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Likelihood-Based Inference in Cointegrated Vector Autoregressive Models$
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Søren Johansen

Print publication date: 1995

Print ISBN-13: 9780198774501

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198774508.001.0001

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(p.239) Weak Convergence of Probability Measures on Rp and C[0,1]

(p.239) Weak Convergence of Probability Measures on Rp and C[0,1]

Likelihood-Based Inference in Cointegrated Vector Autoregressive Models

Søren Johansen

Oxford University Press

The purpose of this appendix is to explain the concept of weak convergence on C[0,1], the space of continuous functions on the unit interval [0,1]. It explains what is behind the formulae involving Brownian motion and stochastic integrals, which appear in the discussion of the limit distributions in cointegration theory. We discuss the existence of stochastic processes like Brownian motion, and find distributions of suitable functionals of Brownian motion using the continuous mapping theorem.

Keywords:   Brownian motion, continuous mapping theorem, stochastic integral, weak convergence

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