The dual-carbon strategy is a basic national policy to ensure high-quality and sustainable development of China’s economy. Scientific understanding of carbon price fluctuations aids in mitigating investment risks, fostering a steady development of the carbon market, and enhancing the domestic carbon market’s pricing competence in the global market. Notably, the carbon trading prices in China exhibit significant volatility and periodic variations, underscoring the imperative to enhance a unified carbon market nationwide. This article selects Shenzhen’s monthly carbon emissions trading price data from August 2013 to February 2023 to represent the national carbon market price. Based on the analysis of massive data, multivariate analysis methods such as H-P filtering method and ARCH clustering model were used to study the fluctuation patterns and cyclical characteristics of Shenzhen’s carbon emissions trading prices. The results show that: The domestic carbon price has the remarkable feature of “falling in fluctuation”, showing four complete cycles, with each cycle time range of 10-26 months; The peak and valley values show a downward trend of varying degrees, with the peak and valley values changing from positive to negative, and the cycle types show a steep downward trend; The carbon price yield series has ARCH effect. The research results reveal the basic laws of my country’s carbon price fluctuations and provide theoretical basis and data support for improving the global pricing capability of the domestic carbon market.