On estimating the diffusion coefficient

Dohnal, Gejza

doi:10.2307/3214063

Cited by 73 publications

(42 citation statements)

References 2 publications

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“…Motivation for analyzing the method described in Section 3 is in the fact that it can provide us with useful estimators of the parameters. It is well known that in a such way obtained AMLE of diffusion coefficient parameter σ is consistent and asymptotically normally distributed over fixed observational time interval [0, T ] when δ n,T → 0 (see [10] in case where all drift parameters are known, and see [14] in general cases). The same holds in ergodic diffusion cases when T → +∞ in a way that δ n,T = T /n → 0 for appropriate equidistant sampling (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Estimating a class of diffusions from discrete observations via approximate maximum likelihood method

Huzak

2017

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An approximate maximum likelihood method of estimation of diffusion parameters (ϑ, σ) based on discrete observations of a diffusion X along fixed time-interval [0, T ] and Euler approximation of integrals is analyzed. We assume that X satisfies a SDE of form dXt = µ(Xt, ϑ) dt + √ σb(Xt) dWt, with non-random initial condition. SDE is nonlinear in ϑ generally. Based on assumption that maximum likelihood estimatorθ T of the drift parameter based on continuous observation of a path over [0, T ] exists we prove that measurable estimator (θ n,T ,σ n,T ) of the parameters obtained from discrete observations of X along [0, T ] by maximization of the approximate log-likelihood function exists,σ n,T being consistent and asymptotically normal, andθ n,T −θ T tends to zero with rate √ δ n,T in probability when δ n,T = max 0≤i

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Section: Introductionmentioning

confidence: 99%

Estimating a class of diffusions from discrete observations via approximate maximum likelihood method

Huzak

2017

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“…In the limit it corresponds to continuous-time observations where the diffusion function is known exactly, see Section 3. Dohnal (1987) and Genon-Catalot & Jacod (1994), among others, have studied parameter estimation via contrasts, local asymptotic (mixed) normality properties, and optimal random sampling times. Several authors study the asymptotic behaviour as ½ ¼ of non-parametric esti-mators as well: the estimators are based on kernel methods (Florens-Zmirou, 1993;Jacod, 2000) or wavelet methods (Genon-Catalot et al, 1992;Hoffmann, 1999;Honoré, 1997); see also the references in those papers.…”

Section: Introductionmentioning

confidence: 99%

Parametric Inference for Diffusion Processes Observed at Discrete Points in Time: a Survey

Sørensen¹

2004

Int Statistical Rev

159

108

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This paper is a survey of estimation techniques for stationary and ergodic diffusion processes observed at discrete points in time. The reader is introduced to the following techniques: (i) estimating functions with special emphasis on martingale estimating functions and so-called simple estimating functions; (ii) analytical and numerical approximations of the likelihood function which can in principle be made arbitrarily accurate; (iii) Bayesian analysis and MCMC methods; and (iv) indirect inference and EMM which both introduce auxiliary (but wrong) models and correct for the implied bias by simulation.

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“…Recall that when (X i n ) i=0,...,n is observed, Dohnal [2] shows that the statistical problem of estimating σ satisfies the LAMN property. More precisely, his result implies that an asymptotically efficient estimator, σ eff n , of σ 0 must satisfy…”

Section: Introductionmentioning

confidence: 99%

Discrete sampling of an integrated diffusion process and parameter estimation of the diffusion coefficient

Gloter

2000

ESAIM: PS

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Abstract. Let (Xt) be a diffusion on the interval (l, r) and ∆n a sequence of positive numbers tending to zero. We define Ji as the integral between i∆n and (i + 1)∆n of Xs. We give an approximation of the law of (J0, . . . , Jn−1) by means of a Euler scheme expansion for the process (Ji). In some special cases, an approximation by an explicit Gaussian ARMA(1,1) process is obtained. When ∆n = n −1 , we deduce from this expansion estimators of the diffusion coefficient of X based on (Ji). These estimators are shown to be asymptotically mixed normal as n tends to infinity.

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On estimating the diffusion coefficient

Cited by 73 publications

References 2 publications

Estimating a class of diffusions from discrete observations via approximate maximum likelihood method

Estimating a class of diffusions from discrete observations via approximate maximum likelihood method

Parametric Inference for Diffusion Processes Observed at Discrete Points in Time: a Survey

Discrete sampling of an integrated diffusion process and parameter estimation of the diffusion coefficient

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