Footprints of Chaos in the Market: Analyzing Non-Linear Time Series in Financial Markets and Other Natural Systems (Financial Times (Prentice Hall))

If Price Action Is Considered To Be The Product Of A Random Walk Only Unpredictable News Can Affect Prices, And It Is Therefore Impossible To Accurately Predict Market Movement. Richard Urbach Counters This Thinking By Applying A New Set Of Mathematical Techniques To The Financial Markets, Arguing That It Is Possible To Accurately Analyze The Time Series (or 'footprints') Of Chaotic Real Systems, Map Their Underlying Patterns, And Predict Future Trends. Footprints Of Chaos Is The First Book To Examine The Opportunities Presented By This New Thinking, And Is Aimed Directly At The Investment Analysts Who Can Benefit From It.--jacket. Dynamical Systems -- Intuition -- Theory -- Dynamical Systems -- Attractors And Limit Sets -- Bifurcations -- Reducing Flows To Discrete Maps -- Manifolds And Tangent Spaces -- Stable And Unstable Manifolds -- Natural Measure -- Entropy -- Intuition -- Theory -- Shannon Entropy -- Conditional Entropy -- Block Entropy -- Renyi Entropy -- Noise And Measurement Error -- Asymptotic Results -- Algorithms -- Correlation Integral -- Higher Order Correlation Integrals -- Estimation Of Entropy And Its Derivatives By Order-q Correlation Integrals -- Green-savit Statistics -- Estimating Local Statistics -- Entropy For A Gaussian Process -- Bds Statistic -- Phase Space Reconstruction -- Intuition -- Theory -- Embeddings -- Reconstruction Parameters -- Window Size -- Algorithms -- Critical Window ([tau]*[subscript W]) -- Global False Near Neighbors (d[subscript E]) -- Mutual Information And Autocorrelation ([tau]) -- Singular Value Fraction ([tau] Given D[subscript E]) -- Average Displacement ([tau] Given D[subscript E]) -- Fill Factor (d[subscript E] And [tau]) -- Deformation Integral (d[subscript E] And [tau]) -- Trajectory Alignment (d[subscript E] And [tau]) -- Prediction Error (d[subscript E] And [tau]) -- Test For Determinism (d[subscript E] And [tau]) -- Tangent Space Approach (d[subscript A]) -- Local False Near Neighbors (d[subscript A]) -- Fractal Dimension -- Intuition -- Theory -- A Spectrum Of Dimensions -- D[subscript 2] Is Invariant -- The Correlation Exponent -- Convergence -- Scaling Region -- Pitfalls. Richard M.a. Urbach. Includes Bibliographical References (pages 315-317) And Index.