Related papers: Modeling High-Dimensional Unit-Root Time Series

We focus on variational inference in dynamical systems where the discrete time transition function (or evolution rule) is modelled by a Gaussian process. The dominant approach so far has been to use a factorised posterior distribution,…

Identifying the number of factors in a high-dimensional factor model has attracted much attention in recent years and a general solution to the problem is still lacking. A promising ratio estimator based on the singular values of the lagged…

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…

This paper develops an inferential theory for high-dimensional matrix-variate factor models with missing observations. We propose an easy-to-use all-purpose method that involves two straightforward steps. First, we perform principal…

I develop a feasible weighted projected principal component (FPPC) analysis for factor models in which observable characteristics partially explain the latent factors. This novel method provides more efficient and accurate estimators than…

Functional time series (FTS) data have become increasingly available in real-world applications. Research on such data typically focuses on two objectives: curve reconstruction and forecasting, both of which require efficient dimension…

Stationarity is a very common assumption in time series analysis. A vector autoregressive process is stationary if and only if the roots of its characteristic equation lie outside the unit circle, constraining the autoregressive coefficient…

Score-based stochastic denoising models have recently been demonstrated as powerful machine learning tools for conditional and unconditional image generation. The existing methods are based on a forward stochastic process wherein the…

We propose a new framework -- Square Root Principal Component Pursuit -- for low-rank matrix recovery from observations corrupted with noise and outliers. Inspired by the square root Lasso, this new formulation does not require prior…

We tackle the challenges of modeling high-dimensional data sets, particularly those with latent low-dimensional structures hidden within complex, non-linear, and noisy relationships. Our approach enables a seamless integration of concepts…

The method of instrumental variables provides a fundamental and practical tool for causal inference in many empirical studies where unmeasured confounding between the treatments and the outcome is present. Modern data such as the genetical…

This paper is concerned with robust performance criteria for linear continuous time invariant stochastic systems driven by statistically uncertain random processes. The uncertainty is understood as the deviation of imprecisely known…

This paper considers nonparametric estimation and inference in first-order autoregressive (AR(1)) models with deterministically time-varying parameters. A key feature of the proposed approach is to allow for time-varying stationarity in…

We consider the segmentation of set of correlated time-series, the correlation being allowed to take an arbitrary form but being the same at each time-position. We show that encoding the dependency in a factor model enables us to use the…

In this paper, we propose a novel approach to modeling nonstationary spatial fields. The proposed method works by expanding the geographic plane over which these processes evolve into higher dimensional spaces, transforming and clarifying…

We propose tensor time series imputation when the missing pattern in the tensor data can be general, as long as any two data positions along a tensor fibre are both observed for enough time points. The method is based on a tensor time…

This paper addresses the prediction of stationary functional time series. Existing contributions to this problem have largely focused on the special case of first-order functional autoregressive processes because of their technical…

Modern time series forecasting methods, such as Transformer and its variants, have shown strong ability in sequential data modeling. To achieve high performance, they usually rely on redundant or unexplainable structures to model complex…

Factor-based forecasting using Principal Component Analysis (PCA) is an effective machine learning tool for dimension reduction with many applications in statistics, economics, and finance. This paper introduces a Supervised Screening and…

This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection…