Debiasing Continuous-time Nonlinear Autoregressions

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) (, 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.

Tasks

Reproductions