Robust estimation for the covariance matrix of multivariate time series based on normal mixtures

2013 ◽  
Vol 57 (1) ◽  
pp. 125-140 ◽  
Author(s):  
Byungsoo Kim ◽  
Sangyeol Lee
Keyword(s):  
Time Series ◽  
Covariance Matrix ◽  
Robust Estimation ◽  
Multivariate Time Series ◽  
Normal Mixtures

scholarly journals The Nyquist Issue in Linear Inverse Modeling

2019 ◽  
Vol 147 (4) ◽  
pp. 1341-1349 ◽  
Author(s):  
Cécile Penland
Keyword(s):  
Time Series ◽  
Markov Process ◽  
Covariance Matrix ◽  
Inverse Modeling ◽  
Degrees Of Freedom ◽  
Multivariate Time Series ◽  
Statistical Technique ◽  
Natural Mode ◽  
Dimensional System ◽  
Best Fit

Abstract Linear inverse modeling (LIM) is a statistical technique based on covariance statistics that estimates the best-fit linear Markov process to a multivariate time series. An integral, often-ignored part of the technique is a test of whether or not the linear assumptions are valid. One test for linearity is the so-called tau test. While this test can be trusted when it passes, it sometimes fails when it ought to pass. In this article, we discuss one of the reasons for spurious failure, the “Nyquist issue,” which occurs when the lagged covariance matrix used in the analysis is numerically performed at a lag greater than or nearly equal to half the period of a natural mode of variability represented in the time series. As an illustration relevant to a system with many degrees of freedom, but simple enough to solve analytically, we consider a four-dimensional system consisting of two modal pairs. Within this framework, we suggest one solution that can be applied if the time series are long enough. It is hoped that awareness of this issue can prevent misinterpretation of LIM results.

scholarly journals Wind Turbine Gearbox Fault Diagnosis Method Based on Riemannian Manifold

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Shoubin Wang ◽  
Xiaogang Sun ◽  
Chengwei Li
Keyword(s):  
Time Series ◽  
Riemannian Manifold ◽  
Fault Diagnosis ◽  
Wind Turbine ◽  
Covariance Matrix ◽  
Multivariate Time Series ◽  
Time Sequence ◽  
Mechanical Equipment ◽  
Wind Turbine Gearbox ◽  
Diagnosis Method

As multivariate time series problems widely exist in social production and life, fault diagnosis method has provided people with a lot of valuable information in the finance, hydrology, meteorology, earthquake, video surveillance, medical science, and other fields. In order to find faults in time sequence quickly and efficiently, this paper presents a multivariate time series processing method based on Riemannian manifold. This method is based on the sliding window and uses the covariance matrix as a descriptor of the time sequence. Riemannian distance is used as the similarity measure and the statistical process control diagram is applied to detect the abnormity of multivariate time series. And the visualization of the covariance matrix distribution is used to detect the abnormity of mechanical equipment, leading to realize the fault diagnosis. With wind turbine gearbox faults as the experiment object, the fault diagnosis method is verified and the results show that the method is reasonable and effective.

Robust estimation for the covariance matrix of multi-variate time series

2010 ◽  
Vol 32 (5) ◽  
pp. 469-481 ◽  
Author(s):  
Byungsoo Kim ◽  
Sangyeol Lee
Keyword(s):  
Time Series ◽  
Covariance Matrix ◽  
Robust Estimation
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