1981
DOI: 10.1137/0319043
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Recursive Estimation in Diffusion Model

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Cited by 29 publications
(23 citation statements)
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“…Prakasa Rao (1999) derives kernel estimators for a and b by approximating the continuous time likelihood function of x through a kernel function K. In Stanton (1997), kernel estimators for a and b were derived from the properties (13) and (15); whereas in Jiang and Knight (1997) kernel estimators for a and b were obtained by taking into account the properties (12), (16), and the kernel approximation for 1 π (x) d dx π(x) introduced by Banon and Nguyen (1981). It has been proved that these kernel estimators are consistent and asymptotically normal.…”
Section: Estimation Of Both the Drift And Diffusion Coefficientsmentioning
confidence: 99%
“…Prakasa Rao (1999) derives kernel estimators for a and b by approximating the continuous time likelihood function of x through a kernel function K. In Stanton (1997), kernel estimators for a and b were derived from the properties (13) and (15); whereas in Jiang and Knight (1997) kernel estimators for a and b were obtained by taking into account the properties (12), (16), and the kernel approximation for 1 π (x) d dx π(x) introduced by Banon and Nguyen (1981). It has been proved that these kernel estimators are consistent and asymptotically normal.…”
Section: Estimation Of Both the Drift And Diffusion Coefficientsmentioning
confidence: 99%
“…Thus, the monthly, weekly and daily data correspond, respectively, to ∆ = 1/12, 1/52 and 1/252 (there are approximately 252 trading days per year). Given an initial value, one can recursively apply (18) to obtain a sequence of simulated data {X j∆ , j = 1, 2, · · ·}.…”
Section: Simulation Of Stochastic Modelsmentioning
confidence: 99%
“…The problem of estimating the marginal density of a continuous time process has been mainly studied using kernel estimators by Banon [1], Banon and N'Guyen [2], N'Gyen [33], and Bosq [9]. Under some mixing conditions, their pointwise nonintegrated L 2 -risk (namely E½ðf n ðxÞ À f n ðxÞÞ 2 iff n denotes their estimator), reaches the standard rate of convergence T À2s=ð2sþ1Þ when f belongs to the Ho¨lder class C s and s is known, and these rates are minimax in their context.…”
Section: Some Bibliographic Remarksmentioning
confidence: 99%