Detecting Structural Change Point in ARMA Models via Neural Network Regression and LSCUSUM Methods

Area of Science:

• Statistics
• Time Series Analysis
• Machine Learning

Background:

• Change point detection is crucial for analyzing time series data.
• Autoregressive Moving Average (ARMA) models are widely used but require robust change point testing.
• Existing methods may have limitations in parameter estimation and model selection.

Purpose of the Study:

• To develop and evaluate a novel change point testing method for ARMA(p,q) models.
• To integrate neural network regression (NNR) with the location and scale-based cumulative sum (LSCUSUM) technique.
• To assess the performance of the proposed method using simulations and real datasets.

Main Methods:

• Parameter estimation for ARMA models using NNR on a training sample.
• Model order selection (p,q) via Akaike Information Criterion on a validation set.
• Construction of the LSCUSUM test using forecasting errors from the selected ARMA model.

Main Results:

• The NNR-based LSCUSUM test effectively identifies change points in ARMA models.
• Simulations indicate robust performance across various scenarios.
• Application to three real datasets confirms the method's practical utility.

Conclusions:

• The proposed NNR-based LSCUSUM test offers a powerful tool for change point detection in ARMA models.
• Combining NNR with LSCUSUM provides an effective approach for time series analysis.
• The method shows promise for both theoretical and applied statistical research.