Research on Bayesian Estimation Method for Long-Memory Time Series Model Under Structural Mutations

Abstract

Long-memory time series widely exists in macroeconomics, financial volatility and meteorological monitoring data. Traditional long-memory models often ignore structural mutations in time series, which leads to spurious long-memory phenomena and biased parameter estimation results. To solve this problem, this paper constructs a long-memory ARFIMA model with structural break points, and proposes a complete Bayesian estimation framework based on Markov Chain Monte Carlo (MCMC) algorithm. This study introduces a latent mutation state variable to identify unknown structural break positions, derives the posterior distribution of all model parameters, and adopts Gibbs sampling and Metropolis-Hastings hybrid algorithm to realize parameter posterior sampling. Based on Monte Carlo simulation experiments and empirical analysis of S&P 500 index realized volatility data, the results show that the proposed Bayesian estimation method can accurately identify structural break points of time series, effectively eliminate the interference of spurious long memory caused by structural mutations, and has smaller parameter estimation bias and higher robustness than traditional maximum likelihood estimation and non-Bayesian long-memory modeling methods. This method provides an effective modeling and parameter estimation scheme for long-memory time series with structural mutations.