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Estimation du comportement asymptotique des autocovariances et autocorrelations empiriques de processus multivariéeas
Author(s) -
Et Alain Berlinet,
Franco Christian
Publication year - 1999
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3316109
Subject(s) - estimator , mathematics , series (stratigraphy) , range (aeronautics) , covariance , sample (material) , statistics , physics , composite material , thermodynamics , paleontology , materials science , biology
Abstract Statistics based on the sample autocovariances are widely used in time‐series analysis. Estimators of the asymptotic covariance between the sample autocovariances are commonly derived from the so‐called Bartlett's formula. However, this formula essentially holds for linear processes. This entails that for a wide range of nonlinear time series the above‐mentioned estimators are not suitable. In this paper the behaviour of an alternative estimator is studied within the framework of centered or uncentered multivariate strongly mixing processes. Applications to differential functions of sample autocovariances, such as the sample autocorrelations, are considered.