Dynamic Systems, Sequential and Time Series Analysis

We introduce a novel Bayesian framework for estimating time-varying volatility by extending the Random Walk Stochastic Volatility (RWSV) model with a new Dynamic Shrinkage Process (DSP) in (log) variances. Unlike classical Stochastic Volatility or GARCH-type models with restrictive parametric stationarity assumptions, our proposed Adaptive Stochastic Volatility (ASV) model provides smooth yet dynamically adaptive estimates of evolving volatility and its uncertainty (vol of vol). We derive the theoretical properties of the proposed global-local shrinkage prior. Through simulation studies, we demonstrate that ASV exhibits remarkable misspecification resilience with low prediction error across various data generating scenarios in simulation. Furthermore, ASV's capacity to yield locally smooth and interpretable estimates facilitates a clearer understanding of underlying patterns and trends in volatility. Additionally, we propose and illustrate an extension for Bayesian Trend Filtering simultaneously in both mean and variance. Finally, we show that this attribute makes ASV a robust tool applicable across a wide range of disciplines, including in finance, environmental science, epidemiology, and medicine, among others. This is joint work with Jason B. Cho.  

Observations in various applications are frequently represented as a time series of multidimensional arrays, called tensor time series, preserving the inherent multidimensional structure. In this paper, we present a factor model approach, in a form similar to tensor CANDECOMP/PARAFAC (CP) decomposition, to the analysis of high-dimensional dynamic tensor time series. As the loading vectors are uniquely defined but not necessarily orthogonal, it is significantly different from the existing tensor factor models based on Tucker-type tensor decomposition. The model structure allows for a set of uncorrelated one-dimensional latent dynamic factor processes, making it much more convenient to study the underlying dynamics of the time series. A new high-order projection estimator is proposed for such a factor model, utilizing the special structure and the idea of the higher order orthogonal iteration procedures commonly used in Tucker-type tensor factor model and general tensor CP decomposition procedures. Theoretical investigation provides statistical error bounds for the proposed methods, which shows the significant advantage of utilizing the special model structure. Simulation study is conducted to further demonstrate the finite sample properties of the estimators. Real data application is used to illustrate the model and its interpretations. 

The moving sum (MOSUM) test statistic is popular for multiple change-point detection due to its simplicity of implementation and effective control of the significance level for multiple testing. However, its performance heavily relies on the selection of the bandwidth parameter for the window size, which is extremely difficult to determine in advance. To address this issue, we propose an adaptive MOSUM method, applicable in both multiple and high-dimensional time series models. Specifically, we adopt an $\ell^2$-norm to aggregate MOSUM statistics cross-sectionally, and take the maximum over time and bandwidth candidates. We provide the asymptotic distribution of the test statistics, accommodating general weak temporal and cross-sectional dependence. By employing a screening procedure, we can consistently estimate the number of change points, and the convergence rates for the estimated timestamps and sizes of the breaks are presented. The asymptotic properties and the estimation precision are demonstrated by extensive simulation studies. Furthermore, we present an application using real-world COVID-19 data from Brazil, wherein we observe distinct outbreak stages among subjects of different age groups and geographic locations.