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A Two-Stage Realized Volatility Approach To Estimation Of Diffusion Processes With Discrete Data, Peter C. B. Phillips, Jun Yu
A Two-Stage Realized Volatility Approach To Estimation Of Diffusion Processes With Discrete Data, Peter C. B. Phillips, Jun Yu
Research Collection School Of Economics
This paper motivates and introduces a two-stage method of estimating diffusion processes based on discretely sampled observations. In the first stage we make use of the feasible central limit theory for realized volatility, as developed in [Jacod, J., 1994] and [Barndorff-Nielsen, O., Shephard, N., 2002], to provide a regression model for estimating the parameters in the diffusion function. In the second stage, the in-fill likelihood function is derived by means of the Girsanov theorem and then used to estimate the parameters in the drift function. Consistency and asymptotic distribution theory for these estimates are established in various contexts. The finite …
Maximum Likelihood And Gaussian Estimation Of Continuous Time Models In Finance, Peter C. B. Phillips, Jun Yu
Maximum Likelihood And Gaussian Estimation Of Continuous Time Models In Finance, Peter C. B. Phillips, Jun Yu
Research Collection School Of Economics
This paper overviews maximum likelihood and Gaussian methods of estimating continuous time models used in finance. Since the exact likelihood can be constructed only in special cases, much attention has been devoted to the development of methods designed to approximate the likelihood. These approaches range from crude Euler-type approximations and higher order stochastic Taylor series expansions to more complex polynomial-based expansions and infill approximations to the likelihood based on a continuous time data record. The methods are discussed, their properties are outlined and their relative finite sample performance compared in a simulation experiment with the nonlinear CIR diffusion model, which …