Fully Nonparametric Estimation of Scalar Diffusion Models
We propose a functional estimation procedure for homogeneous stochastic differential equations based on a discrete sample of observations and with minimal requirements on the data generating process. We show how to identify the drift and diffusion function in situations where one or the other function is considered a nuisance parameter. The asymptotic behavior of the estimators is examined as the observation frequency increases and as the time span lengthens (that is, we implement both infill and long span asymptotics). We prove consistency and convergence to mixtures of normal laws, where the mixing variates depend on the chronological local time of the underlying process, that is the time spent by the process in the vicinity of a spatial point. The estimation method and asymptotic results apply to both stationary and nonstationary processes.
|Date of creation:||Sep 2001|
|Date of revision:|
|Publication status:||Published in Econometrica (2003), 71(1): 241-283|
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- Hardle, W., 1992.
"Applied Nonparametric Methods,"
9204, Catholique de Louvain - Institut de statistique.
- HÄRDLE, Wolfgang, 1992. "Applied nonparametric methods," CORE Discussion Papers 1992003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Hardle, W., 1992. "Applied Nonparametric Methods," Papers 9206, Tilburg - Center for Economic Research.
- Härdle, W.K., 1992. "Applied Nonparametric Methods," Discussion Paper 1992-6, Tilburg University, Center for Economic Research.
- Wolfgang Hardle & Oliver Linton, 1994. "Applied Nonparametric Methods," Cowles Foundation Discussion Papers 1069, Cowles Foundation for Research in Economics, Yale University.
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- Yacine Ait-Sahalia, 1995. "Testing Continuous-Time Models of the Spot Interest Rate," NBER Working Papers 5346, National Bureau of Economic Research, Inc.
- Peter C.B. Phillips, 1998. "Econometric Analysis of Fisher's Equation," Cowles Foundation Discussion Papers 1180, Cowles Foundation for Research in Economics, Yale University.
- Ait-Sahalia, Yacine, 1996.
"Nonparametric Pricing of Interest Rate Derivative Securities,"
Econometric Society, vol. 64(3), pages 527-60, May.
- Yacine Ait-Sahalia, 1995. "Nonparametric Pricing of Interest Rate Derivative Securities," NBER Working Papers 5345, National Bureau of Economic Research, Inc.
- Oliver LINTON, .
"Applied nonparametric methods,"
Statistic und Oekonometrie
9312, Humboldt Universitaet Berlin.
- repec:dgr:kubcen:19926 is not listed on IDEAS
- repec:cup:etheor:v:13:y:1997:i:5:p:615-45 is not listed on IDEAS
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