Unique decomposition of low-order time series

2015 ◽  
Vol 45 (11) ◽  
pp. 3357-3366
Author(s):  
Eugene Seneta ◽  
Simon Ku
Keyword(s):  
Time Series ◽  
Unique Decomposition ◽  
Low Order

scholarly journals Combined asteroseismology, spectroscopy, and astrometry of the CoRoT B2V target HD 170580

2019 ◽  
Vol 624 ◽  
pp. A75 ◽  
Author(s):  
C. Aerts ◽  
M. G. Pedersen ◽  
E. Vermeyen ◽  
L. Hendriks ◽  
C. Johnston ◽  
...  
Keyword(s):  
Time Series ◽  
Massive Star ◽  
Rotation Period ◽  
Stellar Structure ◽  
Atomic Diffusion ◽  
High Mass ◽  
High Signal ◽  
Hydrogen Burning ◽  
Average Rotation ◽  
Low Order

Context. Space asteroseismology reveals that stellar structure and evolution models of intermediate- and high-mass stars are in need of improvement in terms of angular momentum and chemical element transport. Aims. We aim to probe the interior structure of a hot, massive star in the core-hydrogen-burning phase of its evolution. Methods. We analysed CoRoT space photometry, Gaia DR2 space astrometry, and high-resolution high signal-to-noise HERMES and HARPS time-series spectroscopy of the slowly rotating B2V star HD 170580. Results. From the time-series spectroscopy, we derive v sin i = 4 ± 2 km s−1, where the uncertainty results from the complex pulsational line-profile variability that has been so far ignored in the literature. We detect 42 frequencies with amplitudes above five times the local noise level. Amongst these we identify five rotationally split triplets and one quintuplet. Asteroseismic modelling based on CoRoT, Gaia DR2, and spectroscopic data leads to a star of M ∼ 8 M⊙ near core-hydrogen exhaustion and an extended overshoot zone. The detected low-order pressure-mode frequencies cannot be fit within the uncertainties of the CoRoT data by models without atomic diffusion. Irrespective of this limitation, the low-order gravity modes reveal HD 170580 to be a slow rotator with an average rotation period between 73 and 98 d and a hint of small differential rotation. Conclusions. Future Gaia DR3 data taking into account the multiplicity of the star, along with long-term TESS photometry would allow us to put better observational constraints on the asteroseismic models of this blue evolved massive star. Improved modelling with atomic diffusion, including radiative levitation, is needed to achieve compliance with the low helium surface abundance of the star. This poses immense computational challenges but is required to derive the interior rotation and mixing profiles of this star.

Predicting Monsoon Intraseasonal Precipitation using a Low-Order Nonlinear Stochastic Model

2018 ◽  
Vol 31 (11) ◽  
pp. 4403-4427 ◽  
Author(s):  
Nan Chen ◽  
Andrew J. Majda ◽  
C. T. Sabeerali ◽  
R. S. Ajayamohan
Keyword(s):  
Time Series ◽  
Stochastic Model ◽  
Large Scale ◽  
Hidden Variables ◽  
Longwave Radiation ◽  
Reconstruction Algorithm ◽  
Daily Precipitation Data ◽  
Intraseasonal Oscillations ◽  
Nonlinear Stochastic Model ◽  
Low Order

Abstract The authors assess the predictability of large-scale monsoon intraseasonal oscillations (MISOs) as measured by precipitation. An advanced nonlinear data analysis technique, nonlinear Laplacian spectral analysis (NLSA), is applied to the daily precipitation data, resulting in two spatial modes associated with the MISO. The large-scale MISO patterns are predicted in two steps. First, a physics-constrained low-order nonlinear stochastic model is developed to predict the highly intermittent time series of these two MISO modes. The model involves two observed MISO variables and two hidden variables that characterize the strong intermittency and random oscillations in the MISO time series. It is shown that the precipitation MISO indices can be skillfully predicted from 20 to 50 days in advance. Second, an effective and practical spatiotemporal reconstruction algorithm is designed, which overcomes the fundamental difficulty in most data decomposition techniques with lagged embedding that requires extra information in the future beyond the predicted range of the time series. The predicted spatiotemporal patterns often have comparable skill to the MISO indices. One of the main advantages of the proposed model is that a short (3 year) training period is sufficient to describe the essential characteristics of the MISO and retain skillful predictions. In addition, both model statistics and prediction skill indicate that outgoing longwave radiation is an accurate proxy for precipitation in describing the MISO. Notably, the length of the lagged embedding window used in NLSA is crucial in capturing the main features and assessing the predictability of MISOs.

scholarly journals Evaluation of Hurricane Wind Speed Analyses in a Simulation of Hurricane Earl (2010) Using Low-Order Wavenumbers

2017 ◽  
Vol 145 (8) ◽  
pp. 3223-3245 ◽  
Author(s):  
George Andrew Soukup ◽  
Frank D. Marks
Keyword(s):  
Time Series ◽  
Steady State ◽  
Wind Speed ◽  
Data Collection ◽  
Surface Wind ◽  
Time Interval ◽  
System Sensitivity ◽  
Sensitivity Experiments ◽  
Hurricane Wind ◽  
Low Order

To determine how well a low-order wavenumber representation describes a hurricane wind speed field, given its natural variability in space and time, low-order wavenumber representations were calculated for hourly “snapshots” of the 10-m wind speed field generated by the current operational hurricane model. Two distinct periods were examined: the first when the storm is in a reasonably steady state over 7–8 h and the second where the storm is changing its internal structure over a similar time interval. Observing system sensitivity experiments were also performed using wind speed field time series obtained from interpolation of the model snapshots for each of the two periods. The time series were sampled along the flight legs of a typical “figure four” aircraft flight pattern to simulate the surface wind data collection process to ascertain the effects of the wind speed field’s temporal and spatial variability upon the low-order wavenumber analyses. The comparison between the model wind speed field at any time and the wavenumber representations during the “steady state” period shows that the essential features of the wind speed field are captured by wavenumbers 0 and 1 and that including up to wavenumber 3 practically reproduces the model field. However, in the “nonsteady” period the wavenumber 0 and 1 representation is frequently unable to capture the essential characteristics of the wind speed field. The observing system sensitivity experiments suggest that when the primary circulation is rapidly changing in amplitude and/or structure during the data collection period, the low-order wavenumbers analysis of the wind speed field will only represent the temporal mean structure.

Increment-Vector Methodology: Transforming Non-Stationary Series to Stationary Series

1998 ◽  
Vol 35 (1) ◽  
pp. 64-77 ◽  
Author(s):  
Zhao-Guo Chen ◽  
Oliver D. Anderson
Keyword(s):  
Time Series ◽  
General Theory ◽  
Time Series Analysis ◽  
Spatial Process ◽  
Second Moment ◽  
Series Analysis ◽  
Low Order

In time series analysis, it is well-known that the differencing operator ∇d may transform a non-stationary series, {Z(t)} say, to a stationary one, {W(t)} = ∇dZ(t)}; and there are many procedures for analysing and modelling {Z(t)} which exploit this transformation. Rather differently, Matheron (1973) introduced a set of measures on Rn that transform an appropriate non-stationary spatial process to stationarity, and Cressie (1988) then suggested that specialized low-order analogues of these measures, called increment-vectors, be used in time series analysis. This paper develops a general theory of increment-vectors which provides a more powerful transformation tool than mere simple differencing. The methodology gives a handle on the second-moment structure and divergence behaviour of homogeneously non-stationary series which leads to many important applications such as determining the correct degree of differencing, forecasting and interpolation.

Delay Identification in Thermoacoustics

2021 ◽  
Author(s):  
F. Gant ◽  
G. Ghirardo ◽  
A. Cuquel ◽  
M. R. Bothien
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Additive White Gaussian Noise ◽  
A Priori ◽  
Accurate Estimate ◽  
Combustion Noise ◽  
Unknown Parameters ◽  
Acoustic Damping ◽  
The Stability ◽  
Low Order

Abstract The stability of thermoacoustic systems is often regulated by the time delay between acoustic perturbations and corresponding heat release fluctuations. An accurate estimate of this value is of great importance in applications, since even small modifications can introduce significant changes in the system behavior Different studies show that the nonlinear delayed dynamics typical of these systems can be well captured with low-order models. In the present work, a method is introduced to estimate the most likely value of the time delay of a single thermoacoustic mode from a measured acoustic pressure signal. The mode of interest is modeled by an oscillator equation, with a nonlinear delayed forcing term modeling the deterministic flame contribution and an additive white Gaussian noise to embed the stochastic combustion noise. Additionally, other thermoacoustic relevant parameters are estimated. The model accounts for a flame gain, for a flame saturation coefficient, for a linear acoustic damping and for the background combustion noise intensity. The pressure data time series is statistically analyzed and the set of unknown parameters is identified. Validation is performed with respect to synthetically generated time series and low order model simulations, for which the underlying delay is known a priori. A discussion follows about the accuracy of the method, in particular a comparison with existing methods is drawn.

Inferring dynamic gene regulatory networks with low-order conditional independencies – an evaluation of the method

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Hamda B. Ajmal ◽  
Michael G. Madden
Keyword(s):  
Time Series ◽  
Gene Regulatory Networks ◽  
Regulatory Networks ◽  
Time Series Data ◽  
Simulated Data ◽  
Dynamic Bayesian Networks ◽  
Series Data ◽  
Gene Regulatory ◽  
Lasso Method ◽  
Low Order

AbstractOver a decade ago, Lèbre (2009) proposed an inference method, G1DBN, to learn the structure of gene regulatory networks (GRNs) from high dimensional, sparse time-series gene expression data. Their approach is based on concept of low-order conditional independence graphs that they extend to dynamic Bayesian networks (DBNs). They present results to demonstrate that their method yields better structural accuracy compared to the related Lasso and Shrinkage methods, particularly where the data is sparse, that is, the number of time measurements n is much smaller than the number of genes p. This paper challenges these claims using a careful experimental analysis, to show that the GRNs reverse engineered from time-series data using the G1DBN approach are less accurate than claimed by Lèbre (2009). We also show that the Lasso method yields higher structural accuracy for graphs learned from the simulated data, compared to the G1DBN method, particularly when the data is sparse ($n{< }{< }p$). The Lasso method is also better than G1DBN at identifying the transcription factors (TFs) involved in the cell cycle of Saccharomyces cerevisiae.

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