Approximate Maximum Likelihood Estimation of Discretely Observed Diffusion Processes
Author : Rolf Poulsen
Publisher :
Page : 34 pages
File Size : 23,57 MB
Release : 1999
Category :
ISBN :
Author : Rolf Poulsen
Publisher :
Page : 34 pages
File Size : 23,57 MB
Release : 1999
Category :
ISBN :
Author :
Publisher :
Page : pages
File Size : 28,25 MB
Release : 1993
Category :
ISBN :
Author : 余定宏
Publisher :
Page : pages
File Size : 38,85 MB
Release : 2017
Category :
ISBN :
Author : Christiane Fuchs
Publisher : Springer Science & Business Media
Page : 439 pages
File Size : 22,72 MB
Release : 2013-01-18
Category : Mathematics
ISBN : 3642259693
Diffusion processes are a promising instrument for realistically modelling the time-continuous evolution of phenomena not only in the natural sciences but also in finance and economics. Their mathematical theory, however, is challenging, and hence diffusion modelling is often carried out incorrectly, and the according statistical inference is considered almost exclusively by theoreticians. This book explains both topics in an illustrative way which also addresses practitioners. It provides a complete overview of the current state of research and presents important, novel insights. The theory is demonstrated using real data applications.
Author : Phillip John Paine
Publisher :
Page : 344 pages
File Size : 28,41 MB
Release : 2015
Category : Diffusion processes
ISBN :
Author : Jaya P. N. Bishwal
Publisher : Springer
Page : 271 pages
File Size : 12,16 MB
Release : 2007-09-26
Category : Mathematics
ISBN : 3540744487
Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modeling complex phenomena. The subject has attracted researchers from several areas of mathematics. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods.
Author : Yacine Aït-Sahalia
Publisher :
Page : 64 pages
File Size : 21,73 MB
Release : 1998
Category : Diffusion processes
ISBN :
When a continuous-time diffusion is observed only at discrete dates, not necessarily close together, the likelihood function of the observations is in most cases not explicitly computable. Researchers have relied on simulations of sample paths in between the observations points, or numerical solutions of partial differential equations, to obtain estimates of the function to be maximized. By contrast, we construct a sequence of fully explicit functions which we show converge under very general conditions, including non-ergodicity, to the true (but unknown) likelihood function of the discretely-sampled diffusion. We document that the rate of convergence of the sequence is extremely fast for a number of examples relevant in finance. We then show that maximizing the sequence instead of the true function results in an estimator which converges to the true maximum-likelihood estimator and shares its asymptotic properties of consistency, asymptotic normality and efficiency. Applications to the valuation of derivative securities are also discussed.
Author : Peter C. B. Phillips
Publisher :
Page : 28 pages
File Size : 21,62 MB
Release : 2013
Category :
ISBN :
This paper motivates and introduces a two-stage method for 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 recently developed in Barndorff-Nielsen and Shephard (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 sample performance of the proposed method is compared with that of the approximate maximum likelihood method of Aiuml;t-Sahalia (2002).
Author : Aleksandar Mijatovic
Publisher :
Page : 0 pages
File Size : 32,36 MB
Release : 2009
Category :
ISBN :
This paper studies an approximation method for the log likelihood function of a non-linear diffusion process using the bridge of the diffusion. The main result (Theorem 1) shows that this approximation converges uniformly to the unknown likelihood function and can therefore be used efficiently with any algorithm for sampling from the law of the bridge. We also introduce an expected maximum likelihood (EML) algorithm for inferring the parameters of discretely observed diffusion processes. The approach is applicable to a subclass of non-linear SDEs with constant volatility and drift that is linear in the model parameters. In this setting globally optimal parameters are obtained in a single step by solving a square linear system whose dimension equals the number of parameters in the model. Simulation studies to test the EML algorithm show that it performs well when compared with algorithms based on the exact maximum likelihood as well as closed-form likelihood expansions.
Author : Mathieu Kessler
Publisher : CRC Press
Page : 507 pages
File Size : 41,6 MB
Release : 2012-05-17
Category : Mathematics
ISBN : 1439849765
The seventh volume in the SemStat series, Statistical Methods for Stochastic Differential Equations presents current research trends and recent developments in statistical methods for stochastic differential equations. Written to be accessible to both new students and seasoned researchers, each self-contained chapter starts with introductions to th