Mathematical Sciences Department PhD Dissertation Defense - Yanzhao Wang "New developments in sequential change point detection for time series and spatio-temporal analysis" (UH 420)
12:00 pm to 2:00 pm
Mathematical Sciences Department
PhD Dissertation Defense
Thursday, May 4, 2023
12:00 pm - 2:00 pm
Unity Hall 420
and Zoom Meeting ID: 943 5731 6287
Title: New developments in sequential change point detection for time
series and spatio-temporal analysis
Abstract: Abrupt aberrations in stochastic systems often result from external factors of interest, such as changes in trading intensity patterns or outbreaks of infectious diseases. These factors can introduce abnormal observations into the corresponding data collection systems. However, the data being monitored typically involve multiple sources, high dimensionality, and convoluted mutual dependence. To promptly detect any change points within complex streaming data, my dissertation research focuses on developing efficient methods for sequential change point detection and multivariate time series modeling.
First, we focus on the study of online structural break detection in financial durations. We propose an ensemble non-parametric methodology that leverages asymptotic theories and re-sampling approaches for robust structural break detection, integrated with semi-parametric model inference techniques. By detecting changes in the pattern of financial durations, practitioners can take advantage of short-term profit opportunities through volatility-related option trading or adjust their position to mitigate the impact of sell-offs in the high-frequency financial market.
Second, we develop a Bayesian hierarchical framework with bivariate temporal effect and latent level-correlated effect for multivariate discrete-valued financial time series. Our framework enables the analysis of how count data relates to relevant covariates and provides forecasts for future individual count data. Additionally, it establishes a connection between time-varying observational correlation and latent correlations to more accurately quantify the association between transaction counts at various risk levels. The INLA implementation of this framework grants computational efficiency and flexibility for large-scale numerical studies.
Third, to address the complexity of the surveillance data, such as the spatio-temporal interdependence, we synthesize relevant techniques from the previous two research projects and propose an iterative sequential outbreak detection procedure for online spatio-temporal daily count data. Specifically, we develop a Bayesian online spatio-temporal outbreak detection with prior updating and p-value adaptation (BOSTON-PUPA) procedure. This iterative procedure involves the generalized Poisson distribution (GPD) model and supports synchronous surveillance over multiple locations with a controlled false detection rate as well as high sensitivity against outbreaks in a wide range of signal-to-noise ratios.
Our research tackles various sequential change point problems across different scenarios, providing efficient modeling for multivariate time series and corresponding sequential change point detection techniques for time-dependent and spatio-temporal data. These methodologies have been successfully applied in real-world applications such as finance and public health, where they offer high-quality statistical inference in an online fashion and can be easily extended to other domains using a similar framework.
Jian Zou, Worcester Polytechnic Institute (Advisor)
Nalini Ravishanker, University of Connecticut
Zheyang Wu, Worcester Polytechnic Institute
Fangfang Wang, Worcester Polytechnic Institute
Qingshuo Song, Worcester Polytechnic Institute