Nonparametric curve estimation from time series. (English) Zbl 0697.62038

Lecture Notes in Statistics, 60. Berlin etc.: Springer-Verlag. viii, 153 p. DM 36.00 (1989).
A very frequent question in economics which is quite often asked in time series analysis is the one after the value of future observations. One wants to know whether some regularly observed economic indicator follows certain regularities; once a regularity is detected, prediction and also speculation can be based on it. There are more prediction problems than just this one: in medicine, dike and water resources management, prediction of future values of time series are important tools for planning and inference. A common statistical approach for solving such problems is to postulate a certain parametric model.
This book constructs bridges between two major themes in mathematical statistics: Time series and smoothing. In the last years, emphasis of statistics has been more on the theoretical properties of time series and curve estimation. As a consequence both themes have been intensively studied from a mathematical point of view. The contents are the following: 1. Introduction; 2. Dependent samples; 3. Regression estimation and time series analysis; 4. Density estimation; 5. Distribution and hazard function estimation; 6. How to select the smoothing parameter.
The book shows the enormous increase of interest in nonparametric curve estimation, as well as in parameter free approaches. The purpose of this very useful and interesting monograph is to study nonparametric smoothing techniques for time series and to provide mathematical tools for nonparametric estimation under general dependence assumptions.
Reviewer: T.Postelnicu


62G05 Nonparametric estimation
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62-02 Research exposition (monographs, survey articles) pertaining to statistics
62M20 Inference from stochastic processes and prediction