Weak convergence to the matrix stochastic integral \(\int ^{1}_{0}B\,dB'\)

DOI10.1016/0047-259X(88)90039-5zbMath0629.62091MaRDI QIDQ1094062

Peter C. B. Phillips

Publication date: 1988

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

zbMATH Keywords

invariance principlesvector autoregressionsintegrated processesnear integrated time seriesvector ARIMA processesvector Brownian motionweak convergence of sample covariance matricesweak convergence to matrix stochastic integrals

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Stochastic integrals (60H05)

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Bootstrap inference in systems of single equation error correction models ⋮ Asymptotic theory of estimation of parameters in autoregressive models under general set-up of the roots ⋮ Non‐stationary autoregressive processes with infinite variance ⋮ A SIEVE BOOTSTRAP TEST FOR COINTEGRATION IN A CONDITIONAL ERROR CORRECTION MODEL ⋮ On the performance of the DHF tests against nonstationary alternatives ⋮ TIME-VARYING COINTEGRATION ⋮ Testing the Cointegrating Rank with Uncorrelated but Dependent Errors ⋮ A Stastistical Analysis of Cointegration for I(2) Variables ⋮ UNIT ROOT AND COINTEGRATING LIMIT THEORY WHEN INITIALIZATION IS IN THE INFINITE PAST ⋮ Block Bootstrap Theory for Multivariate Integrated and Cointegrated Processes

Cites Work

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• On strong invariance principles under dependence assumptions
• A maximal inequality and dependent strong laws
• Approximation theorems for independent and weakly dependent random vectors
• The Limiting Distribution of the Serial Correlation Coefficient in the Explosive Case
• Multiple Time Series Regression with Integrated Processes
• Towards a unified asymptotic theory for autoregression
• Almost sure invariance principles for partial sums of weakly dependent random variables
• Regression Theory for Near-Integrated Time Series
• Time Series Regression with a Unit Root

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