Nonparametric Statistics for Stochastic Processes: Estimation and Prediction (Lecture Notes in Statistics, Vol 110)

This work discusses discrete time and continuous time, with emphasis on the kernel methods. Recent results concerning optimal and superoptimal convergence rates are presented, and the implementation of the method is discussed. This Book Provides A Mathematically Rigorous Treatment Of The Theory Of Nonparametric Estimation And Prediction For Stochastic Processes. It Discusses Discrete Time And Continuous Time, And The Emphasis Is On The Kernel Methods. Several New Results Are Presented Concerning Optimal And Superoptimal Convergence Rates. How To Implement The Method Is Discussed In Detail And Several Numerical Results Are Presented. This Book Will Be Of Interest To Specialists In Mathematical Statistics And To Those Who Wish To Apply These Methods To Practical Problems Involving Time Series Analysis. Contents: Synopsis -- Inequalities For Mixing Processes -- Density Estimation For Discrete Time Processes -- Regression Estimation And Prediction For Discrete Time Processes -- Density Estimation For Continuous Time Processes -- Regression Estimates And Prediction In Continuous Time -- Appendix -- Bibliography -- Index. D. Bosq. Includes Bibliographical References And Index. This book is devoted to the theory and applications of nonparametric functional estimation and prediction. The second edition is extensively revised and contains two new chapters. One discusses the surprising local time density estimator. The other gives a detailed account of the implementation of nonparametric methods and practical examples in economics, finance, and physics. A comparison with ARMA and ARCH methods shows the efficiency of nonparametric forecasting. The book assumes a knowledge of classical probability theory and statistics.