Towards a general theory for nonlinear locally stationary processes
Towards a general theory for nonlinear locally stationary processes
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DOI：
10.3150/17-bej1011
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发表时间：
2017-04
期刊：
影响因子：
1.5
通讯作者：
R. Dahlhaus;S. Richter;W. Wu
中科院分区：
文献类型：
--
作者：
R. Dahlhaus;S. Richter;W. Wu
本文提出了基于平稳近似和平稳导数的局部平稳过程的一般理论。对于服从平稳近似和导数展开的过程，证明了大数定律、中心极限定理以及确定性和随机偏置展开。此外，还证明了该方法适用于一般的非线性非平稳马尔可夫模型。此外，本文还应用所得结果推导了该模型中参数曲线的极大似然估计的渐近性质。
In this paper some general theory is presented for locally stationary processes based on the stationary approximation and the stationary derivative. Laws of large numbers, central limit theorems as well as deterministic and stochastic bias expansions are proved for processes obeying an expansion in terms of the stationary approximation and derivative. In addition it is shown that this applies to some general nonlinear non-stationary Markov-models. In addition the results are applied to derive the asymptotic properties of maximum likelihood estimates of parameter curves in such models.