Monitoring procedure for parameter change in causal time series

TL;DR

This paper introduces a new sequential method for detecting parameter changes in a wide class of causal time series models, improving detection accuracy and efficiency over existing methods.

Contribution

The paper presents a novel change detection procedure based on quasi-likelihood estimators that does not require historical data for updates, with proven asymptotic properties and practical applications.

Findings

The new procedure accurately detects parameter changes in simulated data.

It outperforms some existing methods in detection delay and accuracy.

Applied to stock indices, it effectively identifies multiple structural breaks.

Abstract

We propose a new sequential procedure to detect change in the parameters of a process $ X= (X_t)_{t\in \Z}$ belonging to a large class of causal models (such as AR($\infty$), ARCH($\infty$), TARCH($\infty$), ARMA-GARCH processes). The procedure is based on a difference between the historical parameter estimator and the updated parameter estimator, where both these estimators are based on a quasi-likelihood of the model. Unlike classical recursive fluctuation test, the updated estimator is computed without the historical observations. The asymptotic behavior of the test is studied and the consistency in power as well as an upper bound of the detection delay are obtained. Some simulation results are reported with comparisons to some other existing procedures exhibiting the accuracy of our new procedure. The procedure is also applied to the daily closing values of the Nikkei 225, S$&$P 500 and FTSE 100 stock index. We show in this real-data applications how the procedure can be used to solve off-line multiple breaks detection.