind farm power, a hybrid prediction model with empirical mode decomposition (EMD), chaotic theory, and grey theory is constructed. The EMD is used to decompose the wind farm power into several intrinsic mode function (IMF) components and one residual component. The grey forecasting model is used to predict the residual component. For the IMF components, identify their characteristics, if it is chaotic time series use largest Lyapunov exponent prediction method to predict. If not, use grey forecasting model to predict. Prediction results of residual component and all IMF components are aggregated to produce the ultimate predicted result for wind farm power. The ultimate predicted result shows that the proposed method has good prediction accuracy, can be used for short-term prediction of wind farm power.     

Ghost length, cone length and complete level of DG modules

In this paper, we introduce a new numerical invariant complete level for a DG module over a local chain DG algebra and give a characterization of it in terms of ghost length. We also study some of its upper bounds. The cone length of a DG module is an invariaut closely related with the invariant level. We discover some important results on it.     

Optimal control of sea level in a tidal basin by means of the Pontryagin maximum principle

The maximum principle has been applied in optimizing the sea level, induced by a tidal component, in a small basin. The water level control has been simulated by means of gate operations acting at the open mouth of the tidal basin. The main feature of the model is that the control operations do not require complete closure of the basin but only a variable reduction of its mouth. Although the equations describing the dynamics of the basin have been simplified, the results obtained are expected to be of practical use.     

Common volatility and correlation clustering in asset returns

We present a new multivariate framework for the estimation and forecasting of the evolution of financial asset conditional correlations. Our approach assumes return innovations with time dependent covariances. A Cholesky decomposition of the asset covariance matrix, with elements written as sines and cosines of spherical coordinates allows for modelling conditional variances and correlations and guarantees its positive definiteness at each time t. As in Christodoulakis and Satchell [Christodoulakis, G.A., Satchell, S.E., 2002. Correlated ARCH (CorrARCH): Modelling the time-varying conditional correlation between financial asset returns. European Journal of Operational Research 139 (2), 350–369] correlation is generated by conditionally autoregressive processes, thus allowing for an autocorrelation structure for correlation. Our approach allows for explicit out-of-sample forecasting and is consistent with stylized facts as time-varying correlations and correlation clustering, co-movement between correlation coefficients, correlation and volatility as well as between volatility processes (co-volatility). The latter two are shown to depend on correlation and volatility persistence. Empirical evidence on a trivariate model using monthly data from Dow Jones Industrial, Nasdaq Composite and the 3-month US Treasury Bill yield supports our theoretical arguments.     

上海市PM2.5浓度的分析与预测

针对上海市PM2.5的浓度进行动态分析及预测.通过使用Page检验分析了上海市PM2.5浓度近几年的变化趋势;然后建立时间序列ARIMA模型对PM2.5浓度日数据进行拟合分析与预测.在此基础上通过引入影响PM2.5浓度的其他因素建立带时间序列误差的回归模型以及引入波动率因素建立带波动率方程的模型改进原时间序列ARIMA模型;通过比较样本外预测的效果,结果表明改进后的两个模型其结果均优于已知文献中的ARIMA模型.     

Persistence and global stability in a delayed Leslie-Gower type three species food chain

Our investigation concerns the three-dimensional delayed continuous time dynamical system which models a predator-prey food chain. This model is based on the Holling-type II and a Leslie-Gower modified functional response. This model can be considered as a first step towards a tritrophic model (of Leslie-Gower and Holling-Tanner type) with inverse trophic relation and time delay. That is when a certain species that is usually eaten can consume immature predators. It is proved that the system is uniformly persistent under some appropriate conditions. By constructing a proper Lyapunov function, we obtain a sufficient condition for global stability of the positive equilibrium.