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Detecting Linear and Nonlinear Dependence in Stock Returns: New Methods Derived from Chaos Theory

Interest in the relevance of nonlinear dynamics to fields such as finance and economics has spurred the development of new methods of analysis for time series data. Early tests for chaos led to problems when applied to financial and economic data. This motivated development of the BDS family of statistics to test for nonlinearity generally. More recently, another method of analysis has been introduced into the scientific literature. It uses a test for chaos which is relatively simple and appropriate for financial data. A quantitative version of this test is developed here and is used to analyze stock return data.