Quasi maximum likelihood estimation for strongly mixing state space models and multivariate L\'evy-driven CARMA processes
Quasi maximum likelihood estimation for strongly mixing state space models and multivariate L\'evy-driven CARMA processes
复制标题
强混合状态空间模型和多元 Levy 驱动的 CARMA 过程的准最大似然估计
DOI：
10.1214/12-ejs743
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
R. Stelzer
中科院分区：
文献类型：
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作者：
E. Schlemm;R. Stelzer
本文考虑了一般非高斯离散时间线性状态空间模型和等距离观测的多元L 'evy驱动的连续时间自回归滑动平均（MCARMA）过程的拟极大似然（QML）估计.在离散时间环境下，我们证明了在标准矩假设和状态空间模型输出过程的强混合条件下，QML估计的强相合性和渐近正态性。在本文的第二部分中，我们研究了等距采样连续时间状态空间模型的概率和分析性质，并将我们的结果从离散时间设置导出离散记录的MCARMA过程的QML估计的渐近性质。在自然可识别条件下，估计量再次一致，并渐近正态分布的任何采样频率。我们还证明了我们的方法的实用性，通过模拟研究和计量经济学的数据例子。
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.
高频采样稳定CARMA过程周期图的极限行为
影响因子：
1.4
作者：
通讯作者：
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影响因子：
1
作者：
P. Brockwell;Jens-Peter Kreiss;Tobias Niebuhr
通讯作者：
P. Brockwell;Jens-Peter Kreiss;Tobias Niebuhr
高频采样 MCARMA 模型的极限理论
影响因子：
1.2
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