Nonparametric Statistics for Stochastic Processes: Estimation and Prediction

This book is devoted to the theory and applications of nonparametic functional estimation and prediction. Chapter 1 provides an overview of inequalities and limit theorems for strong mixing processes. Density and regression estimation in discrete time are studied in Chapter 2 and 3. The special rates of convergence which appear in continuous time are presented in Chapters 4 and 5. This second edition is extensively revised and it contains two new chapters. Chapter 6 discusses the surprising local time density estimator. Chapter 7 gives a detailed account of implementation of nonparametric method and practical examples in economics, finance and physics. Comarison with ARMA and ARCH methods shows the efficiency of nonparametric forecasting. The prerequisite is a knowledge of classical probability theory and statistics. Denis Bosq is Professor of Statistics at the Unviersity of Paris 6 (Pierre et Marie Curie). He is Editor-in-Chief of "Statistical Inference for Stochastic Processes" and an editor of "Journal of Nonparametric Statistics". He is an elected member of the International Statistical Institute. He has published about 90 papers or works in nonparametric statistics and four books.

Recently new developments have taken place in the theory of nonpara- metric statistics for stochastic processes. Optimal asymptotic results have been obtained and special behaviour of estimators and predictors in con- tinuous time has been pointed out. This book is devoted to these questions. It also gives some indica- tions about implementation of nonparametric methods and comparison with parametric ones, including numerical results. Ma.ny of the results presented here are new and have not yet been published, expecially those in Chapters IV, V and VI. Apart from some improvements and corrections, this second edition con- tains a new chapter dealing with the use of local time in density estimation. I am grateful to W. Hardie, Y. Kutoyants, F. Merlevede and G. Oppenheim who made important remarks that helped much to improve the text. I am greatly indebted to B. Heliot for her careful reading of the manus- cript which allowed to ameliorate my english. I also express my gratitude to D. Blanke, L. Cotto and P. Piacentini who read portions of the manuscript and made some useful suggestions. I also thank M. Gilchrist and J. Kimmel for their encouragements. My aknowlegment also goes to M. Carbon, M. Delecroix, B. Milcamps and J .M. Poggi who authorized me to reproduce their numerical results. My greatest debt is to D. Tilly who prepared the typescript with care and efficiency. Preface to the second edition This edition contains some improvements and corrections, and two new chapters.

Inequalities for Mixing Processes.- Density Estimation for Discrete Time Processes.- Regression Estimation and Prediction for Discrete Time Processes.- Kernel Density Estimation for Continuous Time Processes.- Regression Estimation and Prediction in Continuous Time.- The Local Time Density Estimator.- Implementation of Nonparametric Method and Numerical Appliations.