Research

Publications:

Performance of Empirical Risk Minimization for Linear Regression with Dependent Data (with Christian Brownlees)

Econometric Theory, forthcoming.

This paper establishes bounds on the performance of empirical risk minimization for large-dimensional linear regression. We generalize existing results by allowing the data to be dependent and heavy-tailed. The analysis covers both the cases of identically and heterogeneously distributed observations. Our analysis is nonparametric in the sense that the relationship between the regressand and the regressors is not specified. The main results of this paper show that the empirical risk minimizer achieves the optimal performance (up to a logarithmic factor) in a dependent data setting.

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Community Detection in Partial Correlation Network Models (with Christian Brownlees and Gabor Lugosi)

Journal of Business and Economic Statistics, 2022, 40:1, 216-226. DOI: 10.1080/07350015.2020.1798241  

We introduce a class of partial correlation network models with a community structure for large panels of time series. In the model, the series are partitioned into latent groups such that correlation is higher within groups than between them. We then propose an algorithm that allows one to detect the communities using the eigenvectors of the sample covariance matrix. We study the properties of the procedure and establish its consistency. The methodology is used to study real activity clustering in the U.S.

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Detecting Groups in Large Vector Autoregressions (with Christian Brownlees) 

Journal of Econometrics, 2021, 225:1, 2-26.  DOI: 10.1016/j.jeconom.2021.03.012

This work introduces the stochastic block vector autoregressive (SB-VAR) model. In this class of vector autoregressions, the time series are partitioned into latent groups such that spillover effects are stronger among series that belong to the same group than otherwise. A key question that arises in this framework is how to detect the latent groups from a sample of observations generated by the model. To this end, we propose a group detection algorithm based on the eigenvectors of a function of the estimated autoregressive matrices. We establish that the proposed algorithm consistently detects the groups when the cross-sectional and time-series dimensions are sufficiently large. The methodology is applied to study the group structure of a panel of risk measures of top financial institutions in the United States and a panel of word counts extracted from Twitter.

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Working papers:

Performance of Empirical Risk Minimization For Principal Component Regression (with Christian Brownlees and Yaping Wang)

This paper establishes bounds on the predictive performance of empirical risk minimization for principal component regression. Our analysis is nonparametric, in the sense that the relation between the prediction target and the predictors is not specified. In particular, we do not rely on the assumption that the prediction target is generated by a factor model. The main result of this paper shows that empirical risk minimization for principal component regression is consistent for prediction and, under appropriate conditions, it achieves optimal performance (up to a logarithmic factor).

Detecting Giver and Receiver Spillover Groups in Large Vector Autoregressions 

I propose an algorithm that partitions the series of a large vector autoregression (VAR) into groups based on the spillover structure. The novelty of the procedure is that it is capable of simultaneously detecting both the giver and receiver group structures. I study the properties of the algorithm when the data are generated by a class of network-based VAR models and show that it consistently detects the groups within this class. The methodology is applied to study the spillover group structure in a panel of volatility measures for the constituents of the S&P 100.