Debiasing Continuous-time Nonlinear Autoregressions

Simon Kuang; Xinfan Lin

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arXiv · 2504.05525

Debiasing Continuous-time Nonlinear Autoregressions

Simon Kuang·Xinfan Lin

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Abstract

We study how to identify a class of continuous-time nonlinear systems defined by an ordinary differential equation affine in the unknown parameter. We define a notion of asymptotic consistency as $(n, h) \to (\infty, 0)$, and we achieve it using a family of direct methods where the first step is differentiating a noisy time series and the second step is a plug-in linear estimator. The first step, differentiation, is a signal processing adaptation of the nonparametric statistical technique of local polynomial regression. The second step, generalized linear regression, can be consistent using a least squares estimator, but we demonstrate two novel bias corrections that improve the accuracy for finite $h$. These methods significantly broaden the class of continuous-time systems that can be consistently estimated by direct methods.

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Simon Kuang, Xinfan Lin. 2025-04-07. Debiasing Continuous-time Nonlinear Autoregressions. https://arxiv.org/abs/2504.05525

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