A likelihood ratio approach to sequential change point detection for a general class of parameters

TL;DR

This paper introduces a likelihood ratio-based sequential change point detection method for multivariate time series, which is self-normalized, asymptotically reliable, and outperforms existing procedures in simulations and real data analysis.

Contribution

It presents a novel likelihood ratio approach for sequential change detection that does not require variance estimation and is applicable to a broad class of parameters.

Findings

The new method achieves asymptotic level α and consistency.

It outperforms existing procedures in simulation studies.

Successfully applied to real index price data.

Abstract

In this paper we propose a new approach for sequential monitoring of a parameter of a $d$-dimensional time series, which can be estimated by approximately linear functionals of the empirical distribution function. We consider a closed-end-method, which is motivated by the likelihood ratio test principle and compare the new method with two alternative procedures. We also incorporate self-normalization such that estimation of the long-run variance is not necessary. We prove that for a large class of testing problems the new detection scheme has asymptotic level $\alpha$ and is consistent. The asymptotic theory is illustrated for the important cases of monitoring a change in the mean, variance and correlation. By means of a simulation study it is demonstrated that the new test performs better than the currently available procedures for these problems.Finally the methodology is illustrated by a small data example investigating index prices from the dot-com bubble.