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Anomaly Detection in High-Dimensional Bank Account Balances via Robust Methods

Federico Maddanu, Tommaso Proietti, Riccardo Crupi

TL;DR

This work tackles point anomaly detection in high-dimensional bank balance time series by deploying two robust paradigms: distance-based estimators (OGK, MRCD, COM) on trend-removed residuals and forecasting-based models (RobHAR, RobNHAR) that operate directly on robust residuals to avoid high-dimensional covariances. Through simulations and large-scale ISP data, the authors show robust residual approaches are essential when trend and seasonality are present, with forecasting-based methods offering scalable real-time capability; COM and RobAR provide competitive performance at lower computational cost. The study also uses CUSUM-inspired classification to distinguish between additive outliers and level-shift outliers and leverages clustering to refine contaminated series, identifying a small, highly anomalous subset for targeted forecasting. Overall, the methods detect a meaningful fraction of daily transactions as potential anomalies while enabling practical deployment on datasets with up to millions of time series.

Abstract

Detecting point anomalies in bank account balances is essential for financial institutions, as it enables the identification of potential fraud, operational issues, or other irregularities. Robust statistics is useful for flagging outliers and for providing estimates of the data distribution parameters that are not affected by contaminated observations. However, such a strategy is often less efficient and computationally expensive under high dimensional setting. In this paper, we propose and evaluate empirically several robust approaches that may be computationally efficient in medium and high dimensional datasets, with high breakdown points and low computational time. Our application deals with around 2.6 million daily records of anonymous users' bank account balances.

Anomaly Detection in High-Dimensional Bank Account Balances via Robust Methods

TL;DR

This work tackles point anomaly detection in high-dimensional bank balance time series by deploying two robust paradigms: distance-based estimators (OGK, MRCD, COM) on trend-removed residuals and forecasting-based models (RobHAR, RobNHAR) that operate directly on robust residuals to avoid high-dimensional covariances. Through simulations and large-scale ISP data, the authors show robust residual approaches are essential when trend and seasonality are present, with forecasting-based methods offering scalable real-time capability; COM and RobAR provide competitive performance at lower computational cost. The study also uses CUSUM-inspired classification to distinguish between additive outliers and level-shift outliers and leverages clustering to refine contaminated series, identifying a small, highly anomalous subset for targeted forecasting. Overall, the methods detect a meaningful fraction of daily transactions as potential anomalies while enabling practical deployment on datasets with up to millions of time series.

Abstract

Detecting point anomalies in bank account balances is essential for financial institutions, as it enables the identification of potential fraud, operational issues, or other irregularities. Robust statistics is useful for flagging outliers and for providing estimates of the data distribution parameters that are not affected by contaminated observations. However, such a strategy is often less efficient and computationally expensive under high dimensional setting. In this paper, we propose and evaluate empirically several robust approaches that may be computationally efficient in medium and high dimensional datasets, with high breakdown points and low computational time. Our application deals with around 2.6 million daily records of anonymous users' bank account balances.

Paper Structure

This paper contains 19 sections, 27 equations, 11 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Anomaly detection via distance-based methods
  4. Anomaly detection via robust forecasting-based methods
  5. Identification of outliers typology
  6. Simulation study
  7. The data generating process (DGP)
  8. Monte Carlo results
  9. Monte Carlo results
  10. Threshold selection
  11. The ISP dataset
  12. Outliers detection on the ISP dataset
  13. Outliers detection on the $\mathbf{Y}_{5K}$ dataset
  14. Outlier detection on the $\mathbf{Y}_{50K}$ dataset
  15. Outlier detection on the entire dataset $\mathbf{Y}$
  16. ...and 4 more sections

Figures (11)

  • Figure 1: ROC curve for the OGK, MRCD, COM and RobAR(1) methodologies applied to the robust residuals in detecting AOs and LSOs with outlier effect $\delta_i = \lbrace \hat{\sigma}^2_{i,i}, 1.5 \hat{\sigma}^2_{i,i} \rbrace$.
  • Figure 2: Thresholds and linear fit on the log tails of the standardized MD distribution obtained via the COM estimator by considering the DGP in subsection \ref{['DGP']} under the same assumptions of the Monte Carlo experiment in subsection \ref{['MC']}, for a) AO $\delta_i= 1.5 \sigma_{i,i}$, b) AO $\delta_i= \sigma_{i,i}$, c) LSO $\delta_i= 1.5 \sigma_{i,i}$ and d) LSO $\delta_i= \sigma_{i,i}$.
  • Figure 3: 12 bank account balances time series randomly extracted from the main dataset.
  • Figure 4: Histograms of the mean, median, standard deviation, MAD, kurtosis, skewness, $\beta_{\nu,1}$, $\beta_{\nu,2}$, amplitudes, and phases for the first two harmonics. The latter are computed using the parameters in Equation \ref{['mdltrend']}.
  • Figure 5: Outliers histograms for the five methodologies by considering the reduced $\mathbf{Y}_{5K}$ dataset.
  • ...and 6 more figures