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This work concerns the analysis and design of distributed first-order optimization algorithms over time-varying graphs. The goal of such algorithms is to optimize a global function that is the average of local functions using only local…

We investigate the time-varying ARCH (tvARCH) process. It is shown that it can be used to describe the slow decay of the sample autocorrelations of the squared returns often observed in financial time series, which warrants the further…

We describe spatio-temporal random processes using linear mixed models. We show how many commonly used models can be viewed as special cases of this general framework and pay close attention to models with separable or product-sum…

When dealing with time series data, causal inference methods often employ structural vector autoregressive (SVAR) processes to model time-evolving random systems. In this work, we rephrase recursive SVAR processes with possible latent…

Local projection (LP) and structural vector autoregression (SVAR) are commonly employed to estimate dynamic causal effects of macroeconomic policies at multiple horizons. With enough lags as controls, LP estimators have little bias but…

This paper studies the covariance matrix estimation for high-dimensional time series within a new framework that combines low-rank factor and latent variable-specific cluster structures. The popular methods based on assuming the sparse…

High-dimensional time series data appear in many scientific areas in the current data-rich environment. Analysis of such data poses new challenges to data analysts because of not only the complicated dynamic dependence between the series,…

The spatio-temporal autoregressive moving average (STARMA) model is frequently used in several studies of multivariate time series data, where the assumption of stationarity is important, but it is not always guaranteed in practice. One way…

Forecasting the evolution of complex systems is one of the grand challenges of modern data science. The fundamental difficulty lies in understanding the structure of the observed stochastic process. In this paper, we show that every…

We revisit a model for time-varying linear regression that assumes the unknown parameters evolve according to a linear dynamical system. Counterintuitively, we show that when the underlying dynamics are stable the parameters of this model…

Classical spectral methods are subject to two fundamental limitations: they only can account for covariance-related serial dependencies, and they require second-order stationarity. Much attention has been devoted lately to quantile-based…

We introduce a nonparametric nonlinear VAR prewhitened long-run variance (LRV) estimator for the construction of standard errors robust to autocorrelation and heteroskedasticity that can be used for hypothesis testing in a variety of…

For statistical inference of means of stationary processes, one needs to estimate their time-average variance constants (TAVC) or long-run variances. For a stationary process, its TAVC is the sum of all its covariances and it is a multiple…

We develop a timescale synthesis-based probabilistic approach for the modeling of locally stationary signals. Inspired by our previous work, the model involves zero-mean, complex Gaussian wavelet coefficients, whose distribution varies as a…

We discuss the issue of estimating large-scale vector autoregressive (VAR) models with stochastic volatility in real-time situations where data are sampled at different frequencies. In the case of a large VAR with stochastic volatility, the…

Support vector machine (SVM) has attracted great attentions for the last two decades due to its extensive applications, and thus numerous optimization models have been proposed. To distinguish all of them, in this paper, we introduce a new…

We consider estimation of quantile curves for a general class of nonstationary processes. Consistency and central limit results are obtained for local linear quantile estimates under a mild short-range dependence condition. Our results are…

This paper analyzes Structural Vector Autoregressions (SVARs) where identification of structural parameters holds locally but not globally. In this case there exists a set of isolated structural parameter points that are observationally…

Geographical and Temporal Weighted Regression (GTWR) model is an important local technique for exploring spatial heterogeneity in data relationships, as well as temporal dependence due to its high fitting capacity when it comes to real…

The problem of broad practical interest in spatiotemporal data analysis, i.e., discovering interpretable dynamic patterns from spatiotemporal data, is studied in this paper. Towards this end, we develop a time-varying reduced-rank vector…