Comparison of Nonlinearity Measures based on Time Series Analysis for Nonlinearity Detection

The main purpose of this paper is a study of the efficiency of different nonlinearity detection methods based on time-series data from a dynamic process as a part of system identification. A very useful concept in measuring the nonlinearity is the definition of a suitable index to measure any deviation from linearity. To analyze the properties of such an index, the observed time series is assumed to be the output of Volterra series driven by a Gaussian input. After reviewing these methods, some modifications and new indices are proposed, and a benchmark simulation study is made. Correlation analysis, harmonic analysis and higher order spectrum analysis are selected methods to be investigated in our simulations. Each method has been validated with its own advantages and disadvantages.