关键词: 长记忆性, 分数布朗运动, 分数CIR模型, 间接推断估计

Abstract: Research shows that the interest rate series has long memory, and this paper uses fractional Brownian motion to replace the geometric Brownian motion in the classical CIR model, constructs a fractional CIR model, and simulates the path of the fractional CIR process through Euler discretization. Because the non-Markov property and the increment of fractional Brownian motion is not independent, the maximum likelihood estimation and Markov chain Monte Carlo method cannot estimate the parameters of fractional CIR model, so indirect inference estimation is introduced. Monte Carlo simulation results show that this method can effectively estimate the parameters of fractional CIR model. This paper makes an empirical analysis with indirect inference estimation based on SHIBOR, makes out-of-sample predictions, compares the simulation orbit of the classical CIR model and the fractional O-U process and the fractional CIR model with the real orbit, and concludes that the fractional CIR model is more suitable for the interest rate series with long memory. This paper only focuses on a parameter estimation method for fractional CIR model; in the future, we will continue to explore other methods and compare the effectiveness and robustness of these methods.

Key words: Long Memory, Fractional Brownian Motion, Fractional CIR Model, Indirect Inference Estimation