Efficient Estimation for Ergodic Diffusions Sampled at High Frequency
CREATES Research Paper No. 2007-46
34 Pages Posted: 24 Jun 2008
Date Written: December 22, 2007
Abstract
A general theory of efficient estimation for ergodic diffusions sampled at high frequency is presented. High frequency sampling is now possible in many applications, in particular in finance. The theory is formulated in term of approximate martingale estimating functions and covers a large class of estimators including most of the previously proposed estimators for diffusion processes, for instance GMM-estimators and the maximum likelihood estimator. Simple conditions are given that ensure rate optimality, where estimators of parameters in the diffusion coefficient converge faster than estimators of parameters in the drift coefficient, and for efficiency. The conditions turn out to be equal to those implying small delta-optimality in the sense of Jacobsen and thus gives an interpretation of this concept in terms of classical statistical concepts. Optimal martingale estimating functions in the sense of Godambe and Heyde are shown to be give rate optimal and efficient estimators under weak conditions.
Keywords: Approximate martingale estimating functions, discrete time observation of a diffusion, efficiency, Euler approximation, generalized method of moments, optimal estimating function, optimal rate, small delta-optimality
JEL Classification: C22, C32
Suggested Citation: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
Nonparametric Pricing of Interest Rate Derivative Securities
-
Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes
-
Maximum-Likelihood Estimation of Discretely Sampled Diffusions: A Closed-Form Approach
-
Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-Form Approach
-
Is the Short Rate Drift Actually Nonlinear?
By David A. Chapman and Neil D. Pearson
-
Nonparametric Density Estimation and Tests of Continuous Time Interest Rate Models
-
Maximum Likelihood Estimation of Generalized Ito Processes with Discretely Sampled Data
By Andrew W. Lo
-
Maximum Likelihood Estimation of Generalized Ito Processes with Discretely Sampled Data
By Andrew W. Lo
-
Closed-Form Likelihood Expansions for Multivariate Diffusions