Chaos is a seemingly irregular movement, which refers to a deterministic nonlinear system. Without any additional random factors, random-like behavior (inherent randomness) can occur. With the popularization of computer technology and the emergence of new interdisciplinary subjects, the research of chaos science has developed rapidly with the rapid development of modern science and technology. In the modern material world, from the universe to elementary particles, chaos theory is everywhere. These basic substances are also governed by chaos theory. Chaos appears in nonlinear dynamic system because objects always follow the trajectory and state of the previous stage in its evolution process, which leads to unpredictable, uncertain and irregular effects. The causes of chaos reflect three basic characteristics of chaos, namely, inherent randomness, initial value sensitivity and irregular order. The so-called "a tiny difference, a thousand miles lost" is the best annotation to chaos. Specifically, chaos, especially an object or system that is easy to change, is a very simple movement in the initial state, but after certain rules are constantly changing, its consequences are often unexpected, which is the chaotic state. However, this chaotic state is very different from ordinary and unorganized chaotic state. After a long and complete analysis, we can sort out one or several specific laws. Although chaos was originally used to explain natural phenomena, it is particularly common in the humanities and social fields, because there are many connections and constraints between things in the humanities and social fields. 1985 After chaos was first discovered in the economic system, with the development of chaos theory and computer technology, more and more economists began to use chaos theory as a tool to study and discuss social economy, including finance, currency and financial issues, especially the research on stock price index in the securities market. Power spectrum and correlation dimension are important methods to distinguish chaotic features qualitatively and quantitatively. On the one hand, on the basis of previous studies, this paper introduces several stock index data preprocessing methods widely used in literature, such as daily yield method and logarithmic linear trend elimination method, and introduces the min-max standardization method commonly used in statistics. Qualitative and quantitative methods are used to verify the chaos of data samples, and the influence of these data preprocessing methods on the chaotic judgment of stock market is analyzed. On the other hand, based on the same data sample, this paper analyzes and compares the influence of two time delay algorithms: C-C algorithm and mutual information method on chaos judgment in stock market. This paper is a new exploration on the study of chaos judgment in the stock market. This paper focuses on the analysis of data preprocessing methods, and the research and technical realization of the two most commonly used time delay algorithms. At the end of the article, how to reduce the degree of chaos and the autocorrelation of stock index data and restore the fluctuation of stock index to become a barometer of real social economy will become an important aspect of chaos research in the stock market in the future. This paper is of positive significance to the pretreatment of chaotic time series of stock index and the analysis and research of the application of chaos science in stock market, and can provide some reference for the application research of chaos theory in stock market and other complex economic systems in the future.