As a typical complex system, the stock market has attracted the attention of scholars and investors to comprehensively understand its fractal characteristics and analyze its market efficiency. Firstly, this paper proposes an asymmetric, detrended fluctuation analysis based on overlapping sliding windows (OSW-A-MFDFA). It reduces the generation of fluctuation errors, and the calculation results are more robust and reliable. The advantage of the OSW-A-MFDFA is that it not only can reveal the multifractal characteristics of time series clearly, but also can further accurately analyze the asymmetry of fractal characteristics under different trends. Secondly, this paper focuses on the variation in the width difference and height difference of the multifractal spectrum under different trends. Finally, based on multifractality, this paper proposes a comprehensive indicator MED that can be used to measure market efficiency, which is characterized by traversing all fluctuation orders. The application revealed many interesting findings in style stock indices. Style stock indices have asymmetric multifractal characteristics, and there are significant differences in the fractal spectrum of different style assets. Moreover, the market efficiency of style stock indices is time-varying, which can be reasonably explained from the perspective of the adaptive market hypothesis.

Technological innovation, the financial market, and the real economy are mutually promoting and restricting. Considering the interference of market-noise information, this paper applies the wavelet-denoising method of the soft- and hard-threshold compromise functions to process the original information so as to eliminate the noise information, and combines multifractal detrended cross-correlation analysis with the sliding-window approach, focusing on the change in the Hurst index and the parameter change in the multifractal spectrum to explore the interaction in between. The research results show that there is a certain cross-correlation among technological-innovation, financial-market, and real-economy indices. Firstly, the cross-correlation among them has significant multifractal characteristics rather than single-fractal characteristics. Secondly, the fractal characteristics reveal the long memory of the interaction among the three indices. Thirdly, there are also obvious differences in the degree of local chaos and volatility of the interaction. Fourthly, the cross-correlation among technological-innovation, financial-market, and real-economy indices has significant multifractal characteristics rather than single-fractal characteristics. In comparison, the cross-correlation multifractal characteristics among technological innovation, the financial market, and the real economy are time-varying, and the cross-correlation multifractal characteristics between the technological-innovation index and the real-economy index are the most obvious.

This study aims to establish and refine a deep learning-based predictive model for power quality risk spillover trends, thereby addressing the challenges posed by the escalating diversity and adaptability of power systems in the evolution of the renewable energy industry. Initially, the study introduces the concept of power quality risk spillover, referring to the influence exerted by power quality issues in one region on other regions. This influence initiates a chain reaction, ultimately leading to a more widespread deterioration in power quality. Then, the advantages and applications of the deep learning model in power quality risk spillover trend prediction are expounded. During the model development process, we employed deep learning algorithms such as the multilayer perceptron and extended short-term memory network, tailored specifically to the unique characteristics of power quality data. To enhance the model's predictive accuracy and stability, we implemented optimization strategies encompassing data preprocessing, feature engineering, and model integration. Our experimental findings demonstrate that the optimized model exhibits remarkable precision and stability in anticipating power quality risk spillover trends, thereby offering robust support for risk management and ensuring the stable operation of power systems. This study provides a valuable exploration and practice for the application and development of a power quality risk spillover trend prediction model based on deep learning.