Why Study Nonlinear Time Series Analysis?

Abstract

Nonlinear Time Series Analysis (NLTS) provides a mathematically rigorous collection of techniques designed to reconstruct real-world system dynamics from time series data on a single variable or multiple causally-related variables. NLTS facilitates scientific inquiry that emphasizes strong supportive evidence, well-conducted and thorough inquiry, and realism. Data provide an essential evidentiary portal to a reality to which we have only limited access. Random-appearing data do not prove that underlying dynamic process are subject to exogenous inherently-random forces. The possibility exists that observed volatility is generated by inherently-unstable, deterministic, and nonlinear real-world dynamic systems. NLTS allows the data to speak regarding which type of system dynamics generated them. It is capable of detecting linear as well as nonlinear deterministic system dynamics, and diagnosing the presence of linear stochastic dynamics. Our objective is to use NLTS to uncover the structure best corresponding to reality whether it be linear, nonlinear, deterministic, or stochastic. Accurate diagnosis of real-world dynamics from observed data is crucial to develop valid theory, and to formulate effective public policy based on theory.