A Simple Approach to the Parametric Estimation of Potentially Nonstationary Diffusions

By F. Bandi, Peter C. B. Phillips. 2005

57 citations recorded by the source corpus.

A simple and robust approach is proposed for the parametric estimation of scalar homogeneous stochastic differential equations. We specify a parametric class of diffusions and estimate the parameters of interest by minimizing criteria based on the integrated squared difference between kernel estimates of the drift and diffusion functions and their parametric counterparts. The procedure does not require simulations or approximations to the true transition density and has the simplicity of standard nonlinear least-squares methods in discrete-time. A complete asymptotic theory for the parametric estimates is developed. The limit theory relies on infill and long span asymptotics and is robust to deviations from stationarity, requiring only recurrence.

Subfields: Finance, Global and Planetary Change, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/07246ee111f7661390e8831b56b97ec7618f9668

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Citations in the corpus

Bias in the estimation of the mean reversion parameter in continuous time models (2012, methodology): “To understand the behavior of the actual bias in Model (1) and the performance of (12), we simulate 756 daily observations (i.”
A specification test for nonlinear nonstationary models (2012, methodology): “Recent research on the nonparametric modeling of nonstationary data opens up some new possibilities that seem relevant to applications in many fields, including nonlinear diffusion models in continuous time [Bandi and Phillips (2003, 2007)] and cointegration models in economics and finance.”
Efficient Minimum Distance Estimation with Multiple Rates of Convergence (2012, unknown): “Bandi and Phillips (2007) embed this joint increasing/fixed-domain asymptotic in a minimum distance problem where sample counterparts of both the drift and the diffusion terms are obtained by kernel smoothing.”
Realized Variance and Market Microstructure Noise (2006, methodology): “Related to the pres nt context is the use of infill asymptotics for estimation P. R. Hansen and A. Lunde: Realized Variance and MMS Noise of diffusions, see Bandi & Phillips (2004).”