一种面向工作负载预测的基于小波变换的特征提取方法

在资源受限条件下,根据数据挖掘任务在执行过程中实时产生的资源和任务状态来准确地预测任务执行时间是非常重要的。为有效地使用时间序列数据实现准确预测,提出一种降载策略来确定预测的切入点和数据处理方案。该策略使用动态时间规整(Dynamic Time Warping, DTW)距离度量子序列与整个序列之间相似度的变化以确定用于预测的数据,然后利用小波变换计算小波系数并提取小波系数的能量值作为预测的特征,最后预测任务执行时间。实验结果表明,该方法提取的特征信息包含原序列较多信息,在预测任务执行时间方面具有较高的准确性。     

基于VMD循环随机跳跃状态网络的时间序列长期预测

由于混沌系统的演化规律复杂,直接对混沌时间序列进行长期预测通常难以达到较好的效果.针对此问题,利用变分模态分解方法将混沌时间序列转化为一系列特征子序列,利用排列熵评估选取子序列个数的合理性,保证特征子序列包含了原序列长期演化趋势.此外,提出一种改进的确定性循环跳跃状态网络作为子序列的预测模型,该网络模型中的储备池采用单向环状连接和双向随机跳跃的拓扑结构,能够避免储备池确定连接结构造成的预测精度较低和随机连接造成网络的不稳定性问题.通过所提出模型对时间序列进行长期预测,采用多种评估手段对预测结果进行分析, 表明所提出模型对于长期预测具有较大的优势.     

Using a Stochastic Complexity Measure to Check the Efficient Market Hypothesis

The weak form of the Efficient Market Hypothesis (EMH) states that current market price reflects fully the information from past prices and rules out prediction based on price data alone. No recent test of time series of stock returns rejects this weak-form hypothesis. This research offers another test of the weak form of the EHM that leads to different conclusions for some time series.The stochastic complexity of a time series is a measure of the number of bits needed to represent and reproduce the information in the time series. In an efficient market, compression of the time series is not possible, because there are no patterns and the stochastic complexity is high. In this research, Rissanen's context tree algorithm is used to identify recurring patterns in the data, and use them for compression. The weak form of the EMH is tested for 13 international stock indices and for all the stocks that comprise the Tel-Aviv 25 index (TA25), using sliding windows of 50, 75, and 100 consecutive daily returns. Statistically significant compression is detected in ten of the international stock index series. In the aggregate, 60% to 84% of the TA25 stocks tested demonstrate compressibility beyond randomness. This indicates potential market inefficiency.     

Stock time series pattern matching: Template-based vs. rule-based approaches

One of the major duties of financial analysts is technical analysis. It is necessary to locate the technical patterns in the stock price movement charts to analyze the market behavior. Indeed, there are two main problems: how to define those preferred patterns (technical patterns) for query and how to match the defined pattern templates in different resolutions. As we can see, defining the similarity between time series (or time series subsequences) is of fundamental importance. By identifying the perceptually important points (PIPs) directly from the time domain, time series and templates of different lengths can be compared. Three ways of distance measure, including Euclidean distance (PIP-ED), perpendicular distance (PIP-PD) and vertical distance (PIP-VD), for PIP identification are compared in this paper. After the PIP identification process, both template- and rule-based pattern-matching approaches are introduced. The proposed methods are distinctive in their intuitiveness, making them particularly user friendly to ordinary data analysts like stock market investors. As demonstrated by the experiments, the template- and the rule-based time series matching and subsequence searching approaches provide different directions to achieve the goal of pattern identification.     

基于异时间窗划分的时间序列聚类

针对相同时间窗对时间序列进行子序列划分的缺点,提出一种异时间窗的子序列划分方法。为解决划分得到的子序列长度不同,而使用动态时间弯曲算法进行子序列相似性度量的计算速度慢的问题,给出一种不规则时间序列距离度量算法。对异时间窗的子序列划分方法和不规则时间序列距离度量算法进行了实验,结果证明了二者的优越性。     

Measuring the Efficiency of the Intraday Forex Market with a Universal Data Compression Algorithm

Universal compression algorithms can detect recurring patterns in any type of temporal data—including financial data—for the purpose of compression. The universal algorithms actually find a model of the data that can be used for either compression or prediction. We present a universal Variable Order Markov (VOM) model and use it to test the weak form of the Efficient Market Hypothesis (EMH). The EMH is tested for 12 pairs of international intra-day currency exchange rates for one year series of 1, 5, 10, 15, 20, 25 and 30 min. Statistically significant compression is detected in all the time-series and the high frequency series are also predictable above random. However, the predictability of the model is not sufficient to generate a profitable trading strategy, thus, Forex market turns out to be efficient, at least most of the time.      

Financial forecasting using ANFIS networks with Quantum-behaved Particle Swarm Optimization

To be successful in financial market trading it is necessary to correctly predict future market trends. Most professional traders use technical analysis to forecast future market prices. In this paper, we present a new hybrid intelligent method to forecast financial time series, especially for the Foreign Exchange Market (FX). To emulate the way real traders make predictions, this method uses both historical market data and chart patterns to forecast market trends. First, wavelet full decomposition of time series analysis was used as an Adaptive Network-based Fuzzy Inference System (ANFIS) input data for forecasting future market prices. Also, Quantum-behaved Particle Swarm Optimization (QPSO) for tuning the ANFIS membership functions has been used. The second part of this paper proposes a novel hybrid Dynamic Time Warping (DTW)-Wavelet Transform (WT) method for automatic pattern extraction. The results indicate that the presented hybrid method is a very useful and effective one for financial price forecasting and financial pattern extraction.     

A hybrid procedure for stock price prediction by integrating self-organizing map and genetic programming

Stock price prediction is a very important financial topic, and is considered a challenging task and worthy of the considerable attention received from both researchers and practitioners. Stock price series have properties of high volatility, complexity, dynamics and turbulence, thus the implicit relationship between the stock price and predictors is quite dynamic. Hence, it is difficult to tackle the stock price prediction problems effectively by using only single soft computing technique. This study hybridizes a self-organizing map (SOM) neural network and genetic programming (GP) to develop an integrated procedure, namely, the SOM-GP procedure, in order to resolve problems inherent in stock price predictions. The SOM neural network is utilized to divide the sample data into several clusters, in such a manner that the objects within each cluster possess similar properties to each other, but differ from the objects in other clusters. The GP technique is applied to construct a mathematical prediction model that describes the functional relationship between technical indicators and the closing price of each cluster formed in the SOM neural network. The feasibility and effectiveness of the proposed hybrid SOM-GP prediction procedure are demonstrated through experiments aimed at predicting the finance and insurance sub-index of TAIEX (Taiwan stock exchange capitalization weighted stock index). Experimental results show that the proposed SOM-GP prediction procedure can be considered a feasible and effective tool for stock price predictions, as based on the overall prediction performance indices. Furthermore, it is found that the frequent and alternating rise and fall, as well as the range of daily closing prices during the period, significantly increase the difficulties of predicting.     

一种基于DTW聚类的水文时间序列相似性挖掘方法

水文时间序列相似性挖掘是水文时间序列挖掘的重要方面,对洪水预报、防洪调度等具有重要意义。针对水文数据的特点,提出了一种基于DTW聚类的水文时间序列相似性挖掘方法。该方法先对数据进行小波去噪、特征点分段以及语义划分,再基于DTW距离对划分后的子序列做层次聚类并符号化;然后根据符号序列间的编辑距离筛选候选集;最后通过序列间的DTW距离进行精确匹配,获取相似水文时间序列。以滁河六合站的日水位数据进行实验,结果表明,所提方法能够有效地缩小候选集,提高查找语义相似的水文时间序列的效率。     

Pattern discovery in data streams under the time warping distance

Subsequence matching is a basic problem in the field of data stream mining. In recent years, there has been significant research effort spent on efficiently finding subsequences similar to a query sequence. Another challenging issue in relation to subsequence matching is how we identify common local patterns when both sequences are evolving. This problem arises in trend detection, clustering, and outlier detection. Dynamic time warping (DTW) is often used for subsequence matching and is a powerful similarity measure. However, the straightforward method using DTW incurs a high computation cost for this problem. In this paper, we propose a one-pass algorithm, CrossMatch, that achieves the above goal. CrossMatch addresses two important challenges: (1) how can we identify common local patterns efficiently without any omission? (2) how can we find common local patterns in data stream processing? To tackle these challenges, CrossMatch incorporates three ideas: (1) a scoring function, which computes the DTW distance indirectly to reduce the computation cost, (2) a position matrix, which stores starting positions to keep track of common local patterns in a streaming fashion, and (3) a streaming algorithm, which identifies common local patterns efficiently and outputs them on the fly. We provide a theoretical analysis and prove that our algorithm does not sacrifice accuracy. Our experimental evaluation and case studies show that CrossMatch can incrementally discover common local patterns in data streams within constant time (per update) and space.     

Time series classification with feature covariance matrices

In this work, a novel approach utilizing feature covariance matrices is proposed for time series classification. In order to adapt the feature covariance matrices into time series classification problem, a feature vector is defined for each point in a time series. The feature vector comprises local and global information such as value, derivative, rank, deviation from the mean, the time index of the point and cumulative sum up to the point. Extracted feature vectors for the time instances are concatenated to construct feature matrices for the overlapping subsequences. Covariances of the feature matrices are used to describe the subsequences. Our main purpose in this work is to introduce and evaluate the feature covariance representation for time series classification. Therefore, in classification stage, firstly, 1-NN classifier is utilized. After showing the effectiveness of the representation with 1-NN classifier, the experiments are repeated with SVM classifier. The other novelty in this work is that a novel distance measure is introduced for time series by feature covariance matrix representation. Conducted experiments on UCR time series datasets show that the proposed method mostly outperforms the well-known methods such as DTW, shapelet transform and other state-of-the-art techniques.     

基于滑动平均与分段线性回归的时间序列相似性

针对时间序列相似性度量中欧氏距离对异常数据敏感以及DTW距离算法效率低的问题,提出基于滑动平均与分段线性回归的时间序列相似性方法。首先,使用初始可变滑动平均算法以及分段线性回归对原始时间序列进行数据变换,并将分段线性回归的参数(截距与距离)集作为时间序列的特征,以实现时间序列的特征提取和数据降维;然后,利用动态时间弯曲距离进行距离计算。该方法在时间序列相似性上与DTW算法的性能相近,但是在算法效率上几乎提高了96%。实验结果验证了该方法的有效性与准确性。     

Hierarchical clustering of time series data with parametric derivative dynamic time warping

Dynamic Time Warping (DTW) is a popular and efficient distance measure used in classification and clustering algorithms applied to time series data. By computing the DTW distance not on raw data but on the time series of the (first, discrete) derivative of the data, we obtain the so-called Derivative Dynamic Time Warping (DDTW) distance measure. DDTW, used alone, is usually inefficient, but there exist datasets on which DDTW gives good results, sometimes much better than DTW. To improve the performance of the two distance measures, we can combine them into a new single (parametric) distance function. The literature contains examples of the combining of DTW and DDTW in algorithms for supervised classification of time series data. In this paper, we demonstrate that combination of DTW and DDTW can also be applied in a method of time series clustering (unsupervised classification). In particular, we focus on a hierarchical clustering (with average linkage) of univariate (one-dimensional) time series data. We construct a new parametric distance function, combining DTW and DDTW, where a single real number parameter controls the contribution of each of the two measures to the total value of the combined distances. The parameter is tuned in the initial phase of the clustering algorithm. Using this technique in clustering methods requires a different approach (to address certain specific problems) than for supervised methods. In the clustering process we use three internal cluster validation measures (measures which do not use labels) and three external cluster validation measures (measures which do use clustering data labels). Internal measures are used to select an optimal value of the parameter of the algorithm, where external measures give information about the overall performance of the new method and enable comparison with other distance functions. Computational experiments are performed on a large real-world data base (UCR Time Series Classification Archive: 84 datasets) from a very broad range of fields, including medicine, finance, multimedia and engineering. The experimental results demonstrate the effectiveness of the proposed approach for hierarchical clustering of time series data. The method with the new parametric distance function outperforms DTW (and DDTW) on the data base used. The results are confirmed by graphical and statistical comparison.     

Predicting economic time series using a nonlinear deterministic technique

In this paper, a deterministic predictive technique is introduced, which is based on the embedding theorem by Takens and the recently developed wavelet networks. Several economic time series are tested by using this technique. As a result, the predicted values correspond quite well with the actual values. It shows that some economic time series are predictable by using a deterministic approach. Furthermore, the effects of using smoothing techniques (e.g., moving average) upon the prediction results are also investigated since there inevitably exists noise in almost all economic time series. Our numerical results show that smoothing like moving average can improve the prediction results for some of our tested time series, and for others predictions without smoothing are even better than with smoothing. This implies that wavelet network is capable of drawing the underlying dynamics directly from noisy economic time series.     

Exact indexing of dynamic time warping

The problem of indexing time series has attracted much interest. Most algorithms used to index time series utilize the Euclidean distance or some variation thereof. However, it has been forcefully shown that the Euclidean distance is a very brittle distance measure. Dynamic time warping (DTW) is a much more robust distance measure for time series, allowing similar shapes to match even if they are out of phase in the time axis. Because of this flexibility, DTW is widely used in science, medicine, industry and finance. Unfortunately, however, DTW does not obey the triangular inequality and thus has resisted attempts at exact indexing. Instead, many researchers have introduced approximate indexing techniques or abandoned the idea of indexing and concentrated on speeding up sequential searches. In this work, we introduce a novel technique for the exact indexing of DTW. We prove that our method guarantees no false dismissals and we demonstrate its vast superiority over all competing approaches in the largest and most comprehensive set of time series indexing experiments ever undertaken.     

基于短序列分组和拼接策略的子序列快速查询算法

子序列查询技术在金融、商业、医疗等领域均有重要应用,但因DTW（dynamic time warping）等相似性比对算法的时间复杂度较高,子序列长度对检索时间影响很大,限制了数据集上长子序列检索的效率。针对这一问题提出一种子序列快速查询算法。首先对数据集中特定长度下所有子序列进行分组并标记出代表性子序列;然后在查询时将查询序列切分成定长的小段序列,并用DTW算法确定与小段序列相似的代表子序列候选集;最后对候选集进行序列拼接,获取到查询结果序列。实验表明新算法效率较典型算法提高约10倍。     

风电机组齿轮箱的多变量时间序列故障预警

针对风电机组故障预警中，原始动态时间规整（DTW）算法无法有效度量风电机组多变量时间序列数据之间距离的问题，提出一种基于犹豫模糊集的动态时间规整（HFS-DTW）算法。该算法是原始DTW算法的一种扩展算法，可对单变量和多变量时间序列数据进行距离度量，且精度与速度较原始DTW算法更优。以子时间序列相似度距离为目标函数，使用帝国竞争算法（ICA）优化了HFS-DTW算法中的子序列长度和步距参数。算例研究表明与仅DTW算法和非参数最优的HFS-DTW算法相对比，参数最优的HFS-DTW可挖掘更多的多维特征点信息，输出的多维特征点相似序列具有更丰富细节；且基于所提算法可提前10天预警风电机组齿轮箱故障。     

Predicting the direction,maximum, minimum and closing prices of daily Bitcoin exchange rate using machine learning techniques

Bitcoin is the most accepted cryptocurrency in the world, which makes it attractive for investors and traders. However, the challenge in predicting the Bitcoin exchange rate is its high volatility. Therefore, the prediction of its behavior is of great importance for financial markets. In this way, recent studies have been carried out on what internal and/or external Bitcoin information is relevant to its prediction. The increased use of machine learning techniques to predict time series and the acceptance of cryptocurrencies as financial instruments motivated the present study to seek more accurate predictions for the Bitcoin exchange rate. In this way, in a first stage of the proposed methodology, different feature selection techniques were evaluated in order to obtain the most relevant attributes for the predictions. In the sequence, it was analyzed the behavior of Artificial Neural Networks (ANN), Support Vector Machines (SVM) and Ensemble algorithms (based on Recurrent Neural Networks and the k-Means clustering method) for price direction predictions. Likewise, the ANN and SVM were employed for regression of the maximum, minimum and closing prices of the Bitcoin. Moreover, the regression results were also used as inputs to try to improve the price direction predictions. The results showed that the selected attributes and the best machine learning model achieved an improvement of more than 10%, in accuracy, for the price direction predictions, with respect to the state-of-the-art papers, using the same period of information. In relation to the maximum, minimum and closing Bitcoin prices regressions, it was possible to obtain Mean Absolute Percentage Errors between 1% and 2%. Based on these results, it was possible to demonstrate the efficacy of the proposed methodology when compared to other studies.     

Speeding up dynamic time warping distance for sparse time series data

Dynamic time warping (DTW) distance has been effectively used in mining time series data in a multitude of domains. However, in its original formulation DTW is extremely inefficient in comparing long sparse time series, containing mostly zeros and some unevenly spaced nonzero observations. Original DTW distance does not take advantage of this sparsity, leading to redundant calculations and a prohibitively large computational cost for long time series. We derive a new time warping similarity measure (AWarp) for sparse time series that works on the run-length encoded representation of sparse time series. The complexity of AWarp is quadratic on the number of observations as opposed to the range of time of the time series. Therefore, AWarp can be several orders of magnitude faster than DTW on sparse time series. AWarp is exact for binary-valued time series and a close approximation of the original DTW distance for any-valued series. We discuss useful variants of AWarp: bounded (both upper and lower), constrained, and multidimensional. We show applications of AWarp to three data mining tasks including clustering, classification, and outlier detection, which are otherwise not feasible using classic DTW, while producing equivalent results. Potential areas of application include bot detection, human activity classification, search trend analysis, seismic analysis, and unusual review pattern mining.     

A two-stage architecture for stock price forecasting by integrating self-organizing map and support vector regression

Stock price prediction has attracted much attention from both practitioners and researchers. However, most studies in this area ignored the non-stationary nature of stock price series. That is, stock price series do not exhibit identical statistical properties at each point of time. As a result, the relationships between stock price series and their predictors are quite dynamic. It is challenging for any single artificial technique to effectively address this problematic characteristics in stock price series. One potential solution is to hybridize different artificial techniques. Towards this end, this study employs a two-stage architecture for better stock price prediction. Specifically, the self-organizing map (SOM) is first used to decompose the whole input space into regions where data points with similar statistical distributions are grouped together, so as to contain and capture the non-stationary property of financial series. After decomposing heterogeneous data points into several homogenous regions, support vector regression (SVR) is applied to forecast financial indices. The proposed technique is empirically tested using stock price series from seven major financial markets. The results show that the performance of stock price prediction can be significantly enhanced by using the two-stage architecture in comparison with a single SVR model.