SDVAR Algorithm for Detecting Fraud in Telecommunications

This paper presents a procedure for estimating VAR using Sequential Discounting VAR (SDVAR) algorithm for online model learning to detect fraudulent acts using the telecommunications call detailed records (CDR). The volatility of the VAR is observed allowing for non-linearity, outliers and change points based on the works of [1]. This paper extends their procedure from univariate to multivariate time series. A simulation and a case study for detecting telecommunications fraud using CDR illustrate the use of the algorithm in the bivariate setting.

Authors:

• Fatimah Almah Saaid
• Darfiana Nur
• Robert King

Keywords:

• Telecommunications Fraud
• SDVAR Algorithm
• Multivariate time series
• Vector Autoregressive
• Change points.

References:

[1] J. Takeuchi and K. Yamanishi, "A unifying framework for detecting
outliers and change points from time series," IEEE Transactions on
Knowledge and Data Engineering, vol. 18(4), pp. 482-492, 2006.
[2] G. Weiss, Networking and Telecommunications: Concepts, Methodologies,
Tools and Applications, ch. Data Mining in the Telecommunications
Industry, pp. 486-491. IGI Global, 2010.
[3] Y. Kawahara, T. Yairi, and K. Machida, "Change-point detection in
time-series data based on subspace identification," in Seventh IEEE
International Conference on Data Mining (ICDM), pp. 559-564, 2007.
[4] C. Erdman and J. Emerson, "A fast bayesian change point analysis for
the segmentation," Bioinformatics, vol. 24(19), p. 21432148, 2008.
[5] P. Chu and X. Zhao, "Bayesian change-point analysis of tropical cyclone
activity: The central north pacific case," Journal of Climate, vol. 17(24),
pp. 4893-4901, 2004.
[6] V. Moskvina and A. Zhigljavsky, "An algorithm based on singular spectrum
analysis for change-point detection," Communication in Statistics:
Simulation & Computation, vol. 32(2), pp. 319-352, 2003.
[7] H. Zhang, R. Dantu, and J. Cangussu, "Change point detection based
on call detail records," in IEEE International Conference on Intelligence
and Security Informatics, 2009 (ISI 09), 2009.
[8] B.-K. Yi, N. Sidiropoulos, T. Johnson, H. Jagadish, C. Faloutsos, and
A. Biliris, "Online data mining for co-evolving time sequences," in
Proceedings of the 16th International Conference in Data Engineering,
2000.
[9] H. L¨utkepohl, Introduction to multiple time series analysis. Berlin, New
York: Springer-Verlag, 1993.
[10] W. Wei, Time Series Analysis: Univariate and Multivariate Methods.
Addison-Wesley Publishing Company, Inc., 1990.
[11] D. Kazakos and P. Papantoni-Kazakos, "Spectral distance measuring
between gaussian processes," IEEE Trans. Automat. Contr. AC-25,
pp. 950-959, 1980.
[12] B. Biller and B. Nelson, "Modeling and generating multivariate timeseries
input processes using a vector autoregressive technique," ACM
Transactions on Modeling and Computer Simulation, vol. 13, no. 3,
pp. 211-237, 2003a.
[13] B. Biller and B. Nelson, "Online companion to modelling and generating
multivariate time series input processes using a vector autoregressive
technique," tech. rep., Department of Industrial Engineering and Management
Sciences, Northwestern University, Evanston Illinois, 2003b.
[14] F. A. Saaid, D. Nur, and R. King, "Change points detection of vector
autoregressive model using sdvar algorithm," in Fifth Annual ASEARC
Conference, (University of Wollongong, Australia), pp. 18-21, 2-3
February 2012.