The Application Of PMCMC In Nonlinear And Non-gaussian State Space Models

In recent years, the state space models have been popularly applied in finance and engineer. However, the facts that the nonlinear and non-Gaussian of time series are common made the classical models under linear and Gaussian hypothesis be challenged. At present, the Kalman filter is the most popular Bayesian filtering method in state space models, but it must be Gaussian. In such situation, the particle filter without the limitation of linear and Gaussian performs better.The particle filter uses the Monte Carlo samples generated by sampling replacing the probability density function. Thanks to this character, it has been widely applied in object tracking and signal processing. Although the filtering problem has been solved, parameter estimate is still puzzling. MCMC is the most popular method for parameter estimate in nonlinear and non-Gaussian models at present, but it is difficult to deal with higher dimensionality and more complex patterns. This article introduced a novel Monte Carlo method called particle Markov chain Monte Carlo(PMCMC). It combines MCMC and SMC approaches for parameter estimate. Certainly, it also takes advantages of both strength of two components and extends the application boundaries.In this paper, we proposed a novel particle local Metropolis–Hastings(PLMH)sampler based on PMCMC algorithm. This method simplifies the sampling in other PMCMC methods and increases the acceptance probability in a MH update. The results prove that the PMCMC method can improved the algorithm and it is workable in research of term structure of interest rates.