TY  - BOOK
AU  - Fasen,Vicky Maria
TI  - Time series regression on integrated continuous-time processes with heavy and light tails
AV  - HB139.T52 ECO 
PY  - 2013///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Time series regression
N2  - 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
UR  - 10.1017/S0266466612000217
ER  -