Combining Data‐Driven Subsampling and Extrema Quadratic Variation Estimators for Diffusion Parameter Identification in SDEs

ABSTRACT We recently introduced a simple method for selecting suitable subsampling rates for the estimation of diffusion coefficients in stochastic differential equations (SDEs) from time series data in scenarios where data and model are compatible only on specific, a priori unknown, scales. The approach is based on analyzing the lengths of monotone segments in the subsampled time series, which should be approximately geometrically distributed with parameter 1/2 to ensure consistency with the behavior of the SDE model on an infinitesimal scale. Once an appropriate subsampling rate has been identified, the diffusion coefficient can be estimated in terms of the quadratic variation of the subsampled data sequence. In this contribution, we investigate a modification of the proposed approach that consists in replacing the standard quadratic variation estimator by a quadratic variation corresponding to the local extrema of the subsampled time series. The modified method is demonstrated and compared with the original method using an application concerning surrogate models for lay‐down curves of filaments in industrial production processes of nonwoven textiles.