Bandi, Federico, Corradi, Valentina and Moloche, Guillermo (2008) Bandwidth selection for continuous-time Markov processes. In: Chicago/London Conference on Financial Markets Part One : What Went Wrong? Financial Engineering, Financial Econometrics, and the Current Stress, City University London, London, 5-6 Dec 2008 (Unpublished)

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Abstract

We propose a theoretical approach to automated bandwidth choice for continuous-time Markov processes. We do so in the context of stationary and nonstationary processes of the recurrent kind. Because the rate of divergence of the process local time affects the rate of convergence of the functional estimates of the process moments, the nonstationary case, for which local time diverges at a generally unknown rate lower than T, is particularly delicate. The procedure consists of two steps. In the first stage, 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 ensures consistency of the infinitesimal variance estimator but does not identify the drift function. Additionally, it does not ensure that the necessary rate conditions for asymptotic normality of the infinitesimal variance are violated. In the second stage, we propose tests of the hypothesis that the bandwidth is either "too small" or "too big" to satisfy all rate conditions. The suggested statistics rely on a simple randomized procedure based on the idea of conditional inference. Importantly, if the null is rejected, then the first-stage bandwidths are kept. Otherwise, the outcomes of the tests indicate whether we should select larger or smaller bandwidths. We study diffusion processes, jump-diffusion processes, as well as processes measured with error as is the case for stochastic volatility modelling by virtue of preliminary high-frequency spot variance estimates, for instance. The finite sample joint behavior of our automated bandwidth selection method, as well as that of the associated (second-step) randomized procedure, are studied via Monte Carlo simulation.

Item Type:	Conference Item (Paper)
Subjects:	H Social Sciences > HB Economic Theory
Divisions:	Faculty of Social Sciences > Economics
Official Date:	6 December 2008
Dates:	Date Event 6 December 2008 Completion
Status:	Not Peer Reviewed
Publication Status:	Unpublished
Version or Related Resource:	Bandi, Federico, Corradi, Valentina and Moloche, Guillermo (2009). Bandwidth selection for continuous-time Markov processes. In: Invited Speaker : Department of Economics, University of Montreal. Montreal, 13 Mar 2009. Bandi, Federico, Corradi, Valentina and Moloche, Guillermo (2009). Bandwidth selection for continuous-time Markov processes. In: Toulouse School of Economics Financial Econometrics Conference. Toulouse, 15-16 May 2009. Bandi, Federico, Corradi, Valentina and Moloche, Guillermo (2009). Bandwidth selection for continuous-time Markov processes. In: Recent Developments in Time Series Econometrics : 3rd Annual Conference. Nottingham, 14-15 Sep 2009.
Conference Paper Type:	Paper
Title of Event:	Chicago/London Conference on Financial Markets Part One : What Went Wrong? Financial Engineering, Financial Econometrics, and the Current Stress
Type of Event:	Conference
Location of Event:	City University London, London
Date(s) of Event:	5-6 Dec 2008
Related URLs:	Other Other Other

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