Low-Frequency Signal Reconstruction and Abrupt Change Detection in Non-stationary Time Series by Enhanced Moving Trend Based Filters

2014 ◽  
pp. 111-125
Author(s):  
Tomasz Pełech-Pilichowski ◽  
Jan T. Duda
Keyword(s):  
Time Series ◽  
Change Detection ◽  
Abrupt Change ◽  
Signal Reconstruction ◽  
Low Frequency ◽  
Stationary Time Series ◽  
Frequency Signal ◽  
Stationary Time ◽  
Abrupt Change Detection

Autoregressive Analysis

1980 ◽  
Vol 23 (2) ◽  
pp. 248-257 ◽  
Author(s):  
David H. Crowell ◽  
Linda E. Kapuniai ◽  
Richard H. Jones ◽  
Glenn Pang-Ching
Keyword(s):  
Time Series ◽  
Change Detection ◽  
Brain Activity ◽  
Newborn Infants ◽  
Stationary Time Series ◽  
Confidence Limits ◽  
Detection Model ◽  
Stationary Time ◽  
Autoregressive Analysis

This report presents an autoregressive technique for detecting statistically significant changes in brain activity to tones. The change detection model is applied to stationary time series electroencephalogram samples from sleeping newborn infants. The electroencephalic responses of neonates to tones are quantified and analyzed in terms of t-statistics. Confidence limits applied to averaged t-statistics objectively and reliably defined statistically significant late components in newborns.

Forecasting import and export volume with a combined model based on wavelet filtering

2016 ◽  
Vol 14 (03) ◽  
pp. 1650018
Author(s):  
Huidian Long ◽  
Guangle Yan
Keyword(s):  
Time Series ◽  
Markov Chain ◽  
High Frequency ◽  
Low Frequency ◽  
Stationary Time Series ◽  
Combined Model ◽  
Model Based ◽  
Stationary Time ◽  
Export Volume ◽  
Import And Export

In this paper, a non-stationary time series prediction method based on wavelet transform is proposed. By wavelet decomposition, the non-stationary time series is decomposed into a low frequency signal and several high frequency signals. The high frequency signals are predicted with auto-regressive integrated moving average (ARIMA) models, and the low frequency is predicted with an improved GM(1,1)-Markov chain combined model based on Taylor approximation. Finally, an improved ARIMA-GM(1,1)-Markov chain combined model is constructed by using wavelet reconstruction. As an example, we use the statistical data of the total import and export volume in China from 2001 to 2014 for a validation of the effectiveness of the combined model.

scholarly journals A Fast Framework for Abrupt Change Detection Based on Binary Search Trees and Kolmogorov Statistic

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Jin-Peng Qi ◽  
Jie Qi ◽  
Qing Zhang
Keyword(s):  
Time Series ◽  
Change Detection ◽  
Large Scale ◽  
Abrupt Change ◽  
Binary Search ◽  
Binary Search Trees ◽  
Search Trees ◽  
Haar Wavelet Transform ◽  
Kolmogorov Statistic ◽  
Abrupt Change Detection

Change-Point (CP) detection has attracted considerable attention in the fields of data mining and statistics; it is very meaningful to discuss how to quickly and efficiently detect abrupt change from large-scale bioelectric signals. Currently, most of the existing methods, like Kolmogorov-Smirnov (KS) statistic and so forth, are time-consuming, especially for large-scale datasets. In this paper, we propose a fast framework for abrupt change detection based on binary search trees (BSTs) and a modified KS statistic, named BSTKS (binary search trees and Kolmogorov statistic). In this method, first, two binary search trees, termed as BSTcA and BSTcD, are constructed by multilevel Haar Wavelet Transform (HWT); second, three search criteria are introduced in terms of the statistic and variance fluctuations in the diagnosed time series; last, an optimal search path is detected from the root to leaf nodes of two BSTs. The studies on both the synthetic time series samples and the real electroencephalograph (EEG) recordings indicate that the proposed BSTKS can detect abrupt change more quickly and efficiently than KS,t-statistic (t), and Singular-Spectrum Analyses (SSA) methods, with the shortest computation time, the highest hit rate, the smallest error, and the highest accuracy out of four methods. This study suggests that the proposed BSTKS is very helpful for useful information inspection on all kinds of bioelectric time series signals.

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