Detecting hidden transient events in noisy nonlinear time-series

The information impulse function (IIF), running Variance, and local Hölder Exponent are three conceptually different time-series evaluation techniques. These techniques examine time-series for local changes in information content, statistical variation, and point-wise smoothness, respectively. Using simulated data emulating a randomly excited nonlinear dynamical system, this study interrogates the utility of each method to correctly differentiate a transient event from the background while simultaneously locating it in time. Computational experiments are designed and conducted to evaluate the efficacy of each technique by varying pulse size, time location, and noise level in time-series. Our findings reveal that, in most cases, the first instance of a transient event is more easily observed with the information-based approach of IIF than with the Variance and local Hölder Exponent methods. While our study highlights the unique strengths of each technique, the results suggest that very robust and reliable event detection for nonlinear systems producing noisy time-series data can be obtained by incorporating the IIF into the analysis.