Abstract:The consumer price index plays an important role in the national macroeconomic analysis, and it is even more important in CPI's modeling prediction. By application of ARCH models under different distributions, a mathematical modeling is made of the consumer price indices from 1990 to 2013 and a contrastive analysis is also made of its ARCH models under different distributions. ARCH models are respectively established under normal distribution, T-distribution and generalized error distribution, finding that the ARCH model has different forecasting effect under different distributions with the GARCH models established under the generalized error distribution having the most accurate predictive power