Mathematical Sciences: "Autoregressive Moving Average ModelSelection

本研究的目的之一是利用谱密度函数的参数和非参数拟合来研究ARMA模型中的模型选择。要开发一种偏差度量，它直接将ARMA模型中的参数估计与谱密度的核非参数估计进行比较，而不是对模型进行拟合，然后查看涉及残差的谱估计。要使用的特定非参数估计器是Gasser-Muller估计器，其将核加权应用于周期图并利用本地带宽选择。本课程将讨论此估计器的最佳带宽选择。将获得选择方法的理论性质，并将通过与当前方法的比较以及广泛的模拟研究来评估该标准的性能。另一个目标是与亚利桑那州立大学生物工程系的同事何杰平合作。他有一个项目的大量数据，这个项目的标题是：“预期扰动下的姿势和肌肉张力的适应”，该项目看起来是非平稳的时间序列数据，但显示了平稳的片段。然后，我们有机会使用标准技术来分析这些部分，包括上一段中开发的部分。此外，我们希望开发新的技术来分析类似的非平稳数据，例如，使用进化频谱。

One goal of this research is to study model selection in ARMA models by utilizing parametric and non-parametric fits of the spectral density function. A measure of discrepancy is to be developed which compares directly the parametric estimate in the ARMA model with a kernel non-parametric estimator of the spectral density, as opposed to fitting the model and then looking at spectrum estimates involving the residuals. The particular nonparametric estimator to be used is a Gasser-Muller estimator which applies kernel weights to the periodogram and utilizes a local bandwidth choice. Optimal bandwidth choices for this estimator will be addressed. Theoretical properties will be obtained for the selection method, and performance of this criteria will be assessed by comparisons with current methods as well as extensive simulation studies. Another goal is the collaboration with a colleague, Jeping He, in the Bioengineering Department at Arizona State University. He has a significant amount of data on a project entitled: "Adaptation in Posture and Muscle Tone in Anticipation of Perturbation" which appears to be nonstationary time series data but shows segments of stationarity. We then have the opportunity to use standard techniques in analyzing the segments including those developed in the previous paragraph. In addition we hope to develop new techniques for analyzing similar nonstationary data using, for example, the evolutionary spectrum.