The Pearson Diffusions: A Class of Statistically Tractable Diffusion Processes
AbstractThe Pearson diffusions form a flexible class of diffusions defined by having linear drift and quadratic squared diffusion coefficient. It is demonstrated that for this class explicit statistical inference is feasible. A complete model classification is presented for the ergodic Pearson diffusions. The class of stationary distributions equals the full Pearson system of distributions. Well-known instances are the Ornstein-Uhlenbeck processes and the square root (CIR) processes. Also diffusions with heavy-tailed and skew marginals are included. Explicit formulae for the conditional moments and the polynomial eigenfunctions are derived. Explicit optimal martingale estimating functions are found. The discussion covers GMM, quasi-likelihood, non-linear weighted least squares estimation and likelihood inference too. The analytical tractability is inherited by transformed Pearson diffusions, integrated Pearson diffusions, sums of Pearson diffusions and Pearson stochastic volatility models. For the non-Markov models, explicit optimal prediction-based estimating functions are found. The estimators are shown to be consistent and asymptotically normal. Copyright (c) Board of the Foundation of the Scandinavian Journal of Statistics 2008.
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Bibliographic InfoArticle provided by Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association in its journal Scandinavian Journal of Statistics.
Volume (Year): 35 (2008)
Issue (Month): 3 ()
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Other versions of this item:
- Michael Sørensen & Julie Lyng Forman, 2007. "The Pearson diffusions: A class of statistically tractable diffusion processes," CREATES Research Papers 2007-28, School of Economics and Management, University of Aarhus.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
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