Abstract: The fluctuation of international crude oil price has an important impact on national economic development and social stability. Considering that the international crude oil price fluctuation structure is easily affected by external factors such as economic and trade, military and political events, firstly the nonhomogeneous hidden Markov model (NHMM) optimized by mutation hybrid particle swarm optimization algorithm is used to intelligently identify the various fluctuation state of Brent crude oil yields. Secondly, based on the identified fluctuation state, the fractionally integrated exponential GARCH model (NHMM-FIEGARCH-GED) combined with NHMM under the generalized error distribution is constructed to predict the crude oil volatility, and the prediction performance is evaluated by using the Model Confidence Set test method. The results show that NHMM-FIEGARCH-GED model has more accurate out-of-sample prediction ability. The crude oil market under the normal fluctuation shows the characteristics of long memory and is very sensitive to the impact of external information shocks, possessing the significant leverage effect; However, the crude oil market under the abnormal fluctuation shows anti-persistence and weak response to external shocks, and the leverage effect is not significant. The crude oil volatility has opposite long-range correlation under different fluctuation states, indicating that the series may have multifractal structure. Therefore, it is further discussed based on multifractal descended moving average method. The results show that the major influencing factor is the heavy-tailed probability distribution of series fluctuations, that is, the impacts of extremely profound external event shocks are the main driver of the multifractal characteristics of international crude oil fluctuations. It can provide new ideas for other scholars to study the volatility of energy or financial markets. At the same time, it can effectively guide relevant institutions, departments and investors to quickly formulate and implement reasonable response strategies in the context of sudden political events and world economic turmoil.

Key words: PSO algorithm; nonhomogeneous hidden Markov model; FIEGARCH model; multifractal characteristic