Real-time detection of a change-point in a linear expectile model

TL;DR

This paper introduces a new real-time change-point detection method for linear expectile models with asymmetric errors and high-dimensional data, using CUSUM-based test statistics derived from expectile derivatives.

Contribution

It develops novel CUSUM-based test statistics for detecting change-points in linear expectile models, including asymptotic analysis and practical implementation with real data examples.

Findings

Test statistics diverge when a change occurs, enabling detection.

Method performs well in simulations compared to other CUSUM statistics.

Real data examples demonstrate practical applicability.

Abstract

In the present paper we address the real-time detection problem of a change-point in the coefficients of a linear model with the possibility that the model errors are asymmetrical and that the explanatory variables number is large. We build test statistics based on the cumulative sum (CUSUM) of the expectile function derivatives calculated on the residuals obtained by the expectile and adaptive LASSO expectile estimation methods. The asymptotic distribution of these statistics are obtained under the hypothesis that the model does not change. Moreover, we prove that they diverge when the model changes at an unknown observation. The asymptotic study of the test statistics under these two hypotheses allows us to find the asymptotic critical region and the stopping time, that is the observation where the model will change. The empirical performance is investigated by a comparative simulation study with other statistics of CUSUM type. Two examples on real data are also presented to demonstrate its interest in practice.