مقدرات بيز لبعض نماذج ماركوف المخفية مع التطبيق

Rp- Bayesian Estimation for some Hidden Markov Models with Application .pdf

Hidden Markov models have witnessed wide interest by researchers, scholars and modern applications, as they are considered a finite set of cases, in which the cases are related to a specific probability distribution.
In order to include the financial aspect with discreet statistical models, and for the importance of this aspect in our lives, especially in the Iraq Stock Exchange, and for the absence of previous studies that dealt with the subject. The researcher decided in this aspect to solve the problem that lies in strengthening the financial aspect, through the possibility of applying hidden models such as CIR and SABR using MCMC, particle filtering and Auxiliary Particle filtering based on real data to estimate parameters.
The aim of this thesis is to estimate the parameters of hidden Markov models using Bayes estimators.
In this thesis, the researcher reviewed three chapters, the first included the introduction, the aim of the study, the problem of the study, and previous studies.
The second, represented by the theoretical aspect, included the most important types of hidden Markov models, methods of Bayes estimators, particle filtering, and Auxiliary particle filtering.
As for the third, which represents the main aspect in this thesis, it is the practical side, which consists of two aspects, the experimental side and the applied side, as the MCMC method was used or employed in the simulation experiment using the program (R 4.2.0) and for three levels of samples (small, medium and large). With different sizes, estimates for the parameters of the CIR and SABR models were calculated using particle filtering and auxiliary particle filtering, and then drawing the generated variables with graphs or shapes to obtain the best results, as well as the experimental side. The practical side was applied to the data. Financial Stock Market (ISX 86) for the period (2017-2019).
Through the study, several conclusions were reached, the most important of which is that particle filtering and auxiliary particle filtering were used to estimate the parameters of the CIR and SABR models, where it was found that the fluctuations in them always remained greater than zero, which is considered the basic condition for estimation. They are the best in estimation, and a number of recommendations were proposed, the most important of which is the need to use the two models for the process of estimating the sale of shares in the Iraq Stock Exchange.