Mathematical Sciences: "Autoregressive Moving Average ModelSelection

数学科学：《自回归移动平均模型选择》

• 批准号: 9631496
• 负责人: Kathryn Prewitt
• 金额: $ 1.8万
• 依托单位: Arizona State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-01 至 1998-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9631496&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Autoregressive; Moving; Average

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.

本研究的目标之一是利用谱密度函数的参数拟合和非参数拟合来研究ARMA模型中的模型选择。将开发一种差异度量方法，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，而不是拟合模型然后查看涉及残差的谱估计。要使用的特殊非参数估计器是Gasser-Muller估计器，它将核权重应用于周期图并利用局部带宽选择。将讨论该估计器的最佳带宽选择。将获得选择方法的理论特性，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（jping He）合作。他在一个项目中有大量的数据，名为“预测扰动时的姿势和肌肉张力的适应”，这似乎是非平稳的时间序列数据，但显示出平稳的片段。然后，我们有机会使用标准技术来分析这些部分，包括在前一段中开发的部分。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，使用进化谱。