Conditional adaptive Bayesian spectral analysis of replicated multivariate time series

2021 ◽  
Author(s):  
Zeda Li ◽  
Scott A. Bruce ◽  
Clinton J. Wutzke ◽  
Yang Long
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Multivariate Time Series

MULTIVARIATE SPECTRAL ANALYSIS USING HILBERT WAVELET PAIRS

2004 ◽  
Vol 02 (04) ◽  
pp. 567-587 ◽  
Author(s):  
BRANDON WHITCHER ◽  
PETER F. CRAIGMILE
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Multivariate Time Series ◽  
Discrete Wavelet ◽  
Pass Filter ◽  
Wavelet Filters ◽  
The Hilbert Transform ◽  
High Pass

We investigate the use of Hilbert wavelet pairs (HWPs) in the non-decimated discrete wavelet transform for the time-varying spectral analysis of multivariate time series. HWPs consist of two high-pass and two low-pass compactly supported filters, such that one high-pass filter is the Hilbert transform (approximately) of the other. Thus, common quantities in the spectral analysis of time series (e.g., power spectrum, coherence, phase) may be estimated in both time and frequency. Compact support of the wavelet filters ensures that the frequency axis will be partitioned dyadically as with the usual discrete wavelet transform. The proposed methodology is used to analyze a bivariate time series of zonal (u) and meridional (v) winds over Truk Island.

Breath-to-breath relationships between respiratory cycle variables in humans at fixed end-tidal Pco 2 and Po 2

1996 ◽  
Vol 81 (5) ◽  
pp. 2287-2296 ◽  
Author(s):  
Thierry Busso ◽  
Pei-Ji Liang ◽  
Peter A. Robbins
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Moving Average ◽  
Multivariate Time Series ◽  
Temporal Changes ◽  
Respiratory Cycle ◽  
Signal Power ◽  
End Tidal ◽  
Fixed End ◽  
Periodic Components

Busso, Thierry, Pei-Ji Liang, and Peter A. Robbins.Breath-to-breath relationships between respiratory cycle variables in humans at fixed end-tidal Pco 2 and Po 2. J. Appl. Physiol. 81(5): 2287–2296, 1996.—This study examined the statistical properties of breath-to-breath variations in the inspiratory and expiratory volumes and times during rest and light exercise. Sixty data sets were analyzed. Initial data and residuals after fitting time-series models were examined for 1) sustained periodicities with use of spectral analysis, 2) temporal changes in signal power with use of evolutionary spectral analysis, and 3) auto- and cross correlations with use of a portmanteau test. The major findings were as follows: 1) no sustained periodic components were detected; 2) temporal changes in signal power were normally present, but these did not affect significantly the results from time-series modeling; 3) for all variables, a simple autoregressive moving average (ARMA) AR1MA1 model generally described the autocorrelation; 4) considerable cross correlation remained between residuals from the AR1MA1 model; 5) relationships between variables could be described by using a multivariate time-series model; 6) residual fluctuations in end-tidal Pco 2 had little influence; and 7) responses were broadly similar between rest and exercise, although some quantitative differences were found. The multivariate model provides a description of the structure of the interrelationships between cycle variables in a quantitative and a qualitative form.

scholarly journals Spectral Analysis of Twin Time Series Designs

1987 ◽  
Vol 36 (1) ◽  
pp. 51-59
Author(s):  
P.C.M. Molenaar ◽  
D.I. Boomsma
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Genetic Analysis ◽  
Multivariate Time Series ◽  
Orthogonal Transformation ◽  
Principal Component ◽  
Spectral Techniques ◽  
Physiological Time ◽  
Oscillatory Character ◽  
Spectral Transforms

AbstractThe genetic analysis of physiological time series has to accommodate the presence of autocorrelation. This can be accomplished by means of orthogonal transformation of the series, thus enabling the use of standard genetic analysis techniques for the sequence of uncorrelated transforms. In view of the oscillatory character which typifies various physiological time series, it is customary to invoke spectral techniques for the analysis of these series. It can be shown that spectral analysis is an orthogonal transformation that asymptotically resembles principal component analysis. Consequently, standard genetic analysis methods for the uncorrelated spectral transforms may be used. This approach will be illustrated with simulated and real (heart rate) data for univariate twin time series. Furthermore, it will be indicated that the proposed analysis can be readily generalized to multivariate time series.

Nonparametric Spectral Analysis of Multivariate Time Series

2020 ◽  
Vol 7 (1) ◽  
pp. 361-386
Author(s):  
Rainer von Sachs
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Cross Correlation ◽  
Life Science ◽  
Multivariate Time Series ◽  
Correlated Data ◽  
Parametric Models ◽  
Applied Statistics ◽  
The Past ◽  
Brain Data

Spectral analysis of multivariate time series has been an active field of methodological and applied statistics for the past 50 years. Since the success of the fast Fourier transform algorithm, the analysis of serial auto- and cross-correlation in the frequency domain has helped us to understand the dynamics in many serially correlated data without necessarily needing to develop complex parametric models. In this work, we give a nonexhaustive review of the mostly recent nonparametric methods of spectral analysis of multivariate time series, with an emphasis on model-based approaches. We try to give insights into a variety of complimentary approaches for standard and less standard situations (such as nonstationary, replicated, or high-dimensional time series), discuss estimation aspects (such as smoothing over frequency), and include some examples stemming from life science applications (such as brain data).

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