Moloche, Guillermo (2001): Local Nonparametric Estimation of Scalar Diffusions.

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Abstract
This paper studies the functional estimation of the drift and diffusion functions for recurrent scalar diffusion processes from equally spaced observations using the local polynomial kernel approach. Almost sure convergence and a CLT for the estimators are established as the sampling frequency and the time span go to infinity. The asymptotic distributions follow a mixture of normal laws. This theory covers both positive and null recurrent diffusions.
Almost sure convergence rates are sometimes path dependent but expected rates can always be characterized in terms of regularly varying functions.
The general theory is specialized for positive recurrent diffusion processes, and it is shown in this case that the asymptotic distributions are normal.
We also obtain the limit theory for kernel density estimators when the process is positive recurrent, namely, requiring only that the invariant probability measure exists. Nonetheless, it is also shown that such an estimator paradoxically vanishes almost surely when the invariant measure is fat tailed and nonintegrable, that is, in the null recurrent case.
Item Type:  MPRA Paper 

Original Title:  Local Nonparametric Estimation of Scalar Diffusions 
English Title:  Local Nonparametric Estimation of Scalar Diffusions 
Language:  English 
Keywords:  Nonparametric estimation, Diffusion processes 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C14  Semiparametric and Nonparametric Methods: General C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C58  Financial Econometrics 
Item ID:  46154 
Depositing User:  Guillermo Moloche 
Date Deposited:  13. Apr 2013 09:59 
Last Modified:  13. Apr 2013 10:17 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/46154 