Bandi, Federico and Corradi, Valentina and Moloche, Guillermo (2009): Bandwidth selection for continuoustime Markov processes.

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Abstract
We propose a theoretical approach to bandwidth choice for continuoustime Markov processes. We do so in the context of stationary and nonstationary processes of the recurrent kind. The procedure consists of two steps. In the first step, by invoking local Gaussianity, we suggest an automated bandwidth selection method which maximizes the probability that the standardized data are a collection of normal draws. In the case of diffusions, for instance, this procedure selects a bandwidth which only ensures consistency of the infinitesimal variance estimator, not of the drift estimator. Additionally, the procedure does not guarantee that the rate conditions for asymptotic normality of the infinitesimal variance estimator are satisfied. In the second step, we propose tests of the hypothesis that the bandwidth(s) are either "too small" or "too big" to satisfy all necessary rate conditions for consistency and asymptotic normality. The suggested statistics rely on a randomized procedure based on the idea of conditional inference. Importantly, if the null is rejected, then the firststage bandwidths are kept. Otherwise, the outcomes of the tests indicate whether larger or smaller bandwidths should be selected. We study scalar and multivariate diffusion processes, jumpdiffusion processes, as well as processes measured with error as is the case, for instance, for stochastic volatility modelling by virtue of preliminary highfrequency spot variance estimates. The finite sample joint behavior of our proposed automated bandwidth selection method, as well as that of the associated (secondstep) randomized procedure, are studied via Monte Carlo simulation.
Item Type:  MPRA Paper 

Original Title:  Bandwidth selection for continuoustime Markov processes 
Language:  English 
Keywords:  Diffusion processes, nonparametric estimation 
Subjects:  C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C32  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C14  Semiparametric and Nonparametric Methods: General C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C52  Model Evaluation, Validation, and Selection C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C15  Statistical Simulation 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 > C0  General > C01  Econometrics 
Item ID:  43682 
Depositing User:  Guillermo Moloche 
Date Deposited:  09. Jan 2013 21:13 
Last Modified:  15. Mar 2015 05:07 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/43682 