Change Point Detection in Time Series Using Higher-Order Statistics: A Heuristic Approach

Changes in the level of a time series are usually attributed to an intervention that affects its temporal evolution. The resulting time series are referred to as interrupted time series and may be used to identify the events that caused the intervention and to quantify their impact. In the present paper, a heuristic method for level change detection in time series is presented. The method uses higher-order statistics, namely, the skewness and the kurtosis, and can identify both the existence of a change in the level of the time series and the time instance when it has happened. The technique is straightforwardly applicable to the detection of outliers in time series and promises to have several applications. The method is tested with both simulated and real-world data and is compared to other popular change detection techniques.

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Level change detection in time series using higher order statistics

2009 16th International Conference on Digital Signal Processing ◽

10.1109/icdsp.2009.5201260 ◽

2009 ◽

Cited By ~ 1

Author(s):

C. S. Hilas ◽

I. T. Rekanos ◽

S. K. Goudos ◽

P. A. Mastorocostas ◽

J. N. Sahalos

Keyword(s):

Time Series ◽

Change Detection ◽

Order Statistics ◽

Higher Order ◽

Higher Order Statistics ◽

Level Change

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Nonlinear Techniques for Signals Characterization

Encyclopedia of Artificial Intelligence ◽

10.4018/978-1-59904-849-9.ch185 ◽

2011 ◽

pp. 1266-1272

Author(s):

Jesús Bernardino Alonso Hernández ◽

Patricia Henríquez Rodríguez

Keyword(s):

Time Series ◽

Signal Processing ◽

Order Statistics ◽

Chaos Theory ◽

Initial Conditions ◽

Digital Signal ◽

Higher Order ◽

Higher Order Statistics ◽

Three Body ◽

Nonlinear Signal

The field of nonlinear signal characterization and nonlinear signal processing has attracted a growing number of researchers in the past three decades. This comes from the fact that linear techniques have some limitations in certain areas of signal processing. Numerous nonlinear techniques have been introduced to complement the classical linear methods and as an alternative when the assumption of linearity is inappropriate. Two of these techniques are higher order statistics (HOS) and nonlinear dynamics theory (chaos). They have been widely applied to time series characterization and analysis in several fields, especially in biomedical signals. Both HOS and chaos techniques have had a similar evolution. They were first studied around 1900: the method of moments (related to HOS) was developed by Pearson and in 1890 Henri Poincaré found sensitive dependence on initial conditions (a symptom of chaos) in a particular case of the three-body problem. Both approaches were replaced by linear techniques until around 1960, when Lorenz rediscovered by coincidence a chaotic system while he was studying the behaviour of air masses. Meanwhile, a group of statisticians at the University of California began to explore the use of HOS techniques again. However, these techniques were ignored until 1980 when Mendel (Mendel, 1991) developed system identification techniques based on HOS and Ruelle (Ruelle, 1979), Packard (Packard, 1980), Takens (Takens, 1981) and Casdagli (Casdagli, 1989) set the methods to model nonlinear time series through chaos theory. But it is only recently that the application of HOS and chaos in time series has been feasible thanks to higher computation capacity of computers and Digital Signal Processing (DSP) technology. The present article presents the state of the art of two nonlinear techniques applied to time series analysis: higher order statistics and chaos theory. Some measurements based on HOS and chaos techniques will be described and the way in which these measurements characterize different behaviours of a signal will be analized. The application of nonlinear measurements permits more realistic characterization of signals and therefore it is an advance in automatic systems development.

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