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.

In the context of the frequent occurrence of extreme events, measuring the tail dependence of financial time series is essential for maintaining the sustainable development of financial markets. In this paper, a multiscale quantile correlation coefficient (MQCC) is proposed to measure the tail dependence of financial time series. The new MQCC method consists of two parts: the multiscale analysis and the correlation analysis. In the multiscale analysis, the coarse graining approach is used to study the financial time series on multiple temporal scales. In the correlation analysis, the quantile correlation coefficient is applied to quantify the correlation strength of different data quantiles, especially regarding the difference and the symmetry of tails. One reason to adopt this method is that the conditional distribution of the explanatory variables can be characterized by the quantile regression, rather than simply by the conditional expectation analysis in the traditional regression. By applying the MQCC method in the financial markets of different regions, many interesting results can be obtained. It is worth noting that there are significant differences in tail dependence between different types of financial markets.

Clarifying the complex interaction between climate risks and the new energy industry chain is of key significance to advancing the energy transition and strengthening industrial chain robustness. This research pairwise-matches the climate physical risk and the climate transition risk with the entire range of the new energy industry chain segments, comprehensively examining the pairwise interactive relationships. By applying the MF-ADCCA series of methods, it was revealed that there are prevalent asymmetric cross-correlated multifractal characteristics between climate risks and the new energy industry. The long-term memory under the upward trend of the market is distinctly stronger than that under the downward trend. Given that this correlation can indirectly reflect market efficiency differences, this paper constructs the Hurst Volatility Sensitivity Index (HVI) and the Hurst Asymmetry Index (HAI) and further proposes the Unified Market Efficiency Index (UMEI). Its innovative advantage resides in the balanced integration of volatility efficiency and structural symmetry, in turn enabling a comprehensive assessment of the new energy market efficiency under climate risk perturbations. Static analysis reveals that the overall market efficiency of the new energy industry under the climate transition risk is generally higher than that under the climate physical risk, and the market efficiency of mature upstream and midstream new energy segments is significantly superior to that of the downstream. Dynamic evolution characteristics indicate that market efficiency has typical time-varying traits, the evolution of which is often driven by significant policies or extreme events. The climate transition risk tends to trigger aperiodic structural adjustments, while the climate physical risk mostly induces periodic efficiency fluctuations. This study furnishes solid evidence for the new energy market in coping with climate risks.