Abstract: This paper puts forward a long memory stochastic conditional durations(LMSCD) model for ultra-high frequency(UHF) durations series,and designs a kind of spectrum likelihood estimation method based on chaos-tabu genetic algorithm.Through Monte Carlo simulation experiments,we prove the feasibility of estimation method.Thereafter,making use of the ultra high frequency data in Shanghai stock market,we construct three different LMSCD models,which are for trade durations LMSCD,price duradons LMSCD and volume durations LMSCD,respectively.We testify the existence of long memory in ultra-high frequency durations series of Chinese stock market.

Key words: Gong memory, LMSCD, chaos-tabu genetic algorithm, spectrum likelihood estimation