一类非线性周期时间序列模型

为了描述周期时间序列中的偏倚和多峰等非线性特征,结合有限混合模型方法,提出混合周期自回归滑动平均时间序列模型（MPARMA）,给出了MPARMA模型的平稳性条件,讨论了期望最大化（EM）算法的应用,通过PM10浓度序列分析,评估了MPARMA模型的表现。     

A time series representation model for accurate and fast similarity detection

Similarity search and detection is a central problem in time series data processing and management. Most approaches to this problem have been developed around the notion of dynamic time warping, whereas several dimensionality reduction techniques have been proposed to improve the efficiency of similarity searches. Due to the continuous increasing of sources of time series data and the cruciality of real-world applications that use such data, we believe there is a challenging demand for supporting similarity detection in time series in a both accurate and fast way. Our proposal is to define a concise yet feature-rich representation of time series, on which the dynamic time warping can be applied for effective and efficient similarity detection of time series. We present the Derivative time series Segment Approximation (DSA) representation model, which originally features derivative estimation, segmentation and segment approximation to provide both high sensitivity in capturing the main trends of time series and data compression. We extensively compare DSA with state-of-the-art similarity methods and dimensionality reduction techniques in clustering and classification frameworks. Experimental evidence from effectiveness and efficiency tests on various datasets shows that DSA is well-suited to support both accurate and fast similarity detection.     

A self-organising mixture autoregressive network for FX time series modelling and prediction

Nowadays a great deal of effort has been made in order to gain advantages in foreign exchange (FX) rates predictions. However, most existing techniques seldom excel the simple random walk model in practical applications. This paper describes a self-organising network formed on the basis of a mixture of adaptive autoregressive models. The proposed network, termed self-organising mixture autoregressive (SOMAR) model, can be used to describe and model nonstationary, nonlinear time series by means of a number of underlying local regressive models. An autocorrelation coefficient-based measure is proposed as the similarity measure for assigning input samples to the underlying local models. Experiments on both benchmark time series and several FX rates have been conducted. The results show that the proposed method consistently outperforms other local time series modelling techniques on a range of performance measures including the mean-square-error, correct trend predication percentage, accumulated profit and model variance.     

Image data compression using autoregressive time series models

A two-dimensional image model is formulated using a seasonal autoregressive time series. With appropriate use of initial conditions, the method of least squares is used to obtain estimates of the model parameters. The model is then used to regenerate the original image. Results obtained indicate this method could be used to code textures for low bit rates or be used in an application of generating compressed background scenes. A differential pulse code modulation (DPCM) scheme is also demonstrated as a means of archival storage of images along with a new quantization technique for DPCM. This quantization technique is compared with standard quantization methods.     

Finding the most unusual time series subsequence: algorithms and applications

In this work we introduce the new problem of finding time seriesdiscords. Time series discords are subsequences of longer time series that are maximally different to all the rest of the time series subsequences. They thus capture the sense of the most unusual subsequence within a time series. While discords have many uses for data mining, they are particularly attractive as anomaly detectors because they only require one intuitive parameter (the length of the subsequence) unlike most anomaly detection algorithms that typically require many parameters. While the brute force algorithm to discover time series discords is quadratic in the length of the time series, we show a simple algorithm that is three to four orders of magnitude faster than brute force, while guaranteed to produce identical results. We evaluate our work with a comprehensive set of experiments on diverse data sources including electrocardiograms, space telemetry, respiration physiology, anthropological and video datasets. Eamonn Keogh is an Assistant Professor of computer science at the University of California, Riverside. His research interests include data mining, machine learning and information retrieval. Several of his papers have won best paper awards, including papers at SIGKDD and SIGMOD. Dr. Keogh is the recipient of a 5-year NSF Career Award for “Efficient discovery of previously unknown patterns and relationships in massive time series databases.” Jessica Lin is an Assistant Professor of information and software engineering at George Mason University. She received her Ph.D. from the University of California, Riverside. Her research interests include data mining and informational retrieval. Sang-Hee Lee is a paleoanthropologist at the University of California, Riverside. Her research interests include the evolution of human morphological variation and how different mechanisms (such as taxonomy, sex, age, and time) explain what is observed in fossil data. Dr. Lee obtained her Ph.D. in anthropology from the University of Michigan in 1999. Helga Van Herle is an Assistant Clinical Professor of medicine at the Division of Cardiology of the Geffen School of Medicine at UCLA. She received her M.D. from UCLA in 1993; completed her residency in internal medicine at the New York Hospital (Cornell University, 1993–1996) and her cardiology fellowship at UCLA (1997–2001). Dr. Van Herle holds a M.Sc. in bioengineering from Columbia University (1987) and a B.Sc. in Chemical Engineering from UCLA (1985)     

Clustering of time series data—a survey

Time series clustering has been shown effective in providing useful information in various domains. There seems to be an increased interest in time series clustering as part of the effort in temporal data mining research. To provide an overview, this paper surveys and summarizes previous works that investigated the clustering of time series data in various application domains. The basics of time series clustering are presented, including general-purpose clustering algorithms commonly used in time series clustering studies, the criteria for evaluating the performance of the clustering results, and the measures to determine the similarity/dissimilarity between two time series being compared, either in the forms of raw data, extracted features, or some model parameters. The past researchs are organized into three groups depending upon whether they work directly with the raw data either in the time or frequency domain, indirectly with features extracted from the raw data, or indirectly with models built from the raw data. The uniqueness and limitation of previous research are discussed and several possible topics for future research are identified. Moreover, the areas that time series clustering have been applied to are also summarized, including the sources of data used. It is hoped that this review will serve as the steppingstone for those interested in advancing this area of research.     

Blind source separation with time series variational Bayes expectation maximization algorithm

This paper presents a variational Bayes expectation maximization algorithm for time series based on Attias? variational Bayesian theory. The proposed algorithm is applied in the blind source separation (BSS) problem to estimate both the source signals and the mixing matrix for the optimal model structure. The distribution of the mixing matrix is assumed to be a matrix Gaussian distribution due to the correlation of its elements and the inverse covariance of the sensor noise is assumed to be Wishart distributed for the correlation between sensor noises. The mixture of Gaussian model is used to approximate the distribution of each independent source. The rules to update the posterior hyperparameters and the posterior of the model structure are obtained. The optimal model structure is selected as the one with largest posterior. The source signals and mixing matrix are estimated by applying LMS and MAP estimators to the posterior distributions of the hidden variables and the model parameters respectively for the optimal structure. The proposed algorithm is tested with synthetic data. The results show that: (1) the logarithm posterior of the model structure increases with the accuracy of the posterior mixing matrix; (2) the accuracies of the prior mixing matrix, the estimated mixing matrix, and the estimated source signals increase with the logarithm posterior of the model structure. This algorithm is applied to Magnetoencephalograph data to localize the source of the equivalent current dipoles.     

Efficient query filtering for streaming time series with applications to semisupervised learning of time series classifiers

In this paper, we define time series query filtering, the problem of monitoring the streaming time series for a set of predefined patterns. This problem is of great practical importance given the massive volume of streaming time series available through sensors, medical patient records, financial indices and space telemetry. Since the data may arrive at a high rate and the number of predefined patterns can be relatively large, it may be impossible for the comparison algorithm to keep up. We propose a novel technique that exploits the commonality among the predefined patterns to allow monitoring at higher bandwidths, while maintaining a guarantee of no false dismissals. Our approach is based on the widely used envelope-based lower-bounding technique. As we will demonstrate on extensive experiments in diverse domains, our approach achieves tremendous improvements in performance in the offline case, and significant improvements in the fastest possible arrival rate of the data stream that can be processed with guaranteed no false dismissals. As a further demonstration of the utility of our approach, we demonstrate that it can make semisupervised learning of time series classifiers tractable. Li Wei is a Ph.D. candidate in the Department of Computer Science & Engineering at the University of California, Riverside. She received her B.S. and M.S. degrees from Fudan University, China. Her research interests include data mining and information retrieval. Eamonn Keogh is an Assistant Professor of computer science at the University of California, Riverside. His research interests include data mining, machine learning and information retrieval. Several of his papers have won best paper awards, including papers at SIGKDD and SIGMOD. Dr. Keogh is the recipient of a 5-year NSF Career Award for “Efficient Discovery of Previously Unknown Patterns and Relationships in Massive Time Series Databases”. Helga Van Herle is an Assistant Clinical Professor of medicine at the Division of Cardiology of the Geffen School of Medicine at UCLA. She received her M.D. from UCLA in 1993; completed her residency in internal medicine at the New York Hospital (Cornell University; 1993–1996) and her cardiology fellowship at UCLA (1997–2001). Dr. Van Herle holds an M.Sc. in bioengineering from Columbia University (1987) and a B.Sc. in chemical engineering from UCLA (1985). Agenor Mafra-Neto, Ph.D., is the CEO of ISCA Technologies, Inc., in California and the founder of ISCA Technologies, LTDA, in Brazil. His research interests include the analysis of insect behavior and communication systems, the manipulation of insect behavior, and the automation of pest monitoring and pest control. Dr. Mafra-Neto is currently coordinating the deployment of area-wide smart sensor and effector networks to micromanage agricultural and public health pests in the field in an automatic fashion. Russell J. Abbott is a Professor of computer science at California State University, Los Angeles, and a member of the staff at the Aerospace Corporation, El Segundo, CA. His primary interests are in the field of complex systems. He is currently organizing a workshop to bring together people working in the fields of complex systems and systems engineering.     

一种时间序列动态聚类的算法

针对时间序列传统静态聚类问题,提出了对时间序列进行动态聚类的方法。该方法首先提取时间序列的关键点集合,根据改进的FCM算法找到动态特征明显的时间序列,再利用提出的动态聚类算法确定此类时间序列在不同时间段的所属类别,在改进的FCM算法中采用兰氏距离可以使其对奇异值不敏感。实验结果反映出动态特征明显的时间序列类别随时间演化的特性,表明了方法的可行性和有效性。与已有算法相比,该方法揭示了时间序列的部分动态特征。该方法还可以运用于研究数据挖掘的其他问题。     

利用自回归模型的平稳时序数据快速辨识算法

由于自回归模型的参数估计可归结为求解一个线性方程组的问题,故其在平稳时序数据的辨识过程中具有广泛的应用场合。提出了一种基于自回归模型的快速辨识算法,首先,以递推的方式对平稳时序数据自相关函数矩阵的秩的下界值进行估计,然后,以该估计值作为自回归模型的起始阶数对系统进行依次的递阶辨识,最后,基于F检验对相邻阶次的拟合误差的变化趋势进行显著性检验,并以检验结果作为算法的结束条件。新算法在保证较高辨识精度的条件下,其计算效能及辨识精度的稳定性均优于现有的自回归模型辨识算法,实验结果验证了新算法的有效性和先进性。     

Formalism for a multiresolution time series database model

We formalise a specialised database management system model for time series using a multiresolution approach. These special purpose database systems store time series lossy compressed in a space-bounded storage. Time series can be stored at multiple resolutions, using distinct attribute aggregations and keeping its temporal attribute managed in a consistent way.The model exhibits a generic approach that facilitates its customisation to suit better the actual application requirements in a given context. The elements, the meaning of which depends on a real application, are of generic nature.Furthermore, we consider some specific time series properties that are a challenge in the multiresolution approach. We also describe a reference implementation of the model and introduce a use case based on real data.     

A bivariate fuzzy time series model to forecast the TAIEX

Fuzzy time series models have been applied to forecast various domain problems and have been shown to forecast better than other models. Neural networks have been very popular in modeling nonlinear data. In addition, the bivariate models are believed to outperform the univariate models. Hence, this study intends to apply neural networks to fuzzy time series forecasting and to propose bivariate models in order to improve forecasting. The stock index and its corresponding index futures are taken as the inputs to forecast the stock index for the next day. Both in-sample estimation and out-of-sample forecasting are conducted. The proposed models are then compared with univariate models as well as other bivariate models. The empirical results show that one of the proposed models outperforms the many other models.     

Prototyping a global algorithm for systematic fire-affected area mapping using MODIS time series data

The remote sensing of Earth surface changes is an active research field aimed at the development of methods and data products needed by scientists, resource managers, and policymakers. Fire is a major cause of surface change and occurs in most vegetation zones across the world. The identification and delineation of fire-affected areas, also known as burned areas or fire scars, may be considered a change detection problem. Remote sensing algorithms developed to map fire-affected areas are difficult to implement reliably over large areas because of variations in both the surface state and those imposed by the sensing system. The availability of robustly calibrated, atmospherically corrected, cloud-screened, geolocated data provided by the latest generation of moderate resolution remote sensing systems allows for major advances in satellite mapping of fire-affected area. This paper describes an algorithm developed to map fire-affected areas at a global scale using Moderate Resolution Imaging Spectroradiometer (MODIS) surface reflectance time series data. The algorithm is developed from the recently published Bi-Directional Reflectance Model-Based Expectation change detection approach and maps at 500 m the location and approximate day of burning. Improvements made to the algorithm for systematic global implementation are presented and the algorithm performance is demonstrated for southern African, Australian, South American, and Boreal fire regimes. The algorithm does not use training data but rather applies a wavelength independent threshold and spectral constraints defined by the noise characteristics of the reflectance data and knowledge of the spectral behavior of burned vegetation and spectrally confusing changes that are not associated with burning. Temporal constraints are applied capitalizing on the spectral persistence of fire-affected areas. Differences between mapped fire-affected areas and cumulative MODIS active fire detections are illustrated and discussed for each fire regime. The results reveal a coherent spatio-temporal mapping of fire-affected area and indicate that the algorithm shows potential for global application.     

AR1MA时间序列模型在电信产品收入预算中的应用

本文通过AR1MA时间序列模型,利用SPSS统计软件对某电信产品收入进行了预测研究。结果表明,模型拟合较好,将模型预测数据与实际数据比较显示,模型预测精度较高。为电信制定经营决策、编制下年度的工作计划提供依据与参考。     

Optimal algorithms for the online time series search problem

In the problem of online time series search introduced by El-Yaniv et al. (2001) [1], a player observes prices one by one over time and shall select exactly one of the prices on its arrival without the knowledge of future prices, aiming to maximize the selected price. In this paper, we extend the problem by introducing profit function. Considering two cases where the search duration is either known or unknown beforehand, we propose two optimal deterministic algorithms respectively. The models and results in this paper generalize those of El-Yaniv et al. (2001) [1].     

Recursive prediction for long term time series forecasting using advanced models

There exists a wide range of paradigms, and a high number of different methodologies that are applied to the problem of time series prediction. Most of them are presented as a modified function approximation problem using input/output data, in which the input data are expanded using values of the series at previous steps. Thus, the model obtained normally predicts the value of the series at a time (t+h) using previous time steps (t-τ₁),(t-τ₂),…,(t-τ_n). Nevertheless, learning a model for long term time series prediction might be seen as a more complicated task, since it might use its own outputs as inputs for long term prediction (recursive prediction). This paper presents the utility of two different methodologies, the TaSe fuzzy TSK model and the least-squares SVMs, to solve the problem of long term time series prediction using recursive prediction. This work also introduces some techniques that upgrade the performance of those advanced one-step-ahead models (and in general of any one-step-ahead model), where they are used recursively for long term time series prediction.     

A clustering procedure for exploratory mining of vector time series

A two-step procedure is developed for the exploratory mining of real-valued vector (multivariate) time series using partition-based clustering methods. The proposed procedure was tested with model-generated data, multiple sensor-based process data, as well as simulation data. The test results indicate that the proposed procedure is quite effective in producing better clustering results than a hidden Markov model (HMM)-based clustering method if there is a priori knowledge about the number of clusters in the data. Two existing validity indices were tested and found ineffective in determining the actual number of clusters. Determining the appropriate number of clusters in the case that there is no a priori knowledge is a known unresolved research issue not only for our proposed procedure but also for the HMM-based clustering method and further development is necessary.     

An integrated temporal data model incorporating time series concept

Most temporal data models have concentrated on describing temporal data based on versioning of objects, tuples or attributes. The concept of time series, which is often needed in temporal applications, does not fit well within these models. The goal of this paper is to propose a generalized temporal database model that integrates the modeling of both version-based and time-series based temporal data into a single conceptual framework. The concept of calendar is also integrated into our proposed model. We also discuss how a conceptual Extended-ER design in our model can be mapped to an object-oriented or relational database implementation.