Estimation and Model Validation of Diffusion Processes
Lindström, Erik LU
(2003)
- Abstract
- Estimation and Model Validation of Diffusion Processes
Abstract
The main motivation for this thesis is the need for estimation and model
validation of diffusion processes, i.e. stochastic processes satisfying
a stochastic differential equation driven by Brownian motion. This class
of stochastic processes is a natural extension of ordinary differential
equations to dynamic, stochastic systems.
However Maximum Likelihood estimation of diffusion processes is in
general not feasible as the transition probability density in not
available in closed form. This problem is tackled in paper A, where an
approximative Maximum... (More) - Estimation and Model Validation of Diffusion Processes
Abstract
The main motivation for this thesis is the need for estimation and model
validation of diffusion processes, i.e. stochastic processes satisfying
a stochastic differential equation driven by Brownian motion. This class
of stochastic processes is a natural extension of ordinary differential
equations to dynamic, stochastic systems.
However Maximum Likelihood estimation of diffusion processes is in
general not feasible as the transition probability density in not
available in closed form. This problem is tackled in paper A, where an
approximative Maximum Likelihood estimator based on numerical solution
of the Fokker-Planck equation is presented.
Closely connected to estimation is the problem of model validation.
Models are usually validated by testing dependence and distributional
properties of the residuals. A numerically stable algorithm for
calculating independent and identically distributed Gaussian residuals
for diffusion processes is introduced in paper B.
Two other validation techniques, based on Gaussian approximations of the
system of stochastic differential equations, are described in paper C.
The approximation makes it possible to use filtering techniques to
calculate standardized residuals, which are tested for dependence using
lag dependent functions.
Finally, a technique is introduced for identification of potential model
deficiencies using the estimated diffusion term. The deficiencies are
investigated by non-parametric regression using e.g. states, input
signals or time as explanatory variables.
Keywords: Stochastic differential equations, Validation, Estimation,
Fokker-Planck equation, Lag Dependent Functions. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/753347
- author
- Lindström, Erik
LU
- supervisor
-
- Jan Holst LU
- organization
- publishing date
- 2003
- type
- Thesis
- publication status
- published
- subject
- language
- English
- LU publication?
- yes
- id
- 4633e48b-8e31-4abe-84b1-e4204ee3387a (old id 753347)
- date added to LUP
- 2016-04-04 13:12:03
- date last changed
- 2022-02-08 02:25:40
@misc{4633e48b-8e31-4abe-84b1-e4204ee3387a,
abstract = {{Estimation and Model Validation of Diffusion Processes<br/><br>
<br/><br>
Abstract<br/><br>
<br/><br>
The main motivation for this thesis is the need for estimation and model <br/><br>
validation of diffusion processes, i.e. stochastic processes satisfying <br/><br>
a stochastic differential equation driven by Brownian motion. This class <br/><br>
of stochastic processes is a natural extension of ordinary differential <br/><br>
equations to dynamic, stochastic systems.<br/><br>
<br/><br>
However Maximum Likelihood estimation of diffusion processes is in <br/><br>
general not feasible as the transition probability density in not <br/><br>
available in closed form. This problem is tackled in paper A, where an <br/><br>
approximative Maximum Likelihood estimator based on numerical solution <br/><br>
of the Fokker-Planck equation is presented.<br/><br>
<br/><br>
Closely connected to estimation is the problem of model validation. <br/><br>
Models are usually validated by testing dependence and distributional <br/><br>
properties of the residuals. A numerically stable algorithm for <br/><br>
calculating independent and identically distributed Gaussian residuals <br/><br>
for diffusion processes is introduced in paper B.<br/><br>
<br/><br>
Two other validation techniques, based on Gaussian approximations of the <br/><br>
system of stochastic differential equations, are described in paper C. <br/><br>
The approximation makes it possible to use filtering techniques to <br/><br>
calculate standardized residuals, which are tested for dependence using <br/><br>
lag dependent functions.<br/><br>
<br/><br>
Finally, a technique is introduced for identification of potential model <br/><br>
deficiencies using the estimated diffusion term. The deficiencies are <br/><br>
investigated by non-parametric regression using e.g. states, input <br/><br>
signals or time as explanatory variables.<br/><br>
<br/><br>
Keywords: Stochastic differential equations, Validation, Estimation, <br/><br>
Fokker-Planck equation, Lag Dependent Functions.}},
author = {{Lindström, Erik}},
language = {{eng}},
note = {{Licentiate Thesis}},
title = {{Estimation and Model Validation of Diffusion Processes}},
year = {{2003}},
}