A Record-Based Block Method for Anomaly Detection in Nonlinear Time Series

Let {X_t , t ≥ 1} be a real-valued time series. A changepoint is said to occur at time t when the local dynamics of the process exhibit a persistent deviation from a reference regime. Motivated by record theory, we introduce a distribution-free framework for changepoint detection based on local power statistics aggregated over sliding blocks. The method operates under piecewise CHARN models and distinguishes between null, transient, and persistent abnormal regimes. The detection rule relies on intra-block exceedance indicators and a tolerance parameter calibrated using asymptotic record counts. We show that under β-mixing conditions, block-level exceedance counts converge to binomial distributions, allowing for tractable inference. Our procedure is developed under the i.i.d., Linear Drift and Yang-Nevzorov models and demonstrates robust performance across simulations. Some adaptive selection strategies for tuning parameters are also presented.>