Using Particle Filtering for Hidden Markov models with application

Abstract

This research includes the study of hidden Markov models, which has witnessed wide interest by researchers, scholars and modern applications, as it is considered as a finite set of cases, in which the cases are related to a certain probability distribution. This research aims to estimate the parameters of the CIR and SABR models using Bayesian particle filtering methods. In this research, he reviewed hidden Markov models and methods of Bayes estimators, and one of the basic methods used in Bayes estimators is the particle filtering method. The practical side of this research dealt with two aspects, namely the experimental side and the applied side. In the experimental side, the particle filtering method was used. In the simulation experiment and for three levels of samples (small, medium and large) and different sizes, by selecting the lowest value to watch the CIR model at different times, in addition to determining the initial value, determining or creating the random error from a specific distribution, and calculating the estimates of the parameters of the CIR and SABR models depending on On the method of the greatest possibility in determining the parameters of the model (σ, β, α) in order to build or generate random processes with random variables that follow the normal distribution, and then draw these generated variables with graphics or shapes to obtain the best results, as well as the experimental side was applied The practical aspect applied to the financial statements of the Iraq Stock Exchange for different years. The study concluded that the particle filtering fluctuations for CIR and SABA estimation were always greater than zero, which is considered the basic condition for estimation.