Modeling noisy time series: Physiological tremor

TL;DR

This paper examines how observational noise affects modeling of physiological tremor time series, comparing linear models with and without noise consideration, and discusses advanced modeling techniques for noisy deterministic and stochastic systems.

Contribution

It introduces a comparative analysis of linear models that include observational noise versus those that ignore it, and discusses state space models and Bock's algorithm for noisy systems.

Findings

Including observational noise improves model accuracy for physiological tremor.

State space models effectively handle noisy stochastic systems.

Bock's algorithm is suitable for modeling noisy deterministic systems.

Abstract

Empirical time series often contain observational noise. We investigate the effect of this noise on the estimated parameters of models fitted to the data. For data of physiological tremor, i.e. a small amplitude oscillation of the outstretched hand of healthy subjects, we compare the results for a linear model that explicitly includes additional observational noise to one that ignores this noise. We discuss problems and possible solutions for nonlinear deterministic as well as nonlinear stochastic processes. Especially we discuss the state space model applicable for modeling noisy stochastic systems and Bock's algorithm capable for modeling noisy deterministic systems.