CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST 2013, 29(4) 392-404 DOI:      ISSN: 1001-4268 CN: 31-1256

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Local Linear Estimations of Time-Varying Parameters for Time-Inhomogeneous Diffusion Models

Wang Jixia, Xiao Qingxian

Business School, University of Shanghai for Science and Technology

Abstract��

This paper studies the local linear
estimations of the time-varying parameters for time-inhomogeneous
diffusion models. Based on discretely observed sample of
time-inhomogeneous diffusion models, the local linear estimations of
the drift parameters are proposed and their standard errors are
discussed. Considering the volatility parameter being positive, we
obtain the kernel weighted estimation of the diffusion parameter by
using locally log-linear fitting, and discuss asymptotic bias,
asymptotic variance and asymptotic normal distribution of volatility
function. It is shown that the local estimations proposed perform
well through simulation studies.

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