标题： 强混合状态空间模型和多维Lévy驱动CARMA过程的准最大似然估计 显示英文标题

标题： Quasi maximum likelihood estimation for strongly mixing state space models and multivariate Lévy-driven CARMA processes

摘要： 我们考虑一般非高斯离散时间线性状态空间模型的准最大似然（QML）估计，以及等间隔观测的多变量Lévy驱动连续时间自回归移动平均（MCARMA）过程。 在离散时间设置中，我们在标准矩假设和状态空间模型输出过程的强混合条件下，证明了QML估计量的一致性和渐近正态性。 在论文的第二部分，我们研究了等间隔采样的连续时间状态空间模型的概率和分析性质，并将离散时间设置中的结果应用于推导离散记录的MCARMA过程的QML估计量的渐近性质。 在自然可识别条件下，对于任何采样频率，估计量再次是一致的且渐近正态分布的。 我们还通过一个模拟研究和一个来自计量经济学的数据示例展示了我们方法的实际适用性。 显示英文摘要

摘要： We consider quasi maximum likelihood (QML) estimation for general non-Gaussian discrete-ime linear state space models and equidistantly observed multivariate L\'evy-driven continuoustime autoregressive moving average (MCARMA) processes. In the discrete-time setting, we prove strong consistency and asymptotic normality of the QML estimator under standard moment assumptions and a strong-mixing condition on the output process of the state space model. In the second part of the paper, we investigate probabilistic and analytical properties of equidistantly sampled continuous-time state space models and apply our results from the discrete-time setting to derive the asymptotic properties of the QML estimator of discretely recorded MCARMA processes. Under natural identifiability conditions, the estimators are again consistent and asymptotically normally distributed for any sampling frequency. We also demonstrate the practical applicability of our method through a simulation study and a data example from econometrics.