We propose a grid-based methodology for online changepoint detection that allows offline changepoint tests to be applied to sequentially observed data. The methodology achieves low update and storage costs by testing for changepoints over a dynamically updating grid of candidate changepoint locations. For a broad class of test statistics, including those based on empirical averages and certain likelihood ratios, we show that the resulting online procedure has update and storage costs that grow at most logarithmically with the sample size. We further show that finite-sample power guarantees for the offline test translate directly into non-asymptotic upper bounds on the detection delay, under a mild robustness assumption. Building upon the methodology, we construct methods for detecting changes in the mean and in the covariance matrix of multivariate data, and prove near-optimal non-asymptotic upper bounds on their detection delays. The effectiveness of the methodology is supported by a simulation study, where we compare its performance for detecting mean changes with that of state-of-the-art online methods. To illustrate its practical applicability, we use the methodology to detect structural changes in currency exchange rates in real time.

翻译：我们提出了一种基于网格的在线变点检测方法，使得离线变点检验能够应用于顺序观测数据。该方法通过动态更新候选变点位置的网格来检测变点，从而实现了较低的更新和存储成本。对于一类广泛的统计量（包括基于经验均值和特定似然比的统计量），我们证明了所得到的在线过程的更新和存储成本随样本量最多以对数方式增长。我们进一步证明，在温和的稳健性假设下，离线检验的有限样本功效保证直接转化为检测延迟的非渐近上界。基于该方法，我们构建了检测多元数据均值和协方差矩阵变化的方法，并证明了其检测延迟接近最优的非渐近上界。仿真研究支持该方法的有效性，其中我们将其检测均值变化的性能与最先进的在线方法进行了比较。为说明实际应用性，我们使用该方法实时检测货币汇率的结构性变化。