The cross-correlation integral: Its features and application to nonstationarity detection in time series |
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Authors: | I. V. Fel’dshtein |
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Affiliation: | (1) Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia |
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Abstract: | A generalization of the correlation integral, called the cross-correlation integral, is suggested. Features of the cross-correlation integral are studied, and a new attribute of a time series is defined. It is viewed as some kind of dimension and is associated with the fill rate of the attractor. It is demonstrated that the cross-correlation integral is calculated in much the same way as the wavelet transform of the density of points in the attractor. The cross-correlation integral is applied to detection of nonstationarity in time series. A comparison with statistical methods is made. |
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