With the rapid development of the Chinese economy, people’s consumption structure has changed, and the investment in art and the tendency towards finance are increasing. The 13th Five Year Plan for the Development of National Cultural Relics clearly proposes to increase the protection of cultural relics and take multiple measures. Artworks have long been an essential investment target in the international capital market and belong to high value-added assets. In order to accurately predict the prices of calligraphy and painting artworks, this study proposes a machine learning based art price prediction method by combining ARCH model and Random Forest Regression (RFR) algorithm. Firstly, this study utilizes the ARCH model to capture the agglomeration effect of volatility in price time series, and reveals the inherent laws and volatility characteristics of price changes. Secondly, the Random Forest Regression (RFR) algorithm is introduced for price prediction. By constructing multiple decision trees and synthesizing their results, the non-linear and high-dimensional features of the data are effectively addressed. Research has shown that the RFR model exhibits high accuracy and stability in predicting art prices with multiple variables and complex relationships.