Limits of the Cross‐Correlation Function in the Analysis of Short Time Series

2001 ◽  
Vol 113 (779) ◽  
pp. 86-97 ◽  
Author(s):  
Roberto Vio ◽  
Willem Wamsteker
Keyword(s):  
Time Series ◽  
Correlation Function ◽  
Cross Correlation ◽  
Cross Correlation Function ◽  
Short Time Series ◽  
The Cross ◽  
Short Time

scholarly journals On the Construction of Bootstrap Confidence Intervals for Estimating the Correlation Between Two Time Series Not Sampled on Identical Time Points

2021 ◽  
Author(s):  
Mario Trottini ◽  
Isabel Vigo ◽  
Juan A. Vargas-Alemañy ◽  
David García-García ◽  
José Fernández
Keyword(s):  
Time Series ◽  
Correlation Function ◽  
Confidence Intervals ◽  
Cross Correlation ◽  
Asymptotic Properties ◽  
Cross Correlation Function ◽  
Bootstrap Confidence Intervals ◽  
Bootstrap Methods ◽  
Time Points ◽  
The Cross

AbstractTwo important issues characterize the design of bootstrap methods to construct confidence intervals for the correlation between two time series sampled (unevenly or evenly spaced) on different time points: (i) ordinary block bootstrap methods that produce bootstrap samples have been designed for time series that are coeval (i.e., sampled on identical time points) and must be adapted; (ii) the sample Pearson correlation coefficient cannot be readily applied, and the construction of the bootstrap confidence intervals must rely on alternative estimators that unfortunately do not have the same asymptotic properties. In this paper it is argued that existing proposals provide an unsatisfactory solution to issue (i) and ignore issue (ii). This results in procedures with poor coverage whose limitations and potential applications are not well understood. As a first step to address these issues, a modification of the bootstrap procedure underlying existing methods is proposed, and the asymptotic properties of the estimator of the correlation are investigated. It is established that the estimator converges to a weighted average of the cross-correlation function in a neighborhood of zero. This implies a change in perspective when interpreting the results of the confidence intervals based on this estimator. Specifically, it is argued that with the proposed modification of the bootstrap, the existing methods have the potential to provide a useful lower bound for the absolute correlation in the non-coeval case and, in some special cases, confidence intervals with approximately the correct coverage. The limitations and implications of the results presented are demonstrated with a simulation study. The extension of the proposed methodology to the problem of estimating the cross-correlation function is straightforward and is illustrated with a real data example. Related applications include the estimation of the autocorrelation function and the periodogram of a time series.

Simultaneous Measurement of Temperature and Velocity Using µPIV

2006 ◽  
Author(s):  
Pramod Chamarthy ◽  
Steven T. Wereley ◽  
Suresh V. Garimella
Keyword(s):  
Brownian Motion ◽  
Correlation Function ◽  
Cross Correlation ◽  
Cross Correlation Function ◽  
Motion Information ◽  
Peak Broadening ◽  
Constant Temperature Water Bath ◽  
Gravity Driven ◽  
The Cross ◽  
Gravity Driven Flow

In μPIV, for a uniform velocity field the displacement of the cross-correlation function gives the velocity of the fluid and the broadening of the peak-width represents the amount of Brownian motion present. In the presence of a linear or a parabolic shear, the shape of the cross-correlation function would have both the Brownian motion information as well as the velocity distribution information. In the present work, the broadening of the cross-correlation function caused by the velocity gradient was subtracted from the total peak broadening in order to isolate the Brownian motion information and thus infer temperature. To the authors' knowledge, this technique has not been applied to measure the temperature of a moving fluid. The experiments were conducted in a gravity driven flow through a tube surrounded by a constant temperature water bath.

scholarly journals Improving the shape of the cross-correlation function for leak detection in a plastic water distribution pipe using acoustic signals

2017 ◽  
Vol 127 ◽  
pp. 24-33 ◽  
Author(s):  
Yan Gao ◽  
Michael J. Brennan ◽  
Yuyou Liu ◽  
Fabrício C.L. Almeida ◽  
Phillip F. Joseph
Keyword(s):  
Correlation Function ◽  
Water Distribution ◽  
Cross Correlation ◽  
Leak Detection ◽  
Acoustic Signals ◽  
Cross Correlation Function ◽  
The Cross

Damage Detection Based on the Cross Correlation Function Amplitude Vector and its Application to the ASCE Benchmark Structure

2007 ◽  
Vol 353-358 ◽  
pp. 2317-2320 ◽  
Author(s):  
Zhe Feng Yu ◽  
Zhi Chun Yang
Keyword(s):  
Correlation Function ◽  
Damage Detection ◽  
Structural Damage ◽  
Cross Correlation ◽  
Relative Difference ◽  
Random Excitation ◽  
Cross Correlation Function ◽  
Vibration Responses ◽  
Specific Frequency ◽  
The Cross

A new method for structural damage detection based on the Cross Correlation Function Amplitude Vector (CorV) of the measured vibration responses is presented. Under a stationary random excitation with a specific frequency spectrum, the CorV of the structure only depends on the frequency response function matrix of the structure, so the normalized CorV has a specific shape. Thus the damage can be detected and located with the correlativity and the relative difference between CorVs of the intact and damaged structures. With the benchmark problem sponsored by ASCE Task Group on Structural Health Monitoring, the CorV is proved an effective approach to detecting the damage in structures subject to random excitations.

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