Analysis of self-similar data by artificial neural networks

Long range dependence is closely linked with self-similar stochastic processes and random fractals, which have been considered extensively for signal processing applications and computer network traffic modeling. The Hurst parameter captures the amount of long-range dependence in a time series. Typically, the analysis of self-similar series is performed using: the variance-time plot, the R/S plot, the periodogram, and Whittle's estimator. The first three are graphical methods, and their accuracy depends strongly on the interpretation of the plot. Whittle's estimator is based on a maximum likelihood technique and offers excellent results; however it is computationally pricey. A new method to estimate the Hurst parameter using artificial neural networks is proposed. Experimental results show that this method outperforms conventional approaches, and can be used on applications where a quick and precise analysis of self-similar data is required.

[1]  M. Taqqu,et al.  Large-Sample Properties of Parameter Estimates for Strongly Dependent Stationary Gaussian Time Series , 1986 .

[2]  Jan Purczynski,et al.  On fast generation of fractional Gaussian noise , 2006, Comput. Stat. Data Anal..

[3]  Walter Willinger,et al.  Experimental queueing analysis with long-range dependent packet traffic , 1996, TNET.

[5]  Derong Liu,et al.  Two approximation methods to synthesize the power spectrum of fractional Gaussian noise , 2007, Comput. Stat. Data Anal..

[6]  Michalis Faloutsos,et al.  Long-range dependence ten years of Internet traffic modeling , 2004, IEEE Internet Computing.

[7]  Robert J. Marks,et al.  Neural Smithing: Supervised Learning in Feedforward Artificial Neural Networks , 1999 .

[8]  Derong Liu,et al.  Synthesis of fractional gaussian noise using linear approximation for generating self-similar network traffic , 2000, CCRV.

[9]  Oliver Rose,et al.  Estimation of the Hurst Parameter of Long-Range Dependent Time Series , 1996 .

[10]  Julio Cesar Ramírez Pacheco,et al.  Local and Cumulative Analysis of Self-similar Traffic Traces , 2006, 16th International Conference on Electronics, Communications and Computers (CONIELECOMP'06).

[11]  Timothy Masters,et al.  Advanced algorithms for neural networks: a C++ sourcebook , 1995 .

[12]  J. R. Wallis,et al.  Some long‐run properties of geophysical records , 1969 .

[13]  M. Tim Jones,et al.  AI Application Programming , 2003 .

[14]  Peter Norvig,et al.  Artificial Intelligence: A Modern Approach , 1995 .

[15]  Ibrahim Matta,et al.  Analytical investigation of the bias effect in variance-type estimators for inference of long-range dependence , 2002, Comput. Networks.

[16]  Alan V. Oppenheim,et al.  Discrete-time Signal Processing. Vol.2 , 2001 .

[17]  Timothy Masters,et al.  Practical neural network recipes in C , 1993 .

[18]  J. Beran.  Statistical methods for data with long-range dependence , 1992 .

[19]  Timothy Masters,et al.  Neural, Novel & Hybrid Algorithms for Time Series Prediction , 1995 .

[20]  J. S. Marron,et al.  LASS: a tool for the local analysis of self-similarity , 2006, Comput. Stat. Data Anal..