Deterministic nonlinearity in the stock returns of major European equity markets and the United States

Abstract

By using recently developed statistical tools designed to overcome some of the limitations often associated with financial data, this study attempts to detect low-dimensional deterministic chaos in five major European stock markets and the United States. Country indexes exhibiting low-dimensional deterministic chaos may contain some informational inefficiency; thus, it may be possible to use nonlinear dynamics to predict future stock returns. The results do not provide evidence of the existence of low-dimensional chaotic systems in any of the examined indexes. As such, the notion of market efficiency in the examined indexes is not threatened by the findings of this study.

A search for long‐range dependence and chaotic structure in Indian stock market

“…It is possible that any structural shift or break ( i.e. nonstationarity) in the time series of returns may cause this strong rejection of the null hypothesis (Pandey, Kohers, & Kohers, 1998). The issue of structural break and resulting nonstationarity of financial time series is highly likely in the case of emerging markets like India which is still passing through various phases of economic and financial reforms.…”

“…Now in order to ascertain whether the data series of returns are, indeed, a result of chaotic process, we further conduct two highly popular tests, namely R/S analysis and estimation of Lyapunov exponent. As pointed by Pandey et al (1998) and Peter (1994), R/S analysis is a more powerful indicator of the persistence of a time series where the influence of a set of past observations on a set of future observation is effectively captured. As a matter of fact, presence of some dependence between observations widely separated in time ( i.e.…”

“…33See, for example, Abhyankar et al (1997), Atchison and White (1996), Gilmore, 1996, and Pandey et al (1998).…”

“…1616Hsieh (1991) argues that the presence of structural changes in the data series may cause rejection of the null hypothesis of IID observations by the BDS test. In this concern, Pandey et al (1998) suggest to divide the entire sample period into sub‐periods and then conduct separate analysis using the BDS test. Following this we divided the data series of market indices (Bank Nifty, CNX IT, BSE 200 and BSE 100) in two sub‐periods and performed the BDS test.…”

The behaviour of US stock prices: Evidence from a threshold autoregressive model

“…One reason for these mixed results could be due to the fact that stock prices are characterized by nonlinearities. To this end, there is a large literature which finds that stock prices are consistent with a nonlinear data generating process (see, inter alia [1,2,4,5,15,17,21,27,29,30]; Kohers et al, 1998). 2 The majority of the studies (see, inter alia [2,17,20,25]) that focus on modeling nonlinearities in stock prices have been based on Chaos models; the findings from this body of research reveal little or no evidence of chaotic nonlinearity.…”