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TIME SERIES REGRESSION ON INTEGRATED CONTINUOUS-TIME PROCESSES WITH HEAVY AND LIGHT TAILS

Published online by Cambridge University Press:  06 July 2012

Vicky Fasen
Vicky Fasen*
Affiliation:
ETH Zürich
*
*Address correspondance to Vicky Fasen, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland; e-mail: vicky.fasen@math.ethz.ch.
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Abstract

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 t-ratio statistic and simulate asymptotic confidence intervals. For the proofs we derive some central limit theorems for multivariate Ornstein–Uhlenbeck processes.

Type
ARTICLES
Information
Econometric Theory , Volume 29 , Issue 1 , February 2013 , pp. 28 - 67
Copyright
Copyright © Cambridge University Press 2012 

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Footnotes

My special thanks go to Holger Rootzén, Carl Lindberg, and their colleagues at the Department of Mathematical Statistics at Chalmers University of Technology for their hospitality during my visit in fall 2008 and, in particular, for calling my attention to the topic of cointegration. I take pleasure in thanking Christoph Ferstl, who has written his diploma thesis (Ferstl, 2009) at the Technische Universität München using some preliminary notes of some earlier results, for having patience with my research progress. Furthermore, I am deeply grateful to some anonymous referees and to Claudia Klüppelberg for some useful comments. Finally, I thank John Nolan for providing me with the toolbox STABLE for Matlab.

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