On detecting determinism and nonlinearity in microelectrode recording signals: Approach based on non-stationary surrogate data methods

Two new surrogate methods, the Small Shuffle Surrogate (SSS) and the Truncated Fourier Transform Surrogate (TFTS), have been proposed to study whether there are some kind of dynamics in irregular fluctuations and if so whether these dynamics are linear or not, even if this fluctuations are modulated by long term trends. This situation is theoretically incompatible with the assumption underlying previously proposed surrogate methods. We apply the SSS and TFTS methods to microelectrode recording (MER) signals from different brain areas, in order to acquire a deeper understanding of them. Through our methodology we conclude that the irregular fluctuations in MER signals possess some determinism.

💡 Research Summary

The paper addresses a fundamental problem in the analysis of micro‑electrode recording (MER) signals: determining whether the irregular fluctuations observed in these recordings are purely stochastic or whether they contain deterministic and possibly nonlinear dynamics, even when the signals are modulated by long‑term trends. Traditional surrogate‑data methods, such as the Amplitude‑Adjusted Fourier Transform (AAFT) or the Iterative AAFT, assume that the underlying time series is stationary—i.e., its statistical properties (mean, variance, autocorrelation) do not change over time. MER signals, however, are notoriously non‑stationary; they combine rapid, high‑frequency bursts with slow drifts that reflect changes in electrode position, tissue properties, or underlying neural state. Because of this incompatibility, conventional surrogate tests can either falsely reject the null hypothesis (by mistaking trend‑induced structure for determinism) or fail to detect genuine nonlinear signatures.

To overcome this limitation, the authors propose two novel surrogate‑generation techniques specifically designed for non‑stationary data:

1. Small Shuffle Surrogate (SSS). The original series is divided into short, overlapping windows of length L (chosen longer than the dominant autocorrelation time but short enough to preserve local dynamics). Within each window the time indices are randomly permuted, thereby destroying any long‑range ordering while preserving short‑range correlation structure and the marginal distribution. By retaining the local deterministic skeleton but eliminating the global trend, SSS enables a test of “short‑term determinism” that is robust to non‑stationarity.

2. Truncated Fourier Transform Surrogate (TFTS). The series is Fourier‑transformed, and a cutoff frequency f_c is selected. Phases of all frequency components below f_c (which carry the bulk of the trend and low‑frequency nonlinear structure) are replaced by random values uniformly distributed on