Time Series with Tailored Nonlinearities

TL;DR

This paper shows how to generate time series with specific nonlinear features by manipulating Fourier phases, explaining the origin of observed scaling behaviors in empirical data like turbulence and finance.

Contribution

It introduces a method to create nonlinear time series through phase constraints, linking phase correlations to nonlinear characteristics and scaling laws.

Findings

Phase correlations can reproduce empirical scaling behaviors.

Tailored phase constraints generate nonlinear time series.

Power law distributions explained by phase correlations.

Abstract

It is demonstrated how to generate time series with tailored nonlinearities by inducing well- defined constraints on the Fourier phases. Correlations between the phase information of adjacent phases and (static and dynamic) measures of nonlinearities are established and their origin is explained. By applying a set of simple constraints on the phases of an originally linear and uncor- related Gaussian time series, the observed scaling behavior of the intensity distribution of empirical time series can be reproduced. The power law character of the intensity distributions being typical for e.g. turbulence and financial data can thus be explained in terms of phase correlations.