Weak convergence to the matrix stochastic integral \(\int ^{1}_{0}B\,dB'\)
type: Item
instance of: scholarly article
title: Weak convergence to the matrix stochastic integral \(\int ^{1}_{0}B\,dB'\)
zbMATH Open document ID: 0629.62091
DOI: 10.1016/0047-259X(88)90039-5
published in: Journal of Multivariate Analysis
publication date: 1988-01-01T00:00:00Z
review text: The asymptotic theory of regression with integrated processes of the ARIMA type frequently involves weak convergence to stochastic integrals of the form \(\int^{1}_{0}W dW\), where W(r) is standard Brownian motion. In multiple regressions and vector autoregressions with vector ARIMA processes, the theory involves weak convergence to matrix stochastic integrals of the form \(\int^{1}_{0}B dB'\), where B(r) is vector Brownian motion with a non-scalar covariance matrix. This paper studies the weak convergence of sample covariance matrices to \(\int^{1}_{0}B dB'\) under quite general conditions. The theory is applied to vector autoregressions with integrated processes.
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60H05
zbMATH DE Number: 4024573
zbMATH Keywords: invariance principles
zbMATH Keywords: near integrated time series
zbMATH Keywords: vector ARIMA processes
zbMATH Keywords: weak convergence to matrix stochastic integrals
zbMATH Keywords: vector Brownian motion
zbMATH Keywords: weak convergence of sample covariance matrices
zbMATH Keywords: vector autoregressions
zbMATH Keywords: integrated processes
author: Peter C. B. Phillips
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4024573