1. What contributions have the authors mentioned in the paper "Efficient importance sampling maximum likelihood estimation of stochastic differential equations" ?
This paper considers ML estimation of a diffusion process observed discretely.. The authors review the most efficient approaches in the literature, and point to some drawbacks.. The authors propose to approximate the loglikelihood using the EIS strategy ( Richard and Zhang, 1998 ), and detail its implementation for univariate homogeneous processes.
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2. What future works have the authors mentioned in the paper "Efficient importance sampling maximum likelihood estimation of stochastic differential equations" ?
The price to pay is in the form of a moderately higher computational burden, which do not preclude however the possibility to set up a Monte Carlo study to analyze the finite sample performance of the approximation strategy.. As benchmark cases the authors considered five stochastic processes commonly adopted in the financial literature to describe the evolution over time of the short term interest rate, and also used by Aı̈t-Sahalia ( 1999 ) to study the performance of his closed-form approximation approach.. The authors plan to explore these developments in future research.. Overall, the comparison with the alternative, state-of-the-art importance sampling strategy suggested by Durham and Gallant ( 2002 ) suggests that EIS seems to provide superior results in terms of loglikelihood approximation and of numerical error in parameter estimation.
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