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In reality, time series subject to the internal/external influence are usually characterized by nonlinearity, uncertainty, and incompleteness. Therefore, how to model the features of time series in nondeterministic environments is still an open problem. In this article, a novel high-order intuitionistic fuzzy cognitive map (HIFCM) is proposed, where intuitionistic fuzzy set (IFS) is introduced into fuzzy cognitive maps with temporal high-order structure. By means of IFS, the ability of model for the representation of uncertainty can be effectively improved. In order to capture the fluctuation features of series data, variational mode decomposition is utilized to decompose time series into sequences of various frequencies, based on which fine feature structures on different scales can be obtained. Each concept of HIFCM corresponds to one decomposed sequence such that casual reasoning can be achieved among the obtained features in various frequencies of time series. All parameters are learned by the particle swarm optimization algorithm. Finally, the performance of the method is verified on the public datasets, and experimental results show the feasibility and effectiveness of the proposed method.

When applying artificial intelligence technology to quantitative trading, high noise and unpredictability of market environment are the first practical problems to be considered. Therefore, how to select the learning features of the market based on rapidly changing financial data is particularly important. In this paper, the real time financial data are first processed by K-line theory, which uses candlesticks as a generalization of price movements over a period of time, so this process can play the role of de-noising. Then, the candlesticks are decomposed into different subparts by mean of a specified spatio-temporal relationship, based on which cluster analysis of the subparts to get the learning features. Further, the learning features that are clustered by the above K-lines are put into the model, and the online adaptive control of the parameters in the unknown environment is realized by the deep reinforcement learning method, so as to realize the high frequency transaction strategy. In order to verify the performance of the model, the data on different financial derivatives transactions such as stocks, financial futures and commodity futures are used. The proposal approach is compared with other methods which are based on price, fuzzified price and K-lines for features learning. In order to verify the accuracy of the proposal approach, prediction-based methods such as recurrent neural network and fuzzy neural network are used for comparison. Experimental results show that the proposed method has higher robustness and prediction accuracy.