Testing fractal connectivity in multivariate long memory processes

Herwig Wendt (1) , Antoine Scherrer (1) , Patrice Abry (1) , Sophie Achard (2)

1 Phys-ENS - Laboratoire de Physique de l'ENS Lyon
2 GIPSA-SIGMAPHY - GIPSA - Signal Images Physique

Within the framework of long memory multivariate processes, fractal connectivity is a particular model, in which the low frequencies (coarse scales) of the interspectrum of each pair of process components are determined by the autospectra of the components. The underlying intuition is that long memories in each components are likely to arise from a same and single mechanism. The present contribution aims at defining and characterizing a statistical procedure for testing actual fractal connectivity amongst data. The test is based on Fisher's Z transform and Pearson correlation coefficient, and anchored in a wavelet framework. Its performance are analyzed theoretically and validated on synthetic data. Its usefulness is illustrated on the analysis of Internet traffic Packet and Byte count time series.

Keywords: Wavelet transform; Long memory; Fractal connectivity; Statistical test; Internet traffic

Domains: Engineering Sciences [physics]; Signal and Image processing; Computer Science [cs]; Signal and Image Processing

Herwig Wendt, Antoine Scherrer, Patrice Abry, Sophie Achard. Testing fractal connectivity in multivariate long memory processes. ICASSP 2009 - IEEE International Conference on Acoustics, Speech and Signal Processing, Apr 2009, Taipei, Taiwan. ⟨ensl-00362174⟩