声明
CONTENTS
ABSTRACT
摘要
1 Introduction
1．1 Research background
1．2 Preliminaries
1．2．1 Iterated function system
1．2．2 Fractal dimension
2 Rational fractal interpolation functions with funct ion scaling factors
2．1 Rational IFS with function scaling factors
2．2 Property analysis of rational FIFs
2．2．1 Smoothness of rational FIFs
2．2．2 Stability of rational FIFs
2．2．3 Convergence of rational FIFs
2．3 Box-counting dimension of rational FIFs
2．4 Numerical examples
Chapter 3 Forecasting algorithm of stock index time series based on rational fractal model
3．1 Determination of function scaling factors
3．2 Forecast ing algorithm
3．3 Quality assessment
4 Empirical analysis and discussion
4．1．2 Results and analysis
4．2 Example 2：comparative experiments using Dow Jones industrial average index in the US
4．2．1 Data sets
4．2．2 Results and analysis
5 Conclusion
References
致谢
