The Sine Cosine Algorithm (SCA) is a population-based optimization algorithm introduced by Mirjalili in 2016, motivated by the trigonometric sine and cosine functions. After providing an overview of the SCA algorithm, we survey a number of SCA variants and applications that have appeared in the literature. We then present the results of a series of computational experiments to validate the performance of the SCA against similar algorithms.

Advances in Sine Cosine Algorithm: A comprehensive survey

Deep learning is well-known for extracting high-level abstract features from a large amount of raw data without relying on prior knowledge, which is potentially attractive in forecasting financial time series. Long short-term memory (LSTM) networks are deemed as state-of-the-art techniques in sequence learning, which are less commonly applied to financial time series predictions, yet inherently suitable for this domain. We propose a novel methodology of deep learning prediction, and based on this, construct a deep learning hybrid prediction model for stock markets—CEEMD-PCA-LSTM. In this model, complementary ensemble empirical mode decomposition (CEEMD), as a sequence smoothing and decomposition module, can decompose the fluctuations or trends of different scales of time series step by step, generating a series of intrinsic mode functions (IMFs) with different characteristic scales. Then, with retaining the most of information on raw data, PCA reduces dimension of the decomposed IMFs component, eliminating the redundant information and improving prediction response speed. After that, high-level abstract features are separately fed into LSTM networks to predict closing price of the next trading day for each component. Finally, synthesizing the predicted values of individual components is utilized to obtain a final predicted value. The empirical results of six representative stock indices from three types of markets indicate that our proposed model outperforms benchmark models in terms of predictive accuracy, i.e., lower test error and higher directional symmetry. Leveraging key research findings, we perform trading simulations to validate that the proposed model outperforms benchmark models in both absolute profitability performance and risk-adjusted profitability performance. Furthermore, model robustness test unveils the more stable robustness compared to benchmark models.

A novel deep learning framework: Prediction and analysis of financial time series using CEEMD and LSTM

Subsequence matching algorithms have many applications on time-series, such as detecting specific patterns on Electrocardiogram (ECG) and temperature data. To the best of author’s knowledge, there are relatively few research studies on time-series fuzzy subsequence matching yet, which better expresses the logic in real life compared to exact subsequence matching. In this paper, we firstly propose Naive Fuzzy Subsequence Matching based on Euclidean Distance (NFSM-ED) and Dynamic Time Warping (NFSM-DTW) for solving fuzzy subsequence matching problem on time-series, which can be treated as a basic benchmark of efficiency and accuracy. Then we extend it to a novel approach called UCR Fuzzy Subsequence Matching (UFSM) algorithm, which is inspired by UCRSuite. Finally, we develop it to Improved Fuzzy Subsequence Matching by kd-tree (IFSM-kd) and R*-tree (IFSM-R*), which can efficiently and effectively perform fuzzy subsequence matching on time-series. Additionally, the experiment results show that IFSM-R* and IFSM-kd are much faster than NFSM-ED, NFSM-DTW and UFSM with nearly no extra memory space required. Furthermore, IFSM-R* supports inserting and deleting indexes compared to IFSM-kd.

Fast fuzzy subsequence matching algorithms on time-series

Traditional time series methods can predict seasonal problems; however, they fail to deliver forecasts for problems with linguistic historical data. An alternative forecasting method, such as fuzzy time series, is required for addressing this type of problem. A limitation of existing fuzzy time series forecasting methods is that they lack persuasiveness in determining the universe of discourse and the lengths of intervals. Two membership function (MF) approaches, namely the cumulative probability distribution approach (CPDA) and minimize entropy principle approach (MEPA), were adopted in this study to solve the aforementioned problem. The CPDA and MEPA are objective and reasonable for enhancing the persuasiveness in determining the universe of discourse, the lengths of intervals, and the MFs of fuzzy time series. The concept of weighted fuzzy relations is also integrated into the aforementioned fuzzy time series forecasting procedures to improve the forecasting accuracy levels. Two data sets, namely the yearly data on enrollments at the University of Alabama and the monthly expenditure in information technology maintenance for an optoelectronics company, were adopted for experiments with different models. The results indicate that the proposed models have higher forecasting accuracy levels than other methods. The proposed models can be used to obtain forecasts for other time-related data sets. Moreover, discretization approaches can be adopted in the future to improve the fuzzification process.

Weighted-fuzzy-relations time series for forecasting information technology maintenance cost

A novel human learning optimization algorithm with Bayesian inference learning

Financial forecasting is an extremely challenging task given the complex, nonlinear nature of financial market systems. To overcome this challenge, we present an intelligent weighted fuzzy time series model for financial forecasting, which uses a sine-cosine adaptive human learning optimization (SCHLO) algorithm to search for the optimal parameters for forecasting. New weighted operators that consider frequency based chronological order and stock volume are analyzed, and SCHLO is integrated to determine the effective intervals and weighting factors. Furthermore, a novel short-term trend repair operation is developed to complement the final forecasting process. Finally, the proposed model is applied to four world major trading markets: the Dow Jones Index (DJI), the German Stock Index (DAX), the Japanese Stock Index (NIKKEI), and Taiwan Stock Index (TAIEX). Experimental results show that our model is consistently more accurate than the state-of-the-art baseline methods. The easy implementation and effective forecasting performance suggest our proposed model could be a favorable market application prospect.

An Intelligent Weighted Fuzzy Time Series Model Based on a Sine-Cosine Adaptive Human Learning Optimization Algorithm and Its Application to Financial Markets Forecasting

Given the potentially high impact of accurate financial market forecasting, there has been considerable research on time series analysis for financial markets. We present a new Intelligent Hybrid Weighted Fuzzy (IHWF) time series model to improve forecasting accuracy in financial markets, which are complex nonlinear time-sensitive systems, influenced by many factors. The IHWF model uniquely combines Empirical Mode Decomposition (EMD) with a novel weighted fuzzy time series method. The model is enhanced by an Adaptive Sine-Cosine Human Learning Optimization (ASCHLO) algorithm to help find optimal parameters that further improve forecasting performance. EMD is a time series processing technique to extract the possible modes of various kinds of institutional and individual investors and traders, embedded in a given time series. Subsequently, the proposed weighted fuzzy time series method with chronological order based frequency and Neighborhood Volatility Direction (NVD) is analyzed and integrated with ASCHLO to determine the effective universe discourse, intervals and weights. In order to evaluate the performance of proposed model, we evaluate actual trading data of Taiwan Capitalization Weighted Stock Index (TAIEX) from 1990 to 2004 and the findings are compared with other well-known forecasting models. The results show that the proposed method outperforms the listing models in terms of accuracy.

An Intelligent and Hybrid Weighted Fuzzy Time Series Model Based on Empirical Mode Decomposition for Financial Markets Forecasting

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An Intelligent Weighted Fuzzy Time Series Model Based on a Sine-Cosine Adaptive Human Learning Optimization Algorithm and Its Application to Financial Markets Forecasting

An Intelligent and Hybrid Weighted Fuzzy Time Series Model Based on Empirical Mode Decomposition for Financial Markets Forecasting