Nonlinear Time Series Modeling: A Unified Perspective, Algorithm, and Application

TL;DR

This paper introduces a unified nonlinear time series analysis framework using data-specific transformations, enabling robust modeling of non-Gaussian and nonlinear processes, demonstrated on financial data with the LPTime algorithm.

Contribution

It presents a novel data-specific transformation approach and the LPTime algorithm for comprehensive nonlinear time series modeling, applicable to complex real-world data.

Findings

LPTime automatically discovers stylized facts in financial data

The framework adapts linear Gaussian models for nonlinear, non-Gaussian processes

Effective analysis demonstrated on S&P 500 return data

Abstract

A new comprehensive approach to nonlinear time series analysis and modeling is developed in the present paper. We introduce novel data-specific mid-distribution based Legendre Polynomial (LP) like nonlinear transformations of the original time series Y(t) that enables us to adapt all the existing stationary linear Gaussian time series modeling strategy and made it applicable for non-Gaussian and nonlinear processes in a robust fashion. The emphasis of the present paper is on empirical time series modeling via the algorithm LPTime. We demonstrate the effectiveness of our theoretical framework using daily S&P 500 return data between Jan/2/1963 - Dec/31/2009. Our proposed LPTime algorithm systematically discovers all the `stylized facts' of the financial time series automatically all at once, which were previously noted by many researchers one at a time.