Nonparametric estimation of the spectral density of amplitude-modulated time series with missing observations

Consider a real-valued and second-order stationary time series with mean zero. The aim is to estimate its spectral density. A minimax solution of this problem is known when either the time series is observed directly, or some observations are missed according to an independent Bernoulli process, or for some special cases when the time series is multiplied by an amplitude-modulating time series with known distribution. It is shown that if a time series of interest, a Bernoulli time series defining missing mechanism, and an amplitude-modulating time series are mutually independent, then the shape of spectral density of an underlying time series of interest can be estimated with the minimax rate known for the case of direct observations. Furthermore, in some special cases the spectral density can be estimated with the minimax rate known for directly observed time series of interest.     

Novel method of identifying time series based on network graphs

In this article, we propose a novel method for transforming a time series into a complex network graph. The proposed algorithm is based on the spatial distribution of a time series. The characteristics of geometric parameters of a network represent the dynamic characteristics of a time series. Our algorithm transforms, respectively, a constant series into a fully connected graph, periodic time series into a regular graph, linear divergent time series into a tree, and chaotic time series into an approximately power law distribution network graph. We find that when the dimension of reconstructed phase space increases, the corresponding graph for a random time series quickly turns into a completely unconnected graph, while that for a chaotic time series maintains a certain level of connectivity. The characteristics of the generated network, including the total edges, the degree distribution, and the clustering coefficient, reflect the characteristics of the time series, including diverging speed, level of certainty, and level of randomness. This observation allows a chaotic time series to be easily identified from a random time series. The method may be useful for analysis of complex nonlinear systems such as chaos and random systems, by perceiving the differences in the outcomes of the systems—the time series—in the identification of the systemic levels of certainty or randomness. © 2011 Wiley Periodicals, Inc. Complexity, 2011     

Self-criticality and stochasticity of an S&P 500 index time series

In this paper, three time series representative of the daily high, low and closing prices of S&P 500 index time series, as from 1 December 1988 to 1 April 1998 are studied. The hypothesis advanced by Osborne that the stock market time series satisfy a log-normal distribution is rejected. The self-critical behavior of these time series is investigated. A fractional Brownian motion model for such time series is supported. Arguments are directed torwards a negation of a chaotic explanation of these time series.     

An eigenvalue approach to the limiting behavior of time series aggregates

Many time series variables such as rainfall, industrial production, and sales exist only in some aggregated forms. To see the implication of time series aggregation it is important to know the limiting behavior of the time series aggregates. From the relationship of autocovariances between the underlying time series variable and its aggregates, we show that the limiting behavior of time series aggregates is closely related to the eigenvalues and the eigenvectors of the aggregation operator. Specifically, the vector of admissible autocorrelations of the limiting model for the time series aggregates is the eigenvector associated with the largest eigenvalue of the aggregation transformation. This provides an interesting and simple method for deriving the limiting model for time series aggregates. Systematic sampling of time series can be treated similarly. The method is illustrated with an empirical example.     

Kolmogorov space in time series data

We provide the proof that the space of time series data is a Kolmogorov space with T₀‐separation axiom using the loop space of time series data. In our approach, we define a cyclic coordinate of intrinsic time scale of time series data after empirical mode decomposition. A spinor field of time series data comes from the rotation of data around price and time axis by defining a new extradimension to time series data. We show that there exist hidden eight dimensions in Kolmogorov space for time series data. Our concept is realized as the algorithm of empirical mode decomposition and intrinsic time scale decomposition, and it is subsequently used for preliminary analysis on the real time series data. Copyright © 2016 John Wiley & Sons, Ltd.     

Mining time series data for segmentation by using Ant Colony Optimization

In trying to distinguish data features within time series data for specific time intervals, time series segmentation technology is often required. This research divides time series data into segments of varying lengths. A time series segmentation algorithm based on the Ant Colony Optimization (ACO) algorithm is proposed to exhibit the changeability of the time series data. In order to verify the effect of the proposed algorithm, we experiment with the Bottom-Up method, which has been reported in available literature to give good results for time series segmentation. Simulation data and genuine stock price data are also used in some of our experiments. The research result shows that time series segmentation run by the ACO algorithm not only automatically identifies the number of segments, but its segmentation cost was lower than that of the time series segmentation using the Bottom-Up method. More importantly, during the ACO algorithm process, the degree of data loss is also less compared to that of the Bottom-Up method.     

基于BP神经网络的时间序列预测问题研究

分析指出了基于标准BP神经网络的时间序列预测问题存在的不足.根据基于BP神经网络的时间序列预测问题的特点,研究给出了一种以y=x作为传递函数的时间序列预测方法,经实例验证表明,给出的以y=x作为传递函数的时间序列预测方法较基于标准BP神经网络的时间序列预测方法具有较好的结果.     

Nonlinear Time Series Analysis Since 1990:Some Personal Reflections

Abstract I reflect upon the development of nonlinear time series analysis since 1990 by focusing on five majorareas of development. These areas include the interface between nonlinear time series analysis and chaos,thenonparametric/semiparametric approach,nonlinear state space modelling,financial time series and nonlinearmodelling of panels of time series.     

金融时间序列的转折点分析

本文讨论了时间序列的预测问题,在摆脱了在传统模型过多假设的基础上,采用对不同类型预测模型进行综合平衡分析的方法,权衡各项指标,以达到发现时间按序列转折点的目的.并以股票序列为例说明所给预测模型的有效性.     

Time series analysis of covariance based on linear transfer function models

In this article, a time series analysis of covariance model is introduced when covariates time series have lead–lag relationship with response time series. Parameter estimation and hypothesis testing for this model are made in spectral domain. We provide an instruction for our approach using a real Hydrological time series data set.

     

A method for finding smoothly varying rules in Multidimensional time series

An approach to discovering rules in nonstationary k-valued Multidimensional time series is proposed. It allows one to discover rules that are subject to “smooth” structural changes with the course of time. A measure of rule similarity is proposed to describe such changes, and its application in the form of weight in the graph of rules is discussed. The discovered rules can be used to predict the next elements in the multidimensional time series, to analyze the phenomenon described by this multidimensional time series, and to model it. This allows one to use the proposed algorithm for predicting time series and for examining and describing the processes that can be represented by a multidimensional time series. Means for the direct practical application of the proposed methods of the analysis and prediction of time series are described, and the use of those methods for the short-range prediction of a real-life multidimensional time series consisting of the stock prices of companies operating in similar fields is discussed.     

Testing coeffcients of AR and bilinear time series models by a graphical approach

AR and bilinear time series models are expressed as time series chain graphical models, based on which, it is shown that the coefficients of AR and bilinear models are the conditional correlation coefficients conditioned on the other components of the time series. Then a graphically based procedure is proposed to test the significance of the coeffcients of AR and bilinear time series. Simulations show that our procedure performs well both in sizes and powers.     

Time reversal, symbolic series and irreversibility of human heartbeat

We study the time reversal properties of time series by means of a ternary coding of the differentiated series. For the symbolic series obtained in this way we show that suitable pairs of ternary words have the same probability if the time series is reversible. This provides tests in which time reversibility is rejected if the estimated probabilities are significantly different. We apply one of these tests to the human heartbeat series extracted from 24 h Holter recordings of 19 healthy subjects. Data analysis shows a highly significant prevalence of irreversibility. Our symbolic approach to time reversal gives further support to the suitability of non-linear modeling of the normal heartbeat.     

复杂系统中混沌排斥子的动力学特性分析及应用研究

研究了由一类复杂系统排斥子所生成的时间序列的分形特征、分维值,利用相空间重构理论对排斥子所生成的混沌时序数据进行了重构．研究了时序数据的零均值处理、傅立叶滤波对预测结果的影响,研究了预测样本值的选取对预测的相对误差、预测长度影响等相关问题．结果表明:该模型对于这类排斥子所生成的时序数据建模和预测都具有实用性,且混沌排斥子样本数据的零均值处理对预测结果有一定的量的改变,但对排斥子样本数据进行Fourier滤波处理会降低预测的精度,这对于复杂系统排斥子的研究有着较为重要的理论和实际意义．     

Stock market forecasting by using a hybrid model of exponential fuzzy time series

The initial aim of this study is to propose a hybrid method based on exponential fuzzy time series and learning automata based optimization for stock market forecasting. For doing so, a two-phase approach is introduced. In the first phase, the optimal lengths of intervals are obtained by applying a conventional fuzzy time series together with learning automata swarm intelligence algorithm to tune the length of intervals properly. Subsequently, the obtained optimal lengths are applied to generate a new fuzzy time series, proposed in this study, named exponential fuzzy time series. In this final phase, due to the nature of exponential fuzzy time series, another round of optimization is required to estimate certain method parameters. Finally, this model is used for future forecasts. In order to validate the proposed hybrid method, forty-six case studies from five stock index databases are employed and the findings are compared with well-known fuzzy time series models and classic methods for time series. The proposed model has outperformed its counterparts in terms of accuracy.     

Graphical modelling of multivariate time series

We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of strong Granger causality and can be applied to time series with non-linear dependences. The models are derived from ordinary time series models by imposing constraints that are encoded by mixed graphs. In these graphs each component series is represented by a single vertex and directed edges indicate possible Granger-causal relationships between variables while undirected edges are used to map the contemporaneous dependence structure. We introduce various notions of Granger-causal Markov properties and discuss the relationships among them and to other Markov properties that can be applied in this context. Examples for graphical time series models include nonlinear autoregressive models and multivariate ARCH models.     

Multi-scale anomaly detection algorithm based on infrequent pattern of time series

In this paper, we propose two anomaly detection algorithms PAV and MPAV on time series. The first basic idea of this paper defines that the anomaly pattern is the most infrequent time series pattern, which is the lowest support pattern. The second basic idea of this paper is that PAV detects directly anomalies in the original time series, and MPAV algorithm extraction anomaly in the wavelet approximation coefficient of the time series. For complexity analyses, as the wavelet transform have the functions to compress data, filter noise, and maintain the basic form of time series, the MPAV algorithm, while maintaining the accuracy of the algorithm improves the efficiency. As PAV and MPAV algorithms are simple and easy to realize without training, this proposed multi-scale anomaly detection algorithm based on infrequent pattern of time series can therefore be proved to be very useful for computer science applications.     

How does innovation's tail risk determine marginal tail risk of a stationary financial time series?

We discuss the relationship between the marginal tail risk probability and theinnovation's tail risk probability for some stationary financial time series models. We firstgive the main results on the tail behavior of a class of infinite weighted sums of randomvariables with heavy-tailed probabilities. And then, the main results are applied to threeimportant types of time series models; infinite order moving averages, the simple bilineartime series and the solutions of stochastic difference equations. The explicit formulasare given to describe how the marginal tail probabilities come from the innovation's tailprobabilities for these time series. Our results can be applied to the tail estimation of timeseries and are useful for risk analysis in finance.     

基于主成分分析的单变量时间序列聚类方法

针对时间序列数据的高维特性,在进行理论分析的基础上,利用主成分分析法提出了一种单变量时间序列数据降维的新方法,进而提出了基于主成分分析的单变量时间序列聚类方法。其主要思想是在线性空间中的同一组基下,用系数之间的相似性来刻画对应时间序列之间相似性,在理论分析过程中,首先对单变量时间序列数据集进行主成分分析,其次分析了单变量时间序列数据集、样本协方差矩阵的特征向量与主成分之间的关系,并证明了由主成分构成的向量组线性无关。为了进一步验证理论分析结果的正确性和所提算法的有效性,分别利用仿真数据和真实的股票数据进行了数值实验。     

A note on the time series which is the product of two stationary time series

The time series […,x_-1y_-1,x₀y₀,x₁y₁,…]> which is the product of two stationary time series x_t and y_t is studied. Such sequences arise in the study of nonlinear time series, censored time series, amplitude modulated time series, time series with random parameters, and time series with missing observations. The mean and autocovariance function of the product sequence are derived.