Estimation of Change Points for Non‐Linear (Auto‐)Regressive Processes Using Neural Network Functions
提出一种基于单隐层神经网络的检验和估计方法，用于检测非线性（自）回归时间序列中的变点，并证明其渐近性质和最优收敛速度，模拟和金融数据应用验证了有效性。
ABSTRACT In this paper, we propose a new test for the detection of a change in a non‐linear (auto‐)regressive time series as well as a corresponding estimator for the unknown time point of the change. To this end, we consider an at‐most‐one‐change model and approximate the unknown (auto‐)regression function by a neural network with one hidden layer. It is shown that the test has asymptotic power of one for a wide range of alternatives, not restricted to changes in the mean of the time series. Furthermore, we prove that the corresponding estimator converges to the true change point with the optimal rate and derive the asymptotic distribution. Some simulations illustrate the behavior of the estimator with a special focus on the misspecified case, where the true regression function is not given by a neural network. Finally, we apply the estimator to some financial data.