Wednesday, Aug 6: 2:00 PM - 3:50 PM
0544
Invited Paper Session
Music City Center
Room: CC-207D
Applied
Yes
Main Sponsor
Business and Economic Statistics Section
Co Sponsors
IMS
Section on Statistical Learning and Data Science
Presentations
Panel vector auto-regressive (VAR) models are widely used to capture the dynamics of multivariate time series across different subpopulations, where each subpopulation shares a common set of variables. In this work, we propose a panel VAR model with a shared low-rank structure, modulated by subpopulation-specific weights, and complemented by idiosyncratic sparse components. To ensure parameter identifiability, we impose structural constraints that lead to a nonsmooth, nonconvex optimization problem. We develop a multi-block Alternating Direction Method of Multipliers (ADMM) algorithm for parameter estimation and establish its convergence under mild regularity conditions. Furthermore, we derive consistency guarantees for the proposed estimators under high-dimensional scaling. The effectiveness of the proposed modeling framework and estimators is demonstrated through experiments on both synthetic data and a real-world neuroscience data set.
The objective of transfer learning is to enhance estimation and inference in a target data by leveraging knowledge gained from additional sources. Recent studies have explored transfer learning for independent observations in complex, high-dimensional models assuming sparsity, yet research on time series models remains limited. Our focus is on transfer learning for sequences of observations with temporal dependencies and a more intricate model parameter structure. Specifically, we investigate the vector autoregressive model (VAR), a widely recognized model for time series data, where the transition matrix can be deconstructed into a combination of a sparse matrix and a low-rank one. We propose a new transfer learning algorithm tailored for estimating high-dimensional VAR models characterized by low-rank and sparse structures. Additionally, we present a novel approach for selecting informative observations from auxiliary datasets. Theoretical guarantees are established, encompassing model parameter consistency, informative set selection, and the asymptotic distribution of estimators under mild conditions. The latter facilitates the construction of entry-wise confidence intervals for model parameters. Finally, we demonstrate the empirical efficacy of our methodologies through both simulated and real-world datasets.
Keywords
Transfer Learning, High-dimensional Estimation, Sparse and Low-Rank Structures
This paper considers the joint estimation and identification of latent group structures in dynamic spatial panel data models with common shocks. We consider a spatial panel data model that allows for both weak and strong cross-sectional correlations, where weak correlations are captured by a spatial structure and strong correlations are captured by a factor structure. The latent group structures allow individuals to be classified into different groups where the number of groups and the group memberships are unknown. The individuals within a group have common slope parameters, while parameter heterogeneity is allowed across the groups. To estimate the number of groups and identify the latent group structures, a pairwise fusion penalized quasi-maximum likelihood approach is proposed. We provide the asymptotic analysis of the proposed approach. The asymptotic analysis demonstrate the desirable properties of the method, including classification consistency, and the oracle property of the post-classification estimator. The proposed method is further illustrated by simulation studies which demonstrate the good finite sample performance of the method, and is applied to the real house price data across 377 Metropolitan Statistical Areas in the US which suggest the presence of group structures.
Keywords
Classification; Common shocks; Latent group structures; Pairwise adaptive; group fused Lasso; Panel data models; Spatial interactions
A sequential testing procedure is proposed to uncover common structures across multiple high-dimensional factor models. The test is motivated by observing data from multiple individuals, which can be modeled through factor models that potentially share information encoded in their respective loading matrices. The introduced sequential procedure allows testing whether these loading matrices are identical up to a rotational change or if only a partial set of column vectors is shared across individuals. The theoretical results cover the asymptotic behavior of the test statistic, supported by a simulation study demonstrating promising empirical test size and power. Finally, the method is applied to investigate the relationship between multiple individuals with anxiety disorder.
Keywords
Common structures, Sequential testing, High-dimensional factor models.
Speaker
Marie Duker, Friedrich-Alexander Universität Erlangen-Nürnberg
Many time series often exhibit heteroskedasticity, posing challenges for analysis. While multivariate generalized autoregressive conditional heteroskedasticity (MGARCH) models offer solutions, they often suffer from overcapitalization, escalating parameter counts with dimensionality. In this presentation, we introduce a parsimonious approach to the vector autoregressive (VAR) model incorporating a heteroskedastic structure within the error terms. Our method provides substantial efficiency gains in model estimation by significantly reducing the number of parameters in the coefficient and conditional covariance matrices of VAR-MGARCH models. By parameterizing our method, redundant information within time series signals is eliminated, significantly reducing model complexity. We investigate the asymptotic properties of estimators and evaluate our approach through simulation studies and real-data analysis, offering enhanced modeling accuracy and computational efficiency for volatile financial time series.
Keywords
Heteroskedasticity, Multivariate GARCH (MGARCH), Parsimonious Modeling.