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

This study considers the change point testing problem in autoregressive moving average (ARMA) (p,q) models through the location and scale-based cumulative sum (LSCUSUM) method combined with neural network regression (NNR). We estimated the model parameters via the NNR method based on the training sample, where a long AR model was fitted to obtain the residuals. Then, we selected the optimal model orders p and q of the ARMA models using the Akaike information criterion based on a validation set. Finally, we used the forecasting errors obtained from the selected model to construct the LSCUSUM test. Extensive simulations and their application to three real datasets show that the proposed NNR-based LSCUSUM test performs well.