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http://dx.doi.org/10.5351/KJAS.2018.31.6.801

Random effect models for simple diffusions  

Lee, Eun-Kyung (Department of Statistics, Ewha Womans University)
Lee, In Suk (Business School, Sogang University)
Lee, Yoon Dong (Business School, Sogang University)
Publication Information
The Korean Journal of Applied Statistics / v.31, no.6, 2018 , pp. 801-810 More about this Journal
Abstract
Diffusion is a random process used to model financial and physical phenomena. When we construct statistical models for repeatedly observed diffusion processes, the idea of random effects needs to be considered. In this research, we introduce random parameters for an Ornstein-Uhlenbeck diffusion model and geometric Brownian motion diffusion model. In order to apply the maximum likelihood estimation method, we tried to build likelihoods in closed-forms, by assuming appropriate distributions for random effects. We applied the random effect models to data consisting of Dow Jones Industrial Average indices recorded daily over 27 years from 1991 to 2017.
Keywords
diffusion; random effects; OU model; GBM model;
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