Looking for systematic approach to select chaos tests

This paper will consider the mathematical definition of chaos (in sense of Devaney) in order to select appropriate chaos tests. The tests chosen according to investigate the properties mentioned in the definition. In fact, these are prerequisites of chaoticity. Either it will be represented that “sensitivity dependence on initial conditions” is not equivalent to chaos, although some researchers considering it. Hence, it is implied that checking all of the properties mentioned in the definition are required to establish chaos.As our case study, some sample stocks were selected from Tehran Stock Exchange (TSE) and the chosen tests implemented on their returns time series. Incoming results indicate that the returns series are not chaotic although their largest Lyapunov exponent are positive. In fact, there is no evidence of unstable periodic orbits in the returns series (as one of the chaos prerequisites). While by using the BDS test and some autoregressive models as filters, some evidence of nonlinearity has been observed in these series. So, using chaos mathematical definition prevents us to misleading results about chaoticity.