On functional limit theorems for multivariate linear processes with applications to sequential estimation

For a multivariate linear process with martingale difference innovations, we prove a random functional limit theorem and propose an almost sure consistent estimator for the limiting covariance matrix. We also consider sequential estimation of the mean vector of the process.

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Bibliographic Details
Published inJournal of statistical planning and inference Vol. 83; no. 1; pp. 11 - 23
Main Authors Fakhre-Zakeri, Issa, Lee, Sangyeol
Format Journal Article
LanguageEnglish
Published Lausanne Elsevier B.V 2000
New York,NY Elsevier Science
Amsterdam
Subjects
Exact sciences and technology
Functional central limit theorem
Limit theorems
Linear process
Martingale
Mathematics
Mixing in the sense of Renyi
Probability and statistics
Probability theory and stochastic processes
Random indices
Sciences and techniques of general use
Sequential estimation
Sequential methods
Statistics
Stochastic processes
62L12
Linear process
Mixing in the sense of Renyi
60G10
60G42
secondary 60G40
primary 60F17
Functional central limit theorem
Martingale
Random indices
Sequential estimation
Multivariate process
Innovation process
Consistent estimator
Covariance matrix
Stochastic process
Limit theorem
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Summary:For a multivariate linear process with martingale difference innovations, we prove a random functional limit theorem and propose an almost sure consistent estimator for the limiting covariance matrix. We also consider sequential estimation of the mean vector of the process.
ISSN:0378-3758
1873-1171
DOI:10.1016/S0378-3758(99)00054-3