Publication Date: September 2001
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.
Diﬀusion, Drift, Inﬁll asymptotics, Kernel density, Local time, Long span asymptotics, Martingale, Nonparametric estimation, Semimartingale, Stochastic diﬀerential equation
JEL Classification Codes: C14, C22
See CFP: 1050