Statistics and Its Interface

Volume 10 (2017)

Number 1

Real-time financial surveillance via quickest change-point detection methods

Pages: 93 – 106

DOI: http://dx.doi.org/10.4310/SII.2017.v10.n1.a9

Authors

Andrey Pepelyshev (Faculty of Mathematics, St. Petersburg State University, Peterhof, St. Petersburg, Russia; and School of Mathematics, Cardiff University, Cardiff, Wales, United Kingdom)

Aleksey S. Polunchenko (Department of Mathematical Sciences, State University of New York, Binghamton, N.Y., U.S.A.)

Abstract

We consider the problem of efficient financial surveillance aimed at “on-the-go” detection of structural breaks (anomalies) in “live”-monitored financial time series. With the problem approached statistically, viz. as that of multicyclic sequential (quickest) change-point detection, we propose a semi-parametric multi-cyclic change-point detection procedure to promptly spot anomalies as they occur in the time series under surveillance. The proposed procedure is a derivative of the likelihood ratio-based Shiryaev–Roberts (SR) procedure; the latter is a quasi-Bayesian surveillance method known to deliver the fastest (in the multi-cyclic sense) speed of detection, whatever be the false alarm frequency. We offer a case study where we first carry out, step by step, a preliminary statistical analysis of a set of real-world financial data, and then set up and devise (a) the proposed SR-based anomaly-detection procedure and (b) the celebrated Cumulative Sum (CUSUM) chart to detect structural breaks in the data. While both procedures performed well, the proposed SR-derivative, conforming to the intuition, seemed slightly better.

Keywords

CUSUM chart, financial surveillance, sequential analysis, Shiryaev–Roberts procedure, quickest change-point detection

2010 Mathematics Subject Classification

Primary 62L10, 62L15. Secondary 62P05.

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