Seasonal trend analysis of image time series

A procedure is introduced for the analysis of seasonal trends in time series of Earth observation imagery. Called Seasonal Trend Analysis (STA), the procedure is based on an initial stage of harmonic analysis of each year in the series to extract the annual and semi‐annual harmonics. Trends in the parameters of these harmonics over years are then analysed using a robust median‐slope procedure. Finally, images of these trends are used to create colour composites highlighting the amplitudes and phases of seasonality trends. The technique specifically rejects high‐frequency sub‐annual noise and is robust to short‐term interannual variability up to a period of 29% of the length of the series. It is, thus, a very effective procedure for focusing on the general nature of longer‐term trends in seasonality.     

Time series clustering in linear time complexity

Data Mining and Knowledge Discovery - With the increasing power of data storage and advances in data generation and collection technologies, large volumes of time series data become available and...     

多时间尺度时间序列趋势预测

针对股票、基金等大量时间序列数据的趋势预测问题，提出一种基于新颖特征模型的多时间尺度时间序列趋势预测算法。首先，在原始时间序列中提取带有多时间尺度特征的特征树，其刻画了时间序列，不仅带有序列在各个层次的特征，同时表示了层次之间的关系。然后，利用聚类挖掘特征序列中的隐含状态。最后，应用隐马尔可夫模型（HMM）设计一个多时间尺度趋势预测算法（MTSTPA），同时对不同尺度下的趋势以及趋势的长度作出预测。在真实股票数据集上的实验中，在各个尺度上的预测准确率均在60%以上，与未使用特征树对比，使用特征树的模型预测效率更高，在某一尺度上准确率高出10个百分点以上。同时，与经典自回归滑动平均模型（ARMA）模型和PHMM（Pattern-based HMM）对比，MTSTPA表现更优，验证了其有效性。     

Detecting trend and seasonal changes in satellite image time series

A wealth of remotely sensed image time series covering large areas is now available to the earth science community. Change detection methods are often not capable of detecting land cover changes within time series that are heavily influenced by seasonal climatic variations. Detecting change within the trend and seasonal components of time series enables the classification of different types of changes. Changes occurring in the trend component often indicate disturbances (e.g. fires, insect attacks), while changes occurring in the seasonal component indicate phenological changes (e.g. change in land cover type). A generic change detection approach is proposed for time series by detecting and characterizing Breaks For Additive Seasonal and Trend (BFAST). BFAST integrates the decomposition of time series into trend, seasonal, and remainder components with methods for detecting change within time series. BFAST iteratively estimates the time and number of changes, and characterizes change by its magnitude and direction. We tested BFAST by simulating 16-day Normalized Difference Vegetation Index (NDVI) time series with varying amounts of seasonality and noise, and by adding abrupt changes at different times and magnitudes. This revealed that BFAST can robustly detect change with different magnitudes (> 0.1 NDVI) within time series with different noise levels (0.01-0.07 σ) and seasonal amplitudes (0.1-0.5 NDVI). Additionally, BFAST was applied to 16-day NDVI Moderate Resolution Imaging Spectroradiometer (MODIS) composites for a forested study area in south eastern Australia. This showed that BFAST is able to detect and characterize spatial and temporal changes in a forested landscape. BFAST is not specific to a particular data type and can be applied to time series without the need to normalize for land cover types, select a reference period, or change trajectory. The method can be integrated within monitoring frameworks and used as an alarm system to flag when and where changes occur.     

二重趋势时间序列的灰色组合预测模型

神经网络、ARIMA等广泛应用于具有趋势变动性和周期波动性的二重趋势特征的时间序列预测,而这些单一的模型难以达到满意的预测效果。提出一种针对该特征的灰色组合模型,其基本思想是：从二重趋势时间序列中分离趋势变动项和周期波动项后,用灰色G（1,1）模型预测趋势变动项,引用BP网络和ARIMA的组合模型预测周期波动项,用乘积模型合成两部分预测值为灰色组合模型的最终预测值。实验表明：该灰色组合模型适应了二重趋势时间序列的特征,具有很好的预测效果。     

基于随机性分析的虚假趋势时间序列判别

针对符合一定数据模式或规律的虚假数据识别问题，提出一种基于随机性分析的虚假趋势时间序列判别方法。该方法在分析时间序列组成的基础上，首先探索虚假趋势时间序列的简单伪造和复杂伪造方式，并将其分解为虚假趋势和虚假随机两部分；然后通过基函数逼近进行时间序列虚假趋势部分的提取，采用随机性理论开展虚假随机部分的分析；最终借助单比特频数和块内频数对虚假随机部分是否具备随机性进行检测，为具有一定趋势特征的虚假时间序列的判别提供了一个解决方案。实验结果表明：该方法能够有效地分解虚假时间序列和提取虚假趋势部分，实现简单伪造数据和复杂伪造数据的判别，支持对通过观测手段或者检测设备所获取的数值型数据的真伪分析，进一步提高了虚假数据可判别范围，平均判别正确率可达74.7%。     

基于趋势转折点的时间序列分段线性表示

分段线性表示是时间序列降维的有效方法。在总结分析序列趋势变化特点的基础上,提出了一种基于趋势转折点的时间序列分段线性表示算法。首先定义了趋势转折点作为时间序列分段点的备选集,以点到区域的距离度量趋势转折点的重要性,再根据给定的阈值选择重要趋势转折点作为分段点,对时间序列进行分段线性表示。通过与其他6种方法进行实验比较,结果表明：所提方法在具有较好的拟合质量和适应能力以及对转折点明显的序列,都表现出较强的抗噪声干扰能力。     

时间序列的非线性趋势预测及应用综述

针对时间序列趋势预测问题,综述了非线性趋势预测技术以及在金融领域的主要应用,重点介绍了非线性方法中的神经网络、支持向量机和混沌理论的基本原理、算法优缺点及主要改进,并介绍这些理论与遗传算法,小波理论等结合的组合预测方法.认为非线性生组合预测是今后时间序列趋势预测的发展方向,最后介绍了非线性趋势预测方法在股票价格走势与变化方向、债券价格、保险公司风险评估以及银行信用风险等方面的应用.     

Estimation in linear discrete systems with multiple time delays

The method of orthogonal projection is used to derive the equations for optimally estimating the state of a nonstationary linear discrete system with multiple time delays. A Kalman-type filter is developed, along with the necessary recursive error and cross error covariance matrix equations. A numerical example is included.     

Fuzzy based trend mapping and forecasting for time series data

The study demonstrates the superiority of fuzzy based methods for non-stationary, non-linear time series. Study is based on unequal length fuzzy sets and uses IF-THEN based fuzzy rules to capture the trend prevailing in the series. The proposed model not only predicts the value but can also identify the transition points where the series may change its shape and is ready to include subject expert’s opinion to forecast. The series is tested on three different types of data: enrolment for Alabama university, sales volume of a chemical company and Gross domestic capital of India: the growth curve. The model is tested on both kind of series: with and without outliers. The proposed model provides an improved prediction with lesser MAPE (mean average percentage error) for all the series tested.     

Social trend tracking by time series based social tagging clustering

Social tagging is widely practiced in the Web 2.0 era. Users can annotate useful or interesting Web resources with keywords for future reference. Social tagging also facilitates sharing of Web resources. This study reviews the chronological variation of social tagging data and tracks social trends by clustering tag time series. The data corpus in this study is collected from Hemidemi.com. A tag is represented in a time series form according to its annotating Web pages. Then time series clustering is applied to group tag time series with similar patterns and trends in the same time period. Finally, the similarities between clusters in different time periods are calculated to determine which clusters have similar themes, and the trend variation of a specific tag in different time periods is also analyzed. The evaluation shows the recommendation accuracy of the proposed approach is about 75%. Besides, the case discussion also proves the proposed approach can track the social trends.     

基于时间序列模型和情感分析的情感趋势预测

为解决传统情感分析方法无法对公众未来情感走势变化有效预测的问题,提出一种将时间序列模型与情感分析相结合的情感趋势预测方法.采用深度学习模型对股市论坛实时评论信息进行情感分类,统计固定时间单位的情感值,构建情感值时间序列,提出ARIMA-GARCH时间序列模型,对情感值时间序列进行建模分析,预测投资者的情感走势.实验结果表明,该方法对于情感趋势的预测结果合理,误差较小.同时,发现投资者情感趋势与股市涨跌幅走势相似,为投资决策提供了参考.     

多特征不确定时间序列的关联趋势分析

针对不确定信息的相似性度量方法无法充分反映信息之间的关联情况,提出了直觉模糊集关联趋势分析法(RTIFS法)。利用直觉模糊集之间的距离表示不确定信息的差别,通过区间数与直觉模糊集之间的等价关系,利用区间数的距离计算直觉模糊集的关联度,最后应用集对分析法对序列间的关联趋势进行分类。RTIFS法将关联度计算的范围推广到不确定信息环境下,并给出多特征序列关联趋势的分类结果。实验结果表明,RTIFS法的分类准确率较高,算法运行时间短。     

Estimation of time series noise covariance using correlation technology

Covariance of clean signal and observed noise is necessary for extracting clean signal from a time series.This is transferred to calculate the covariance of observed noise and clean signal’s MA process,when the clean signal is described by an autoregressive moving average (ARMA) model.Using the correlations of the innovations data from observed time series to form a least-squares problem,a concisely autocovariance least-square (CALS) method has been proposed to estimate the covariance.We also extended our work to the case of unknown MA process coefficients.Comparisons between Odelson’s autocovariance least-square (ALS) estimation algorithm and the proposed CALS method show that the CALS method could get a much more exact and compact estimation of the covariance than ALS and its extended form.     

基于时间序列线性拟合的色谱数据压缩方法

从石油录井色谱数据应用的实际需求出发,提出一种新的时间序列分段拟合算法。该算法通过一次扫描数据,根据中线距离阈值和非单调序列中极值点保持时间段阈值两个约束条件,选择反映序列趋势变化的关键点,然后线性拟合时间序列。实验结果表明该算法能够在保持原始序列主要形态的同时剔除噪音干扰,精确定位单调序列中的突变转折点,发现序列中的尖峰状态。     

一种基于信息熵的时间序列分段线性表示方法

针对部分时间序列具有高维、大数据量及数据更新速度较快的特点, 导致在原始时间序列上难以进行数据挖掘的问题, 提出一种基于信息熵的时间序列分段线性表示方法——PLR_IE。该算法利用信息熵作为评判重要点数量的性能指标, 从序列中提取重要分段点的数量分布情况, 利用重要点组成的序列重新拟合原始时间序列, 为下一步数据挖掘提供基础。实验结果表明, 该方法能高效地提取出序列主要特征、拟合原始序列。     

Neural networks for bandwidth selection in local linear regression of time series

The problem of automatic bandwidth selection in nonparametric regression is considered when a local linear estimator is used to derive nonparametrically the unknown regression function. A plug-in method for choosing the smoothing parameter based on the use of the neural networks is presented. The method applies to dependent data generating processes with nonlinear autoregressive time series representation. The consistency of the method is shown in the paper, and a simulation study is carried out to assess the empirical performance of the procedure.     

Seasonal and trend time series forecasting based on a quasi-linear autoregressive model

Modeling and forecasting seasonal and trend time series is an important research topic in many areas of industrial and economic activity. In this study, we forecast the seasonal and trend time series using a quasi-linear autoregressive model. This quasi-linear autoregressive model belongs to a class of varying coefficient models in which its autoregressive coefficients are constructed by radial basis function networks. A combined genetic optimization and gradient-based optimization algorithm is applied for automatic selection of proper input variables and model-dependent variables, and optimizing the model parameters simultaneously. The model is tested by five monthly time series. We compare the results with those of other various methods, which show the effectiveness of the proposed approach for the seasonal time series.     

An algorithm for time series analysis of linear time-invariant differential equations

For linear time-invariant problems an algorithm is presented that enables fast and accurate time series analysis. The method is based on the assumption that the forcing functions can be expressed by a polygonal course. As a result an exact and therefore unconditional stable numerical procedure is derived.