Time series regression on integrated continuous-time processes with heavy and light tails
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. «
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... »
Keywords:
Brownian motion, central limit theorem, cointegration, continuous time, Lévy process, multivariate regular variation, Ornstein-Uhlenbeck process, point process, t-ratio statistic, Wald statistic.