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

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.

A Chaos Analysis of the Dry Bulk Shipping Market

“…The methodological framework from other research [32,42] has been adopted to study the presence of nonlinearity and chaos. The methods employed herein are presented in Table 1, and their main characteristics are described below.…”

“…Firstly, we define linear and nonlinear series as elsewhere [32]. A stochastic process (X t , t ∈ T) is said to be a linear process if for every t ∈ T X t = ∑ ∞ j=0 β j t−j where a 0 = 1, t , t ∈ T is a process of independent and identically-distributed random variables (iid) with E[X t ] = 0, E X 2 t = σ 2 and ∑ ∞ j=0 β j < ∞.…”

“…As noted above, linear models have proven to be ill-suited for describing and fitting many economic phenomena such as the business cycles. In contrast, the nonlinear approach can capture the features of economic and financial series and their sudden fluctuations, and hence plays a relevant role in economic modeling [32]. Likewise, dynamical systems involving time delays have applications in a number of fields such as biology, population dynamics and economics [33].…”

“…To this end the following methodology is applied to all time series [32]. First, to evaluate stationarity of the BDI series, unit root tests were performed.…”

Complexity in Economic and Social Systems

“…In [14], a few results on the IPO timing properties are considered and discussed. Studying the temporal properties of financial dynamics, which is a property related to their complexity, offers verification for one of the key paradigms of financial markets, namely the efficient market hypothesis [6], and testing for nonlinearity and chaos [15]. Temporal properties of financial dynamics can in turn be one of the consequences of stock liquidity and it is thus important to have a reliable method to quantify it [16].…”