Low Redundancy Estimation of Correlation Matrices for Time Series Using Triangular Bounds

2018 ◽  
pp. 458-470 ◽  
Author(s):  
Erik Scharwächter ◽  
Fabian Geier ◽  
Lukas Faber ◽  
Emmanuel Müller
Keyword(s):  
Time Series ◽  
Correlation Matrices

scholarly journals Versatile Harmonic Tidal Analysis: Improvements and Applications

2009 ◽  
Vol 26 (4) ◽  
pp. 806-817 ◽  
Author(s):  
M. G. G. Foreman ◽  
J. Y. Cherniawsky ◽  
V. A. Ballantyne
Keyword(s):  
Time Series ◽  
Input Data ◽  
Computer Software ◽  
Temperature Time Series ◽  
Correlation Matrices ◽  
Ocean Sciences ◽  
Harmonic Tidal Analysis ◽  
Direct Incorporation ◽  
Temperature Time ◽  
Selection Of

Abstract New computer software that permits more versatility in the harmonic analysis of tidal time series is described and tested. Specific improvements to traditional methods include the analysis of randomly sampled and/or multiyear data; more accurate nodal correction, inference, and astronomical argument adjustments through direct incorporation in the least squares matrix; multiconstituent inferences from a single reference constituent; correlation matrices and error estimates that facilitate decisions on the selection of constituents for the analysis; and a single program that analyzes one- or two-dimensional time series. This new methodology is evaluated through comparisons with results from old techniques and then applied to two problems that could not have been accurately solved with older software. They are (i) the analysis of ocean station temperature time series spanning 25 yr, and (ii) the analysis of satellite altimetry from a ground track whose proximity to land has led to significant data dropout. This new software is free as part of the Institute of Ocean Sciences (IOS) Tidal Package and can be downloaded, along with sample input data and an explanatory readme file.

RANDOM MATRIX THEORY AND FINANCIAL CORRELATIONS

2000 ◽  
Vol 03 (03) ◽  
pp. 391-397 ◽  
Author(s):  
LAURENT LALOUX ◽  
PIERRE CIZEAU ◽  
MARC POTTERS ◽  
JEAN-PHILIPPE BOUCHAUD
Keyword(s):  
Time Series ◽  
Risk Management ◽  
Theoretical Prediction ◽  
Correlation Matrix ◽  
Matrix Theory ◽  
Financial Time Series ◽  
Statistical Structure ◽  
Correlation Matrices ◽  
Financial Time ◽  
Remarkable Agreement

We show that results from the theory of random matrices are potentially of great interest when trying to understand the statistical structure of the empirical correlation matrices appearing in the study of multivariate financial time series. We find a remarkable agreement between the theoretical prediction (based on the assumption that the correlation matrix is random) and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the S&P500 (or other major markets). Finally, we give a specific example to show how this idea can be sucessfully implemented for improving risk management.

FINANCIAL AND OTHER SPATIO-TEMPORAL TIME SERIES: LONG-RANGE CORRELATIONS AND SPECTRAL PROPERTIES

2005 ◽  
Vol 16 (11) ◽  
pp. 1733-1743 ◽  
Author(s):  
A. CHAKRABORTI ◽  
M. S. SANTHANAM
Keyword(s):  
Time Series ◽  
Random Processes ◽  
Coupled Map Lattices ◽  
Fluctuation Analysis ◽  
Correlation Matrices ◽  
Long Range Correlations ◽  
Time Correlations ◽  
Long Time ◽  
Spatio Temporal ◽  
Detrended Fluctuation

In this paper, we review some of the properties of financial and other spatio-temporal time series generated from coupled map lattices, GARCH(1,1) processes and random processes (for which analytical results are known). We use the Hurst exponent (R/S analysis) and detrended fluctuation analysis as the tools to study the long-time correlations in the time series. We also compare the eigenvalue properties of the empirical correlation matrices, especially in relation to random matrices.

scholarly journals Brain networks, dimensionality, and global signal averaging in resting-state fMRI: Hierarchical network structure results in low-dimensional spatiotemporal dynamics

2017 ◽  
Author(s):  
Stephen J Gotts ◽  
Adrian W. Gilmore ◽  
Alex Martin
Keyword(s):  
Time Series ◽  
Resting State ◽  
Brain Networks ◽  
Principal Component ◽  
Resting State Fmri ◽  
Network Clustering ◽  
Correlation Matrices ◽  
Alternative Means ◽  
Low Dimensional ◽  
Effective Dimensionality

ABSTRACTOne of the most controversial practices in resting-state fMRI functional connectivity studies is whether or not to regress out the global average brain signal (GS) during artifact removal. Some groups have argued that it is absolutely essential to regress out the GS in order to fully remove head motion, respiration, and other global imaging artifacts. Others have argued that removing the GS distorts the resulting correlation matrices, qualitatively alters the results of group comparisons, and impairs relationships to behavior. At the core of this argument is the assessment of dimensionality in terms of the number of brain networks with uncorrelated time series. If the dimensionality is high, then the distortions due to GS removal could be effectively negligible. In the current paper, we examine the dimensionality of resting-state fMRI data using principal component analyses (PCA) and network clustering analyses. In two independent datasets (Set 1: N=62, Set 2: N=32), scree plots of the eigenvalues level off at or prior to 10 principal components, with prominent elbows at 3 and 7 components. While network clustering analyses have previously demonstrated that numerous networks can be distinguished with high thresholding of the voxel-wise correlation matrices, lower thresholding reveals a lower-dimensional hierarchical structure, with the first prominent branch at 2 networks (corresponding to the previously described “task-positive”/“task-negative” distinction) and further stable subdivisions at 4, 7 and 17. Since inter-correlated time series within these larger branches do not cancel to zero when averaged, the hierarchical nature of the correlation structure results in much lower effective dimensionality. Consistent with this, partial correlation analyses revealed that network-specific variance remains present in the GS at each level of the hierarchy, accounting for at least 18-20% of the overall GS variance in each dataset. These results demonstrate that GS regression is expected to remove substantial portions of neurogenic brain signals along with artifacts. We highlight alternative means of controlling for residual global artifacts when not removing the GS.

On the asymptotic behavior of the eigenvalue distribution of block correlation matrices of high-dimensional time series

2021 ◽  
Author(s):  
Philippe Loubaton ◽  
Xavier Mestre
Keyword(s):  
Time Series ◽  
Correlation Matrix ◽  
Cross Correlation ◽  
Eigenvalue Distribution ◽  
Time Lags ◽  
Correlation Matrices ◽  
Consecutive Time ◽  
Spectral Statistics ◽  
Mutually Independent ◽  
Scalar Time Series

We consider linear spectral statistics built from the block-normalized correlation matrix of a set of [Formula: see text] mutually independent scalar time series. This matrix is composed of [Formula: see text] blocks. Each block has size [Formula: see text] and contains the sample cross-correlation measured at [Formula: see text] consecutive time lags between each pair of time series. Let [Formula: see text] denote the total number of consecutively observed windows that are used to estimate these correlation matrices. We analyze the asymptotic regime where [Formula: see text] while [Formula: see text], [Formula: see text]. We study the behavior of linear statistics of the eigenvalues of this block correlation matrix under these asymptotic conditions and show that the empirical eigenvalue distribution converges to a Marcenko–Pastur distribution. Our results are potentially useful in order to address the problem of testing whether a large number of time series are uncorrelated or not.

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