Dynamics at Scale: Statistical Frontiers in High-Dimensional and Streaming Time Series

We study real-time detection of low-rank changes in the covariance structure of high-dimensional
streaming data, motivated by robotic swarm monitoring. Building on the spiked covariance model, we
propose the Multi-rank Subspace-CUSUM (MRS-C) procedure, which extends classical CUSUM by
tracking projection energy onto an estimated signal subspace. We analyze performance by characterizing
the expected detection delay (EDD) under a prescribed average run length (ARL), deriving closed-form
asymptotically optimal choices of the window size and drift. We further prove that MRS-C is first-order
asymptotically optimal relative to the oracle Exact CUSUM, with an explicit efficiency constant that
depends on heterogeneity in spike strengths. When the signal rank is unknown, we use a parallel
procedure. Simulations and robotic swarm-behavior data illustrate robustness and effectiveness. This talk is based on recent work Multi-rank subspace change-point detection for monitoring robotic swarms.
Jonghyeok Lee, Yao Xie, Youngser Park, Jason Hindes, Ira Schwartz, Carey Priebe. 2026. 

Network modeling of multivariate time series has emerged as an useful framework for understanding interactions amongst the component of a dynamical system in many areas of biological and social sciences. We develop a method to construct sparse, weighted, directed network where each edge captures how a shock to one component dynamically manifests in the other component using cumulative impulse response functions (cIRF). This is in sharp contrast with existing works, where network edges primarily capture in some form the Granger-causal effects (lead-lag association) among the component time series, and rely on a parsimonious vector autoregressive (VAR) representation of the system. Building upon our previous work on large-scale vector autoregressive moving averages (VARMA), we develop an iterative procedure for estimating cIRF. Using simulation experiments, we show that when the data generating process has a sparse vector moving average (VMA) representation, our method outperforms competing alternatives. We also prove that our algorithm, restricted to any finite number of iterations, consistently estimates impulse responses under high-dimensional asymptotics. Finally, we use our method to construct financial networks from realized volatilities of stock prices before, during and after the US financial crisis of 2007-09. 

Online learning has gained popularity in recent years due to the urgent need to analyse large-scale streaming data, which can be collected in perpetuity and serially dependent. This motivates us to develop the online generalized method of moments (OGMM), an explicitly updated estimation and inference framework in the time series setting. The OGMM inherits many properties of offline GMM, such as its broad applicability to many problems in econometrics and statistics, natural accommodation for over-identification, and achievement of semiparametric efficiency under temporal dependence. As an online method, the key gain relative to offline GMM is the vast improvement in time complexity and memory requirement. Building on the OGMM framework, we propose improved versions of online Sargan--Hansen and structural stability tests following recent work in econometrics and statistics. Through Monte Carlo simulations, we observe encouraging finite-sample performance in online instrumental variables regression, online over-identifying restrictions test, online quantile regression, and online anomaly detection. Interesting applications of OGMM to stochastic volatility modelling and inertial sensor calibration are presented to demonstrate the effectiveness of OGMM.