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Inhaltsverzeichnis

Frontmatter

Synopsis

Abstract
Classically time series analysis has two purposes.One of these is to construct a model which fits the data and then to estimate the model’s parameters. The second object is to use the identified model for prediction.
D. Bosq

Chapter 1. Inequalities for mixing processes

Abstract
In this chapter we present some inequalities for covariances, joint densities and partial sums of stochastic discrete time processes when dependence is measured by strong mixing coefficients. The main tool is coupling with independent random variables. Some limit theorems for mixing processes are given as applications.
D. Bosq

Chapter 2. Density estimation for discrete time processes

Abstract
This chapter deals with nonparametric density estimation for sequences of correlated random variables.
D. Bosq

Chapter 3. Regression estimation and prediction for discrete time processes

Abstract
The construction and study of a nonparametric predictor are the main purpose of this chapter. In practice such a predictor is in general more efficient and more flexible than the predictors based on BOX and JENKINS method, and nearly equivalent if the underlying model is truly linear. This surprising fact will be clarified at the end of the chapter.
D. Bosq

Chapter 4. Kernel density estimation for continuous time processes

Abstract
In this chapter we investigate the problem of estimating density for continuous time processes when continuous or sampled data are available.
D. Bosq

Chapter 5. Regression estimation and prediction in continuous time

Abstract
Despite its great importance in practice, nonparametric regression estimation in continuous time has not been much studied up to now. The current chapter is perhaps the first general work on that topic.
D. Bosq

Chapter 6. The local time density estimator

Abstract
In this Chapter we use local time for constructing an unbiased estimator of density when continuous sample is available. This estimator appears to be natural since it is the density of empirical measure.
D. Bosq

Chapter 7. Implementation of nonparametric method and numerical applications

Abstract
In this final chapter we discuss practical implementation of kernel estimators and predictors and we give numerical examples with some comments. We only examine the case of discrete data.
D. Bosq

Backmatter

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