scholarly journals G-Filtering Nonstationary Time Series

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Mengyuan Xu ◽  
Krista B. Cohlmia ◽  
Wayne A. Woodward ◽  
Henry L. Gray
Keyword(s):  
Time Series ◽  
Stationary Process ◽  
Nonstationary Time Series ◽  
Linear Filter ◽  
Time Varying ◽  
Linear Filtering ◽  
Original Process ◽  
Filtering Method ◽  
Time Deformation ◽  
Time Varying Frequency

The classical linear filter can successfully filter the components from a time series for which the frequency content does not change with time, and those nonstationary time series with time-varying frequency (TVF) components that do not overlap. However, for many types of nonstationary time series, the TVF components often overlap in time. In such a situation, the classical linear filtering method fails to extract components from the original process. In this paper, we introduce and theoretically develop the G-filter based on a time-deformation technique. Simulation examples and a real bat echolocation example illustrate that the G-filter can successfully filter a G-stationary process whose TVF components overlap with time.

scholarly journals Using Time Deformation to Filter Nonstationary Time Series with Multiple Time-Frequency Structures

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Mengyuan Xu ◽  
Wayne A. Woodward ◽  
Henry L. Gray
Keyword(s):  
Time Series ◽  
Nonstationary Process ◽  
Nonstationary Time Series ◽  
Multiple Time ◽  
Linear Filters ◽  
Time Frequency ◽  
Time Deformation ◽  
Structure Simulation ◽  
Different Types ◽  
Time Varying Frequency

For nonstationary time series consisting of multiple time-varying frequency (TVF) components where the frequency of components overlaps in time, classical linear filters fail to extract components. TheG-filter based on time deformation has been developed to extract components of multicomponentG-stationary processes. In this paper, we explore the wide application of theG-filter for filtering different types of nonstationary processes with multiple time-frequency structure. Simulation examples illustrate that theG-filter can be applied to filter a broad range of multicomponent nonstationary process where TVF components may in fact overlap in time.

scholarly journals An Extended Time Series Algorithm for Modal Identification from Nonstationary Ambient Response Data Only

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Chang-Sheng Lin ◽  
Dar-Yun Chiang ◽  
Tse-Chuan Tseng
Keyword(s):  
Time Series ◽  
Arma Model ◽  
Identification Problem ◽  
Nonstationary Time Series ◽  
Modal Identification ◽  
Ambient Vibration ◽  
Time Varying ◽  
Varying Parameters ◽  
Response Data ◽  
Time Varying Parameters

Modal Identification is considered from response data of structural systems under nonstationary ambient vibration. The conventional autoregressive moving average (ARMA) algorithm is applicable to perform modal identification, however, only for stationary-process vibration. The ergodicity postulate which has been conventionally employed for stationary processes is no longer valid in the case of nonstationary analysis. The objective of this paper is therefore to develop modal-identification techniques based on the nonstationary time series for linear systems subjected to nonstationary ambient excitation. Nonstationary ARMA model with time-varying parameters is considered because of its capability of resolving general nonstationary problems. The parameters of moving averaging (MA) model in the nonstationary time-series algorithm are treated as functions of time and may be represented by a linear combination of base functions and therefore can be used to solve the identification problem of time-varying parameters. Numerical simulations confirm the validity of the proposed modal-identification method from nonstationary ambient response data.

scholarly journals Hydrological model performance and parameter estimation in the wavelet-domain

2009 ◽  
Vol 6 (2) ◽  
pp. 2451-2498 ◽  
Author(s):  
B. Schaefli ◽  
E. Zehe
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Time Domain ◽  
Model Performance ◽  
Time Varying ◽  
Wavelet Domain ◽  
Frequency Content ◽  
Time Varying Frequency ◽  
The Time Domain

Abstract. This paper proposes a method for rainfall-runoff model calibration and performance analysis in the wavelet-domain by fitting the estimated wavelet-power spectrum (a representation of the time-varying frequency content of a time series) of a simulated discharge series to the one of the corresponding observed time series. As discussed in this paper, calibrating hydrological models so as to reproduce the time-varying frequency content of the observed signal can lead to different results than parameter estimation in the time-domain. Therefore, wavelet-domain parameter estimation has the potential to give new insights into model performance and to reveal model structural deficiencies. We apply the proposed method to synthetic case studies and a real-world discharge modeling case study and discuss how model diagnosis can benefit from an analysis in the wavelet-domain. The results show that for the real-world case study of precipitation – runoff modeling for a high alpine catchment, the calibrated discharge simulation captures the dynamics of the observed time series better than the results obtained through calibration in the time-domain. In addition, the wavelet-domain performance assessment of this case study highlights which frequencies are not well reproduced by the model, which gives specific indications about how to improve the model structure.

scholarly journals Estimation of Dynamic Networks for High-Dimensional Nonstationary Time Series

Entropy ◽  
2019 ◽  
Vol 22 (1) ◽  
pp. 55 ◽  
Author(s):  
Mengyu Xu ◽  
Xiaohui Chen ◽  
Wei Biao Wu
Keyword(s):  
Time Series ◽  
Structural Breaks ◽  
Dynamic Networks ◽  
Scaling Limit ◽  
Nonstationary Time Series ◽  
Change Points ◽  
High Dimensional ◽  
Time Varying ◽  
Matrix Estimation ◽  
Sample Covariance

This paper is concerned with the estimation of time-varying networks for high-dimensional nonstationary time series. Two types of dynamic behaviors are considered: structural breaks (i.e., abrupt change points) and smooth changes. To simultaneously handle these two types of time-varying features, a two-step approach is proposed: multiple change point locations are first identified on the basis of comparing the difference between the localized averages on sample covariance matrices, and then graph supports are recovered on the basis of a kernelized time-varying constrained L 1 -minimization for inverse matrix estimation (CLIME) estimator on each segment. We derive the rates of convergence for estimating the change points and precision matrices under mild moment and dependence conditions. In particular, we show that this two-step approach is consistent in estimating the change points and the piecewise smooth precision matrix function, under a certain high-dimensional scaling limit. The method is applied to the analysis of network structure of the S&P 500 index between 2003 and 2008.

A uniqueness problem for the envelope of an oscillatory process

1979 ◽  
Vol 16 (04) ◽  
pp. 822-829
Author(s):  
A. M. Hasofer
Keyword(s):  
Stochastic Processes ◽  
Stationary Process ◽  
Transient Processes ◽  
Uniqueness Problem ◽  
Oscillatory Process ◽  
Linear Filter ◽  
Time Varying ◽  
Definition Of ◽  
Oscillatory Processes

In a previous paper, the author has described a method for obtaining envelope processes for oscillatory stochastic processes. These are processes which can be represented as the output of a time-varying linear filter whose input is a stationary process. It is shown in this paper that the proposed definition of the envelope process may not be unique, but may depend on the particular representation of the oscillatory process chosen. It is then shown that for a class of oscillatory processes which is of particular interest, the class of transient processes, there is a class of natural representations which all lead to a unique envelope process.

A uniqueness problem for the envelope of an oscillatory process

1979 ◽  
Vol 16 (4) ◽  
pp. 822-829 ◽  
Author(s):  
A. M. Hasofer
Keyword(s):  
Stochastic Processes ◽  
Stationary Process ◽  
Transient Processes ◽  
Uniqueness Problem ◽  
Oscillatory Process ◽  
Linear Filter ◽  
Time Varying ◽  
Definition Of ◽  
Oscillatory Processes

In a previous paper, the author has described a method for obtaining envelope processes for oscillatory stochastic processes. These are processes which can be represented as the output of a time-varying linear filter whose input is a stationary process.It is shown in this paper that the proposed definition of the envelope process may not be unique, but may depend on the particular representation of the oscillatory process chosen.It is then shown that for a class of oscillatory processes which is of particular interest, the class of transient processes, there is a class of natural representations which all lead to a unique envelope process.

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