Regularized Estimation of High-dimensional Factor-Augmented Vector Autoregressive (FAVAR) Models

Lin, Jiahe; Michailidis, George

doi:10.2139/ssrn.3615069

Cited by 34 publications

(48 citation statements)

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“…group lasso, sparse group lasso, etc.). The results of Basu and Michailidis (2015); Melnyk and Banerjee (2016) and related follow-up work (Raskutti and Yuan (2015); Schweinberger et al (2017); Lin and Michailidis (2017)) indicate that the resulting estimation error rates are those obtained for independent and identically distributed data times a factor that captures the temporal dependence in the data.…”

Section: Introductionmentioning

confidence: 89%

“…Further, we employ a flat (uniform) prior distribution for the error term. Note that the joint maximum likelihood estimation problem for a sparse VAR model, with a sparse error covariance matrix is investigated in Lin and Michailidis (2017). The posterior consistency results are established under mild regularity assumptions on the underlying spectral density and with p = o ( n/ log n ).…”

Section: Introductionmentioning

confidence: 99%

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High-Dimensional Posterior Consistency in Bayesian Vector Autoregressive Models

Ghosh

Khare

Michailidis

2018

Journal of the American Statistical Association

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Vector autoregressive (VAR) models aim to capture linear temporal interdependencies amongst multiple time series. They have been widely used in macroeconomics and financial econometrics and more recently have found novel applications in functional genomics and neuroscience. These applications have also accentuated the need to investigate the behavior of the VAR model in a high-dimensional regime, which provides novel insights into the role of temporal dependence for regularized estimates of the model’s parameters. However, hardly anything is known regarding properties of the posterior distribution for Bayesian VAR models in such regimes. In this work, we consider a VAR model with two prior choices for the autoregressive coefficient matrix: a non-hierarchical matrix-normal prior and a hierarchical prior, which corresponds to an arbitrary scale mixture of normals. We establish posterior consistency for both these priors under standard regularity assumptions, when the dimension p of the VAR model grows with the sample size n (but still remains smaller than n). A special case corresponds to a shrinkage prior that introduces (group) sparsity in the columns of the model coefficient matrices. The performance of the model estimates are illustrated on synthetic and real macroeconomic data sets.

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Section: Introductionmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

High-Dimensional Posterior Consistency in Bayesian Vector Autoregressive Models

Ghosh

Khare

Michailidis

2018

Journal of the American Statistical Association

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“…High dimensional time series analysis and their applications have become increasingly important in diverse domains, including macroeconomics (Kilian & Lütkepohl (2017), Stock & Watson (2016)), financial economics (Billio et al (2012), Lin & Michailidis (2017)), molecular biology (Michailidis & d'Alché Buc (2013)) and neuroscience (Friston et al (2014), Schröder & Ombao (2019)). Such data are usually both cross-correlated and autocorrelated.…”

Section: Introductionmentioning

confidence: 99%

Multiple Change Points Detection in Low Rank and Sparse High Dimensional Vector Autoregressive Models

Bai

Safikhani

Michailidis

2020

IEEE Trans. Signal Process.

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We study the problem of detecting and locating change points in high-dimensional Vector Autoregressive (VAR) models, whose transition matrices exhibit low rank plus sparse structure. We first address the problem of detecting a single change point using an exhaustive search algorithm and establish a finite sample error bound for its accuracy. Next, we extend the results to the case of multiple change points that can grow as a function of the sample size. Their detection is based on a twostep algorithm, wherein the first step, an exhaustive search for a candidate change point is employed for overlapping windows, and subsequently a backwards elimination procedure is used to screen out redundant candidates. The two-step strategy yields consistent estimates of the number and the locations of the change points. To reduce computation cost, we also investigate conditions under which a surrogate VAR model with a weakly sparse transition matrix can accurately estimate the change points and their locations for data generated by the original model. This work also addresses and resolves a number of novel technical challenges posed by the nature of the VAR models under consideration. The effectiveness of the proposed algorithms and methodology is illustrated on both synthetic and two real data sets.

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“…There are also many extensions to the LASSO estimation with dependent data. For example, Basu and Michailidis (2015) study the consistency of the estimator in sparse high-dimensional Gaussian time series models; Kock and Callot (2015) consider the high-dimensional near-oracle inequalities in large vector autoregressive (VAR) models; Lin and Michailidis (2017) look at the regularized estimation and testing for high-dimensional multi-block VAR models. However, the majority of the literature imposes a Gaussian or sub-Gaussian assumption on the error distribution; this is rather restrictive and excludes heavy tail distributions.…”

Section: Introductionmentioning

confidence: 99%

LASSO-driven inference in time and space

et al. 2021

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We consider the estimation and inference in a system of high-dimensional regression equations allowing for temporal and cross-sectional dependency in covariates and error processes, covering rather general forms of weak temporal dependence. A sequence of regressions with many regressors using LASSO (Least Absolute Shrinkage and Selection Operator) is applied for variable selection purpose, and an overall penalty level is carefully chosen by a block multiplier bootstrap procedure to account for multiplicity of the equations and dependencies in the data. Correspondingly, oracle properties with a jointly selected tuning parameter are derived. We further provide high-quality debiased simultaneous inference on the many target parameters of the system. We provide bootstrap consistency results of the test procedure, which are based on a general Bahadur representation for the Z-estimators with dependent data. Simulations demonstrate good performance of the proposed inference procedure. Finally, we apply the method to quantify spillover effects of textual sentiment indices in a financial market and to test the connectedness among sectors.

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Regularized Estimation of High-dimensional Factor-Augmented Vector Autoregressive (FAVAR) Models

Cited by 34 publications

References 0 publications

High-Dimensional Posterior Consistency in Bayesian Vector Autoregressive Models

High-Dimensional Posterior Consistency in Bayesian Vector Autoregressive Models

Multiple Change Points Detection in Low Rank and Sparse High Dimensional Vector Autoregressive Models

LASSO-driven inference in time and space

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