Part One Fractal Time Series 1
1 Introduction to Fractal Time Series 3 Fractal Space, 4 Fractal Time, 5 Fractal Mathematics, 9 The Chaos Game, 10 What Is a Fractal , 12 The Fractal Dimension, 15 Fractal Market Analysis, 17 2 Failure of the Gaussian Hypothesis 18 Capital Market Theory, 19 Statistical Characteristics of Markets, 21 The Term Structure of Volatility, 27 The Bounded Set, 37 Summary, 38 Stable Markets versus Efficient Markets, 41 Information Sets and Investment Horizons, 43 Statistical Characteristics of Markets,...
Part Two Fractal RS Analysis
Having defined the problem in Part One, I offer tools for analysis in Part Two in particular, rescaled range R S analysis. Many of the technical questions I received about the first book dealt with R S analysis and requested details about calculations and significance tests. Parts Two and Three address those issues. R S analysis is a robust analysis technique for uncovering long memory effects, fractal statistical structure, and the presence of cycles. Chapter 4 surveys the conceptual...
Acknowledgments
I would like to thank the following people for their invaluable advice and assistance From PanAgora Asset Management Richard Crowell, Peter Rathjens, John Lewis, Bruce Clarke, Terry Norman, Alan Brown, and Clive Lang. Also Warren Sproul, Earl Keefer, Robert Mellen, Guido DeBoeck, and Ron Brandes for help, ideas, and references. Thanks also to Kristine with a K Lino, David Arrighini, Jim Rullo, and Chuck LeVine of the PanAgora Asset Allocation team, for their indulgence and help. I would also...
Fractal Mathematics
All this conceptual distinction between the world of the Demiurge and the Euclidean geometry of the Good is interesting, but can it be made practical After all, the main advantage of Euclidean geometry is its elegant simplicity. Problems can be approximated using Euclidean geometry, and solved for optimal answers. Models can be easily generated, even if they are gross simplifications. Can these ever increasingly complex forms that we have called fractals also be modeled The answer is Yes....
Part Two Fractal Rs Analysis 1
4 Measuring Memory The Hurst Process and R S Analysis 53 Background Development of R S Analysis, 54 The Joker Effect, 60 Randomness and Persistence Interpreting the Hurst Exponent, 61 R S Analysis A Step-by-Step Guide, 61 An Example The Yen Dollar Exchange Rate, 63 The Random Null Hypothesis, 66 Stochastic Models, 75 Summary, 85 6 Finding Cycles Periodic and Nonperiodic 86 Periodic Cycles, 88 Nonperiodic Cycles, 93 Summary, 102
Fractal Time
This conflict between the symmetry of Euclidean geometry and the asymmetry of the real world can be further extended to our concept of time. Traditionally, events are viewed as either random or deterministic. In the deterministic view, all events through time have been fixed from the moment of creation. This view has been given a theological basis by denominations such as the Calvinists, and scientific endorsement by certain big bang theorists. In contrast, nihilist groups consider all events...