This paper provides closed-form expansions for the transition density and likelihood function of arbitrary multivariate diffusions. The expansions are based on a Hermite series, whose coefficients are calculated explicitly by exploiting the special structure afforded by the diffusion hypothesis. Because the transition function for most diffusion models is not known explicitly, the expansions of this paper can help make maximum-likelihood a practical estimation method for discretely sampled multivariate diffusions. Examples of interest in financial econometrics are included.
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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number
8956.
Length: Date of creation: May 2002 Date of revision: Publication status: published as Ait-Sahalia, Yacine. "Maximum Likelihood Estimation Of Discretely Sampled Diffusions: A Closed-Form Approximation Approach," Econometrica, 2002, v70(1,Jan), 223-262. Handle: RePEc:nbr:nberwo:8956
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Find related papers by JEL classification: C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
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