Ri Xi-Hame, Chen Zhanshou, Liang Yan
School of Mathematics and Statistic, Qinghai Normal University, Xining 810008, China.
The State Key Laboratory of Tibetan Intelligent Information Processing and Application, Xining 810008, China.
Entropy (Basel). 2023 Jan 9;25(1):133. doi: 10.3390/e25010133.
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.
本研究通过基于位置和尺度的累积和（LSCUSUM）方法与神经网络回归（NNR）相结合，考虑自回归移动平均（ARMA）(p,q)模型中的变点检验问题。我们基于训练样本通过NNR方法估计模型参数，其中拟合一个长自回归模型以获得残差。然后，我们基于验证集使用赤池信息准则选择ARMA模型的最优模型阶数p和q。最后，我们使用从所选模型获得的预测误差来构建LSCUSUM检验。大量的模拟及其在三个真实数据集上的应用表明，所提出的基于NNR的LSCUSUM检验表现良好。
