TIME SERIES REGRESSION ON INTEGRATED CONTINUOUS-TIME PROCESSES WITH HEAVY AND LIGHT TAILS
The paper presents a cointegration model in continuous time, where the linear combinations of the integrated processes are modeled by a multivariate Ornstein–Uhlenbeck process. The integrated processes are defined as vector-valued Lévy processes with an additional noise term. Hence, if we observe the process at discrete time points, we obtain a multiple regression model. As an estimator for the regression parameter we use the least squares estimator. We show that it is a consistent estimator and derive its asymptotic behavior. The limit distribution is a ratio of functionals of Brownian motions and stable Lévy processes, whose characteristic triplets have an explicit analytic representation. In particular, we present the Wald and the <italic>t</italic>-ratio statistic and simulate asymptotic confidence intervals. For the proofs we derive some central limit theorems for multivariate Ornstein–Uhlenbeck processes.
Year of publication: |
2013
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Authors: | Fasen, Vicky |
Published in: |
Econometric Theory. - Cambridge University Press. - Vol. 29.2013, 01, p. 28-67
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Publisher: |
Cambridge University Press |
Description of contents: | Abstract [journals.cambridge.org] |
Saved in:
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