This paper aims to further investigate the impact of economic growth on the demand for financial derivatives, provide effective support to financial market participants and investors, and promote the stable development of financial markets. Firstly, time series analysis models, including autoregressive, mixed autoregressive, and moving average regression, are established by considering various factors in the financial market. Secondly, the basic characteristics of financial derivatives are thoroughly analyzed, and relevant variables are selected for explanation. Finally, the paper elucidates the fundamental functions of financial derivatives and their role in economic growth. The empirical results show that the correlation coefficient between non-financial institution derivatives and enterprise value is 0.2049, and the impact of enterprise economic growth on derivatives demand is 0.0003. Through time series analysis, the study reveals the impact mechanisms of economic cycles, business fluctuations, and other factors on the financial derivatives market, providing effective support for investors and participants.