Estimating measurement noise in a time series by exploiting nonstationarity

A measured time series is always corrupted by noise to some degree. Even a rough estimation of the level of noise contained in an experimental time series is valuable. This is so, for example, when one wishes to apply techniques from nonlinear dynamics theory to analyze a time series. However, this is a very difficult problem. It becomes even harder when the measured signal is nonstationary, which is often true in practice. Detecting nonstationarity has been a hot research topic in recent years. However, many researchers stop when they find the time series under study is indeed nonstationary. Here, we exploit the very nature of nonstationarity in a signal to formulate a method for quantitatively estimating the amount of noise contained in the signal. The approach is first verified using computer simulated signals based on the chaotic Lorenz attractors and the Mackey–Glass equations with different parameters and then applied to the clinically measured intracranial EEG signals. It is found that the amount of noise in the EEG signals is around 8.0–8.5% in terms of amplitude. Implications to whether EEG signals are chaotic or not are discussed.