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# Estimation for Persistence Matrix in Multivariate Diffusion Processes

Statistics Seminar2018-06

Topic:Estimation for Persistence Matrix in Multivariate Diffusion Processes

Speaker:Xiaohu Wang, Chinese University of Hong Kong

Time:Thursday, May 17, 14:00-15:00

Place:Room 217, Guanghua Building 2

Abstract:

This paper cares about the estimation of the parameter matrix A in an m-variate linear diffusion process of dX(t)=(AX(t)+b)dt+Σ^{1/2}dW(t). One estimator commonly used in the literature takes the form of Ah=log(F)=-∑_{j=1}^{∞}(I-F)^{j}/j, where F=exp{Ah} could be easily estimated from discrete observations of the process X(t) and h is the length of sampling interval. Although popular, this estimator Ah suffers from two major limitations. First, an extra condition has to be imposed on the estimate of F in order to make the infinite summation convergent. This condition is quite restrictive for many realistic cases. Second, the infinite summation needs to be truncated in order to get an estimate in practice, about which no general guideline has been provided in the literature. This paper proposes an alternative estimator, denoted as A^{?}, to overcomes these two limitations; namely, the proposed estimator involves summation of finite terms only and works well without the extra condition imposed on F. Moreover, the proposed estimator can be further simplified by utilizing the information on the rank of A, which is often suggested by economic theories in co-integrated systems. A general relationship between A^{?}-A and the centered estimator of F is derived in the paper so that the large sample theory of A^{?}-A can be obtained directly from that of the centered estimator of F. We illustrate the use of this relationship by developing the limiting distributions of A^{?}-A for various cases where the process X(t) is a stationary, a pure unit root, or a partially nonstationary process, respectively. Simulations and empirical studies are conducted to illustrate the advantages of the proposed estimator. Although proposed focusing on linear diffusion processes, the estimator is also applicable to diffusion processes with flexible diffusion functions.

Introduction: Dr. Wang Xiaohu is an assistant professor in economics at the Chinese University of Hong Kong. His primary research interests are in econometric theory and financial econometrics. In particular, his research focuses on non-stationary discrete time series and continuous diffusion processes.

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