Periodic pattern analysis of non-uniformly sampled stock market data

Periodic patterns are mined individually on structural and weight aspects of an interaction in a dynamic network. However, these interactions possess a direction aspect too. Moreover, some applications require patterns on both aspects i) on direction and ii) on weight of directed interactions for a better understanding of their behaviour. To the authors' knowledge, no such work is available that mines both types of periodic patterns in a single run. To overcome this limitation, the authors propose a framework to mine periodic patterns on both the aspects. The framework first mines periodic patterns on direction, and then only the edges present in the patterns obtained are considered further for patterns on weight of directed interactions. Further, the patterns are being analysed to develop a better understanding of the dynamic network. To do so, a set of six parameters explained later in the text is proposed to study the behaviour of interactions at microscopic level. The framework is tested on real world and synthetic datasets. The results highlight its practical scalability and prove its efficiency.

Advanced satellite tracking technologies enable biologists to track animal movements at finer spatial and temporal scales. The resulting long-term movement data is very meaningful for understanding animal activities. Periodic pattern analysis can provide insightful approach to reveal animal activity patterns. However, individual GPS data is usually incomplete and in limited lifespan. In addition, individual periodic behaviors are inherently complicated with many uncertainties. In this paper, we address the problem of mining periodic patterns of animal movements by combining multiple individuals with similar periodicities. We formally define the problem of mining common periodicity and propose a novel periodicity measure. We introduce the information entropy in the proposed measure to detect common period. Data incompleteness, noises, and ambiguity of individual periodicity are considered in our method. Furthermore, we mine multiple common periodic patterns by grouping periodic segments w.r.t. the detected period, and provide a visualization method of common periodic patterns by designing a cyclical filled line chart. To assess effectiveness of our proposed method, we provide an experimental study using a real GPS dataset collected on 29 birds in Qinghai Lake, China.

Biological sequence data mining is hot spot in bioinformatics. A biological sequence can be regarded as a set of characters. Time series is similar to biological sequences in terms of both representation and mechanism. Therefore, in the article, biological sequences are represented with time series to obtain biological time sequence (BTS). Hybrid ensemble learning framework (SaPt-CNN-LSTM-AR-EA) for BTS is proposed. Single-sequence and multi-sequence models are respectively constructed with self-adaption pre-training one-dimensional convolutional recurrent neural network and autoregressive fractional integrated moving average fused evolutionary algorithm. In DNA sequence experiments with six viruses, SaPt-CNN-LSTM-AR-EA realized the good overall prediction performance and the prediction accuracy and correlation respectively reached 1.7073 and 0.9186. SaPt-CNN-LSTM-AR-EA was compared with other five benchmark models so as to verify its effectiveness and stability. SaPt-CNN-LSTM-AR-EA increased the average accuracy by about 30%. The framework proposed in this article is significant in biology, biomedicine, and computer science, and can be widely applied in sequence splicing, computational biology, bioinformation, and other fields.

Missing values are a common problem of time series such as sensor-generated data due to issues of data collection, transmission, and storage. To deal with this problem, various data imputation methods have been proposed. Among these methods, variants of recurrent neural networks (RNNs) have attracted a lot of attention as they provide a natural representation of temporal dynamics. Though such methods have been shown to achieve higher imputation accuracy, they mostly focus on the modeling of temporal dynamics from a short-term perspective while ignoring the long-term features such as trend and seasonal information embedded in time series data. In this paper, we investigate different paradigms of time series imputation methods to capture temporal dynamics from both long-term and short-term perspectives. In particular, we propose a new learning paradigm called MuSDRI which combines the time series decomposition method Seasonal Trend decomposition using Loess (STL) with RNNs. Specifically, STL is used to decompose long sequences of time series into trend, seasonal, and remainder components such that long-term dynamics can be revealed; RNNs are used to capture local patterns from the remainder component extracted by STL such that short-term dynamics can be refined. Moreover, MuSDRI is able to handle time series with multiple seasonal patterns by learning their contributions with respect to the imputation task. We evaluate the proposed imputation methods on three real-world datasets. Experimental results show that the imputation methods considering both the long-term and short-term dynamics achieve higher imputation accuracy, and among them MuSDRI in general achieves the best performance.

In this paper, we introduce topological entropy (TE) based on time series, which characterizes the total exponential complexity of a quantified system with a single number. Combined with multiscale theory, we propose geometric entropy (GE), aiming to examine the correlation among different time series. In order to detect the properties of TE and GE, we apply them to an original symbolic method utilized to measure time series irreversibility, namely horizontal visibility algorithm. On this basis, we propose a time series irreversibility measure, i.e., normalized index. Then, we employ TE and GE based on the horizontal visibility graph symbolic algorithm to simulated time series, which is generated by the logistic map with different parameters. Through the comparison of the results, we find out that different simulated data have the same variation tendency of TE, which means that TE is capable of reflecting the similarity among different time series. On the basic of these results, we further analyze the irreversibility of simulated data and also get some interesting findings. From the GE results comparison, we conclude that the GE method can distinguish different time series and expose their correlation efficiently. As a farther validation, we explore the effects of these methods on the analysis of different stock time series. Results show that they can reflect a large number of interrelationships, and successfully quantify the changes in the complexity of different stock market data.

Establishing relationships among patterns in stock market data

Missing data problem is ubiquitous in many real life situations. Information Technology researchers have explored and tried to address this problem in different settings. In this thesis, we undertake research to address missing data problem associated with order book information in stock markets. This is an in-depth and large-scale study with systematic and comprehensive framework to address missing data problem in the finance literature. Orders placed by traders and the corresponding order imbalance (OIB) is informative to predict future stock returns, however, stock exchange rules do not reveal price sensitive complete order book data for traders. Hence, return prediction using the revealed, incomplete trade book data (that contains only matched buy and sell orders and deletes the unmatched orders), does not let traders to completely exploit possible short term trading opportunities. Hence, this can be considered as a classical missing data problem for predicting future returns, by using the information content of order book. This thesis addresses the missing data problem by developing an integrated theoretical framework applied in stock market trading environment. We use relational Markov networks theory and build an empirically testable Algorithm for Imputed Complete Order Book (AICOB). The thesis contributes by developing a new theoretical advancement of information technology research relating to missing data problem and applying it to financial markets. First, the thesis presents the missing data problem as a Missing at Random (MAR) data and builds a systematic framework to estimate single as well as joint log likelihood functions. The thesis demonstrates that estimating by using incomplete records, improves the accuracy of the parameter estimates. Second, the thesis proposes a Relational Markov Network Model for estimation of the joint distribution function of orders, order characteristics and their interactions. Later, the Expectation Maximization Algorithm is proposed to address the missing data problem during the joint estimation procedure. All pooled regression results follow Fama and MacBeth (1973) and Generalized Methods of Moments (GMM) methods. These methods control the cross sectional and time series correlations between the observations and across the pooled stocks. The proposed novel methodology overcomes the estimation problem in the context of missing order book data. Third, the thesis develops an objective evaluation strategy for AICOB, based on efficiency, accuracy and adaptability dimensions. The thesis uses Australian stock market data, which provides not only trade book data but also historical order book data for cross validating the results. This unique setting allows validating the accuracy of AICOB methodology by comparing with complete order book data. The main contribution of the thesis is to show that AICOB based predictions match with the complete order book data. Whereas, trade book based predictions are quite inconsistent to the complete order book data. The AICOB based results are also consistent with the theoretical predictions proposed in finance literature that OIB predicts better as the firm size increases. The results show that large firms, with higher trading activity and more competition for order flows, report more significant OIB prediction of future returns. Trade Book based OIB estimates, which suffer from missing data problem, fail to predict future returns for stock portfolios. Hence, addressing the missing data problem is important before implementing OIB based trading strategies. Overall, the thesis finds that machine learning applications, similar to AICOB, can be helpful in implementing the trading strategies in financial markets. The imputation of missing data, through systematic procedures, based on theoretical distributional properties of the financial variables, can be informative for more accurate prediction of future returns. The thesis contributes towards establishing a common ground for cross-disciplinary research in Finance and Information Technology (IT) by applying the advances in IT research to solve research and corresponding implementation problems in finance. Further, the thesis contributes towards advancing the order imbalance literature by showing that missing data can play a critical role in the predictive ability of order imbalance.

In the present study, two methods, based on entropy optimization principle, to estimate missing (or forecasting) values in the given time series are suggested. In the first method successively replaces the missing values with the parameter value minimizing entropy of multivariate normal distribution representing MaxEnt approximation of the time series which arises by parameterization with a single parameter. In the second method, all missing values are parameterized with multiple parameters for each missing value and are estimated at a time. These methods are applied to biomedical data, missing values of which estimated via Kalman, and comparisons are given. These processes are realized by programs written in MATLAB.

Evaluating the distribution patterns of surface temperature data at Very Long Baseline Interferometry (VLBI)/Global Positioning System (GPS) co-located sites w.r.t. normality is one of the most important issues in modeling surface temperature data over long periods. Such evaluation can generate algorithms for filling in missing data at measurement sites. Some algorithms in the literature, such as those in the study of Cho et al. J Coast Res 65. doi: 10. 2112/SI65-321. 1, (2013), require trend, harmonic, and residual components to fill in the missing data. Trend and harmonic components estimate an optimal model that can be used to assist such algorithms when filling in missing data. The present study is based on the investigation of the normal distribution of the residuals of a surface temperature time series at VLBI/GPS co-located sites, after removing the trend and seasonal effects through harmonic components (inter-daily variations). This study uses surface temperature data collected from the VLBI/GPS co-located sites of two different regions in Europe: Matera (Italy) and Wettzell (Germany). The data collected from these sites form a time series, and time series analyses and conventional k-sigma outlier detection are implemented on these data sets before subjecting them to goodness of fit tests for normality. The residual components of the time series are acquired through a decomposing trend and signal effect from the original time series, assuming that the residuals of the time series are normally distributed. In testing the hypothesis that an observed frequency distribution fits the normal distribution, the following tests are used: Pearson χ2, Kolmogorov-Smirnov, Anderson-Darling, Shapiro-Wilk or Shapiro-Francia, D’Agostino, Jarque-Bera, skewness, and kurtosis tests. Some graphical methods are also applied to support the results of the goodness of fit tests for normality. Some proposals on the application of the goodness of fit tests are put forward, such as the evaluation of the estimation model for trend and harmonic components by considering the properties of the implemented goodness of fit tests. The results of this study can be used to determine the optimal model for estimating trend and harmonic components. The output of the present study is expected to have an important role in modeling surface temperature distributions at co-located VLBI/GPS sites for filling in missing data. Above all, meteorological data, such as temperature, pressure, and humidity, are of specific interest for modeling tropospheric delay, the main error factor in positioning in space geodesy, which in turn makes investigations on the distribution of meteorological data more attractive in geoscience.

Time series cluster kernel for learning similarities between multivariate time series with missing data

Adding the dimension of time to databases produces time series databases (TSDB) and introduces new aspects and difficulties to data mining and knowledge discovery. In this correspondence, we introduce a general methodology for knowledge discovery in TSDB. The process of knowledge discovery in TSDR includes cleaning and filtering of time series data, identifying the most important predicting attributes, and extracting a set of association rules that can be used to predict the time series behavior in the future. Our method is based on signal processing techniques and the information-theoretic fuzzy approach to knowledge discovery. The computational theory of perception (CTP) is used to reduce the set of extracted rules by fuzzification and aggregation. We demonstrate our approach on two types of time series: stock-market data and weather data.

Time series forecasting is the main objective in many life applications such as weather prediction, natural phenomena analysis, financial or economic analysis, etc. In real-life data analysis, missing data can be considered as a feature that the researcher faces because of human error, technical damage, or catastrophic natural phenomena, etc. When one or more observations are missing, it might be urgent to estimate the model as well as to estimate the missing values which lead to a better understanding of the data, and more accurate prediction. Different time series require different effective techniques to have better estimates for those missing values. Traditionally, the missing values are simply replaced by mean and mode imputation, deleted or handled using other methods, which are not convenient enough to address missing values, as those methods can cause bias. One of the most popular models used in estimating time-series data is autoregressive models. Autoregressive models forecast the future values in terms of the previous ones. The first-order autoregressive AR (1) model is the one which the current value is based on the immediately preceding value, then estimating parameters of AR (1) with missing observations is an urgent topic in time series analysis. Many approaches have been developed to address the estimation problems in time series such as ordinary least square (OLS), Yule Walker (YW). Therefore, a suggested method will be introduced to estimate the parameter of the model by using weighted least squares. The properties of the (WLS) estimator are investigated. Moreover, a comparison between those methods using AR (1) model with missing observations is conducted through a Monte Carlo simulation at various sample sizes and different proportions of missing observations, this comparison is conducted in terms of mean square error (MSE) and mean absolute error (MAE). The results of the simulation study state that (WLS) estimator can be considered as the preferable method of estimation. Also, time series real data with missing observations were estimated.

Multivariate time series (MTS) arise due to multisensor data collection in manufacturing. These data are complex in the sense that attributes have a varying scale, volitivity, continuity, and so on, and interattribute dependence also appears, which can mask the inherent information about system health status. Conventional machine learning-based process monitoring techniques are inefficient in predicting faults with MTS—their detection capability heavily relies on the input features, yet the classification power of MTS attributes is weakened by the complexity of multisensor data. Effective feature extraction is, therefore, necessary to facilitate fault prediction with MTS. This study proposes a fault prediction framework for MTS based on bag-of-words (BOW) feature extraction, statistical feature selection, and classification analysis. BOW models are for the first time adopted in a manufacturing context. Their superior capability in information preservation, local pattern recognition, and temporal effect accommodation has overcome the major limitations in current manufacturing practices with MTS. A comprehensive case study demonstrates the desirable performance of this framework on two MTS data sets from paper manufacturing and automotive manufacturing, as well as its superiority over conventional machine learning-based fault prediction. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Process monitoring in a multisensor environment has been a vital interest in manufacturing. The difficulty lies in the lack of detection power in many conventional techniques, e.g., control chart and logistic regression. A critical reason for such failure is the neglect of time effect in MTS—patterns associated with system faults tend to stretch a period, but a conventional control chart or classifier inspects each time stamp separately. Fault detection based on time series sequences is, therefore, essential. However, how to effectively extract features from MTS becomes a challenge. The framework proposed in this study adopts BOW models, specifically symbolic aggregate approximation (SAX), to extract features from MTS sequences, thus substantially improves the detection power against local patterns over time. Many manufacturing multisensor data are subject to such local patterns that point to the root cause of fault, so the proposed framework has a wide application in manufacturing.

The imputation of time series is one of the most important tasks in the homogenization process, the quality and precision of this process will directly influence the accuracy of the time series predictions. This paper proposes two simple algorithms, but quite powerful for univariate time series imputation process, which are based on the means of the nearest neighbors for the imputation of missing data. The first of them Local Average of Neighbors Neighbors (LANN) calculates the missing value from the average of the previous neighbor and the following neighbor to the missing value. The second Local Average of Neighbors Neighbors+ (LANN+), considers a threshold parameter, which allows to differentiate the calculation of the missing values according to the difference between the neighbors: for the differences less than or equal to the threshold the missing value is calculated through of LANN and for major differences the missing value is calculated from the average of the four closest neighbors, two previous and two subsequent to the missing value. Imputation results on different time series are promising.

Multivariate time series often contain missing values for reasons such as failures in data collection mechanisms. Since these missing values can complicate the analysis of time series data, imputation techniques are typically used to deal with this issue. However, the quality of the imputation directly affects the performance of downstream tasks. In this paper, we propose a selective imputation method that identifies a subset of timesteps with missing values to impute in a multivariate time series dataset. This selection, which will result in shorter and simpler time series, is based on both reducing the uncertainty of the imputations and representing the original time series as good as possible. In particular, the method uses multi-objective optimization techniques to select the optimal set of points, and in this selection process, we leverage the beneficial properties of the Multi-task Gaussian Process (MGP). The method is applied to different datasets to analyze the quality of the imputations and the performance obtained in downstream tasks, such as classification or anomaly detection. The results show that much shorter and simpler time series are able to maintain or even improve both the quality of the imputations and the performance of the downstream tasks.