Monitoring of high-dimensional and high-frequency data streams: A nonparametric approach

Abstract

ABSTRACT High-dimensional and high-frequency data streams (HHDS) have become widely available with the prevalence of data-acquisition technologies. Because HHDS have the characteristics of high dimensionality and temporal correlation, traditional statistical process control (SPC) techniques cannot be used directly to address the problem of monitoring HHDS. Most extant monitoring methods commonly assume that the process observations are independent or can be described by some parametric models and face the challenge posed by high-dimensional data. Little research has been conducted on the robust monitoring of HHDS that can simultaneously accommodate high dimensions and high frequencies. Therefore, in this paper, we propose a novel nonparametric approach for monitoring HHDS, based on data decorrelation, dimension reduction, and SPC. Specifically, process observations are first sequentially decorrelated and standardized using Cholesky decomposition, and then the k -nearest neighbors classification algorithm is applied to transform uncorrelated high-dimensional data into one-dimensional data. Finally, the traditional cumulative-sum procedure is used for online monitoring, based on an empirical log-likelihood ratio test. Numerical studies have shown that our monitoring scheme is sufficiently reliable and efficient for the online monitoring of HHDS. An illustrative example about the Dow Jones 30 industrial stock prices is presented to further validate the proposed approach.