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The prediction of time series in multi-steps is of significance in reality. However, considering the uncertainty and high noise existing in time series, the long-term forecasting is still an open problem. By means of granular computing, in this article, a novel spatial–temporal fuzzy information granule (STFIG) model is proposed to achieve the multi-step forecasting of time series. From the perspective of time dimension, by using unequal division method, time series is converted into generalized time-varying fuzzy information granules, where the trend information and dispersion degree of sequence data can be quantitatively described. Moreover, in terms of spatial dimension, the fluctuation information of time series is also calculated and involved into information granules, which can further enhance the semantic representation of sequential data. In order to improve the ability of dealing with uncertainties and fuzziness in time series, the interval type-2 fuzzy set is applied in the granules model. By using synthetic data and real-life time series, experiments are carried out to verify the effectiveness of the proposed scheme, where abundant semantic information and better long-term predictive performance can be obtained. [ABSTRACT FROM AUTHOR]

High noise and strong volatility are the typical characteristics of financial time series. Combined with pseudo-randomness, nonsteady and self-similarity exhibiting in different time scales, it is a challenging issue for the pattern analysis of financial time series. Different from the existing works, in this paper, financial time series are converted into granular complex networks, based on which the structure and dynamics of network models are revealed. By using variable-length division, an extended polar fuzzy information granule (FIGs) method is used to construct granular complex networks from financial time series. Considering the temporal characteristics of sequential data, static networks and temporal networks are studied, respectively. As to the static network model, some features of topological structures of granular complex networks, such as distribution, clustering and betweenness centrality are discussed. Besides, by using the Markov chain model, the transfer processes among different granules are investigated, where the fluctuation pattern of data in the coming step can be evaluated from the transfer probability of two consecutive granules. Shanghai composite index and foreign exchange data as two examples in real life are applied to carry out the related discussion. [ABSTRACT FROM AUTHOR]

The volatility features of financial data would considerably change in different periods, that is one of the main factors affecting the applications of machine learning in quantitative trading. Therefore, to effectively distinguish fluctuation patterns of financial markets can provide meaningful information for the trading decision. In this article, a novel intelligent trading system based on deep fuzzy self-organizing map (DFSOM) companied with GRU networks is proposed, where DFSOM is utilized for the clustering of financial data to acquire multiple fluctuation patterns in an unsupervised way. Firstly, in order to capture the trend features and evade the effect of high noises in financial data, the images of extended candlestick charts instead of raw data are processed and the obtained features are applied for the following unsupervised learning, where candlestick charts are produced with both price and volume information. Secondly, by using the candlestick features, a two-layer deep fuzzy self-organizing map is constructed to carry out the clustering, where two-layer models carry out the clustering in multiple time scales to improve the processing of time-dependent information. Thirdly, GRU networks are used to implement the prediction task, based on which an intelligent trading model is constructed. The feasibility and effectiveness of the proposed method are verified by using various real financial datasets. • A novel two-layer structure of deep fuzzy self-organizing map is proposed. • Image-based analysis and intelligent learning for financial time series. • Multiple features fused by using the extended candlestick charts. [ABSTRACT FROM AUTHOR]

As to the long-term time series forecasting, it is more challenging and practical to obtain the trend information and fluctuation range of sequence data than single-step prediction values. In this article, by means of fuzzy information granules (FIGs) and recurrent fuzzy neural networks, a novel long-term prediction model for time series is proposed. Based on a variable-length division method, generalized zonary time-variant fuzzy information granule (GZT-FIG) is constructed, which can express the variation trend, fluctuation range and dispersion degree of sequence data. Furthermore, in order to improve the anti-noise ability and memory ability, type-2 fuzzy sets and long short-term memory mechanism are introduced into the prediction scheme, based on which a self-evolving interval type-2 LSTM fuzzy neural network (eIT2FNN-LSTM) is provided. Compared with the existing works related to fuzzy-neural models, the involvement of long short-term memory mechanism effectively improves the memory ability to achieve the long-term prediction. In order to verify the validation and effectiveness of the proposed scheme, several groups of experiments, including synthetic sequences and real-life time series, are carried out. The experimental results reveal the better predictive performance and rich semantic information. • A method of unequal dividing the time series based on stepwise linear division is proposed. • A generalized time-variant fuzzy information granule can reflect the trend and the range of data changing. • A distance algorithm to measure the similarity and characterize the correlation degree between two GZT-FIGs. [ABSTRACT FROM AUTHOR]

Most of time series deriving from complex systems in real life is non-stationary, where the data distribution would be influenced by various internal/external factors such that the contexts are persistently changing. Therefore, the concept drift detection of time series has practical significance. In this paper, a novel method called online entropy-based time domain feature extraction (ETFE) for concept drift detection is proposed. Firstly, the empirical mode decomposition based on extrema symmetric extension is used to decompose time series, where features in various time scales can be adaptively extracted. Meanwhile, the end point effect caused by traditional empirical mode decomposition can be avoided. Secondly, by using the entropy calculation, the time-domain features are coarse-grained to quantify the structure and complexity of the time series, among which six kinds of entropy are used for discussion. Finally, a statistical process control method based on generalized likelihood ratio is used to monitor the change of the entropy, which can effectively track the mean and amplitude of the time series. Therefore, the early alarm of concept drift can be given. Synthetic data sets and neonatal electroencephalogram (EEG) recordings with seizures annotations data sets are used to validate the effectiveness and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]