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重尾时间序列的变点检验：缩尾 CUSUM 方法AI 解读

It is well-known that the detection of change-points in heavy-tailed time series is an open problem since the traditional tests may not have a power. This article introduces a winsorized cumulative sum (CUSUM) approach to solve this problem. We begin by investigating the winsorized CUSUM process and then use it to construct the Kolmogorov-Smirnov (KS) test and the Self-normalized (SN) test. Under the null hypothesis, it is shown that each weakly converges to the maximum of a…

非零中位数 GARCH 型噪声下重尾 AR 模型的两步估计AI 解读

This paper develops a novel two-step estimating procedure for heavy-tailed AR models with nonzero median GARCH-type noises, allowing for time-varying volatility. We first establish the self-weighted quantile regression estimator (SQE) across all quantile levels τ∈(0,1) for the AR parameters θ0. We show that the SQE, less a bias, converges weakly to a Gaussian process at a rate of n−1/2. The bias is zero if and only if τ equals τ0, the probability that the noise is less than…