Long-Range Dependence and Self-Similarity
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portes grátis
Long-Range Dependence and Self-Similarity
Taqqu, Murad S. (Boston University); Pipiras, Vladas (University of North Carolina, Chapel Hill)
Cambridge University Press
04/2017
688
Dura
Inglês
9781107039469
15 a 20 dias
Real-world time series rarely satisfy simple assumptions, often exhibiting long-range dependence. Ignoring this undermines accurate detection of trends and other important behavior. This text for graduate students and researchers in statistics and probability is also a reference for specialists in fields such as economics, finance, and hydrology.
List of abbreviations; Notation; Preface; 1. A brief overview of times series and stochastic processes; 2. Basics of long-range dependence and self-similarity; 3. Physical models for long-range dependence and self-similarity; 4. Hermite processes; 5. Non-central and central limit theorems; 6. Fractional calculus and integration of deterministic functions with respect to FBM; 7. Stochastic integration with respect to fractional Brownian motion; 8. Series representations of fractional Brownian motion; 9. Multidimensional models; 10. Maximum likelihood estimation methods; Appendix A. Auxiliary notions and results; Appendix B. Integrals with respect to random measures; Appendix C. Basics of Malliavin calculus; Appendix D. Other notes and topics; Bibliography; Index.
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Real-world time series rarely satisfy simple assumptions, often exhibiting long-range dependence. Ignoring this undermines accurate detection of trends and other important behavior. This text for graduate students and researchers in statistics and probability is also a reference for specialists in fields such as economics, finance, and hydrology.
List of abbreviations; Notation; Preface; 1. A brief overview of times series and stochastic processes; 2. Basics of long-range dependence and self-similarity; 3. Physical models for long-range dependence and self-similarity; 4. Hermite processes; 5. Non-central and central limit theorems; 6. Fractional calculus and integration of deterministic functions with respect to FBM; 7. Stochastic integration with respect to fractional Brownian motion; 8. Series representations of fractional Brownian motion; 9. Multidimensional models; 10. Maximum likelihood estimation methods; Appendix A. Auxiliary notions and results; Appendix B. Integrals with respect to random measures; Appendix C. Basics of Malliavin calculus; Appendix D. Other notes and topics; Bibliography; Index.
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
