Estimation of the Dominating Frequency for Stationary and Nonstationary Fractional Autoregressive Models
Estimation of the Dominating Frequency for Stationary and Nonstationary Fractional Autoregressive Models
复制标题
稳态和非稳态分数自回归模型的主频率估计
DOI：
--
复制
发表时间：
2000
期刊：
影响因子：
--
通讯作者：
Sucharita Ghosh
中科院分区：
文献类型：
--
作者：
J. Beran;Sucharita Ghosh
本研究的动机是对早产儿某些生理系列的研究。问题是该序列是否表现出具有一定支配期的周期性波动。观测序列是非平稳的和/或具有长期依赖性。假设的模型是一个高斯过程Xt，其月差Yt = (1 - B)mXt是平稳的，其谱密度f可能在原点有一个极点（或零）。本文讨论的问题是在开放区间（0,π）中f达到最大局部最大值的频率ωmax的估计。假设过程Xt属于Beran（1995）定义的一类参数模型，以参数向量θ为特征。给出了ωmax的一个估计量，并推导了ωmax的渐近分布，θ用极大似然估计。特别是，从数据中估计m和模拟长内存的分数阶差分参数。模型选择也被纳入。因此，在提议的框架内，获得了一个数据驱动的过程，可以应用于主要兴趣是估计主导频率的情况。仿真研究表明了该方法的有限样本特性。特别是对于短序列，如果局部最大值出现在原点附近，则ωmax的估计是困难的。研究结果由两个数据例子来说明，这些数据例子推动了这项研究。
This paper was motivated by the investigation of certain physiological series for premature infants. The question was whether the series exhibit periodic fluctuations with a certain dominating period. The observed series are nonstationary and/or have long‐range dependence. The assumed model is a Gaussian process Xt whose mth difference Yt = (1 −B)mXt is stationary with a spectral density f that may have a pole (or a zero) at the origin. the problem addressed in this paper is the estimation of the frequency ωmax where f achieves the largest local maximum in the open interval (0, π). The process Xt is assumed to belong to a class of parametric models, characterized by a parameter vector θ, defined in Beran (1995). An estimator of ωmax is proposed and its asymptotic distribution is derived, with θ being estimated by maximum likelihood. In particular, m and a fractional differencing parameter that models long memory are estimated from the data. Model choice is also incorporated. Thus, within the proposed framework, a data driven procedure is obtained that can be applied in situations where the primary interest is in estimating a dominating frequency. A simulation study illustrates the finite sample properties of the method. In particular, for short series, estimation of ωmax is difficult, if the local maximum occurs close to the origin. The results are illustrated by two of the data examples that motivated this research.