@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.}, }