TIME SERIES REGRESSION ON INTEGRATED CONTINUOUS-TIME PROCESSES WITH HEAVY AND LIGHT TAILS
论文提出了连续时间下的协整模型，用最小二乘法估计回归参数，证明了估计量的一致性并推导了其渐近分布，适用于处理重尾和轻尾数据的金融经济时间序列分析。
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.