@article{Vicky_Fasen_CI_1.pdf,
	author = {Fasen, V.},
	title = {Time series regression on integrated continuous-time processes with heavy and light tails},

        journal = {Econometric Theory},
	year = {2013},

        volume = {29},


        number = {1},

        pages = {28-67},


        doi = {10.1017/S0266466612000217},

        language = {en},

        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.},

        keywords = {Brownian motion, central limit theorem, cointegration, continuous time, Lévy process, multivariate regular variation, Ornstein-Uhlenbeck process, point process, t-ratio statistic, Wald statistic.},

	
}