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Closed-Form Likelihood Expansions for Multivariate Time-Inhomogeneous Diffusions

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  • Seungmoon Choi

    (School of Economics, University of Adelaide)

Abstract

The aim of this paper is to find approximate log-transition density functions for multivariate time-inhomogeneous diffusions in closed form. There are many empirical evidences that the underlying data generating processes for many economic variables might change over time. One possible way to explain the time-dependent behavior of state variables is to model the drift or volatility terms as functions of time t as well as state variables. Closed-form likelihood expansions for multivariate time-homogeneous diffusions have been obtained by Ait-Sahalia (2008). This research is built on his work and extends his results to time-inhomogeneous cases. Simulation study reveals that our method yields a very accurate approximate likelihood function that can be a good candidate when the true likelihood function is unavailable.

Suggested Citation

  • Seungmoon Choi, 2010. "Closed-Form Likelihood Expansions for Multivariate Time-Inhomogeneous Diffusions," School of Economics and Public Policy Working Papers 2010-11, University of Adelaide, School of Economics and Public Policy.
    • Handle: RePEc:adl:wpaper:2010-11
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    File URL: https://media.adelaide.edu.au/economics/papers/doc/wp2010-11.pdf
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    Cited by:

    1. Li, Chenxu & Chen, Dachuan, 2016. "Estimating jump–diffusions using closed-form likelihood expansions," Journal of Econometrics, Elsevier, vol. 195(1), pages 51-70.
    2. Choi, Seungmoon, 2015. "Explicit form of approximate transition probability density functions of diffusion processes," Journal of Econometrics, Elsevier, vol. 187(1), pages 57-73.
    3. Bu, Ruijun & Cheng, Jie & Hadri, Kaddour, 2016. "Reducible diffusions with time-varying transformations with application to short-term interest rates," Economic Modelling, Elsevier, vol. 52(PA), pages 266-277.

    More about this item

    Keywords

    likelihood function; multivariate time-inhomogeneous diffusion; reducible diffusions; irreducible diffusions;
    All these keywords.

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