A Comprehensive Framework for Uncovering Non-Linearity and Chaos in Financial Markets: Empirical Evidence for Four Major Stock Market Indices.

Lucia Inglada-Perez

doi:10.3390/e22121435

Abstract

The presence of chaos in the financial markets has been the subject of a great number of studies, but the results have been contradictory and inconclusive. This research tests for the existence of nonlinear patterns and chaotic nature in four major stock market indices: namely Dow Jones Industrial Average, Ibex 35, Nasdaq-100 and Nikkei 225. To this end, a comprehensive framework has been adopted encompassing a wide range of techniques and the most suitable methods for the analysis of noisy time series. By using daily closing values from January 1992 to July 2013, this study employs twelve techniques and tools of which five are specific to detecting chaos. The findings show no clear evidence of chaos, suggesting that the behavior of financial markets is nonlinear and stochastic.

Highlights

Research on modeling financial time series has traditionally assumed linear patterns
Many scholars have empirically studied the existence of nonlinear dynamics in financial series [4], several theoretical models consistent with the presence of nonlinearity in asset prices have arisen [5]
The results suggest that, in all cases except for the exponential generalized autoregressive conditional heteroskedasticity (GARCH) (EGARCH) model in the Dow Jones Index, the CD increases as the embedding dimension increases, the CD is below the expected value for a random process

Summary

Introduction

Research on modeling financial time series has traditionally assumed linear patterns. There is interest in and a need to introduce alternative methods, most of which come from other scientific disciplines such as mathematics, physics and engineering [1], to model the dynamics of financial series, and to detect a possible nonlinear and determinist chaotic behavior. The initial interest in the application of nonlinear models has been extended to solve the question of whether the nonlinear dynamics have a stochastic or deterministic behavior This issue constitutes a key point in the process of modeling and forecasting financial time series. The emergence of new models that deal with the volatility present in financial time series, such as the autoregressive conditional heteroskedasticity

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Results

Conclusion