Factor Models with Sparse VAR Idiosyncratic Components

Krampe, Jonas; Margaritella, Luca

doi:10.48550/arxiv.2112.07149

Cited by 2 publications

(5 citation statements)

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“…Our proposed approach is distinguished from the approach typically taken in factor-adjusted regression problems (Fan et al, 2020(Fan et al, , 2021aKrampe and Margaritella, 2021), which first estimates the latent process on which some sparsity is assumed and then applies a Lasso-type technique to the estimated process for regression parameter estimation. By directly making use of the autocovariance matrix estimators, our proposed regularised Yule-Walker estimators enjoy methodological simplicity as well as theoretical advantages of avoiding the terms arising from controlling the estimation error of the latent process uniformly over time.…”

Section: 3mentioning

confidence: 99%

“…(i) We contribute to the recent and growing literature on factor-adjusted high-dimensional time series modelling (Fan et al, 2020(Fan et al, , 2021aKrampe and Margaritella, 2021), with particular focus on network estimation and forecasting. In doing so, we take the most general approach to factor adjustment based on the generalised dynamic factor model proposed in Forni et al (2000), which encompasses the static models adopted in the above papers as special cases.…”

Section: Introductionmentioning

confidence: 99%

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FNETS: Factor-adjusted network estimation and forecasting for high-dimensional time series

Barigozzi¹,

Cho²,

Owens³

2022

Preprint

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We propose fnets, a methodology for network estimation and forecasting of highdimensional time series exhibiting strong serial-and cross-sectional correlations. We operate under a factor-adjusted vector autoregressive (VAR) model where, after controlling for common factors accounting for pervasive co-movements of the variables, the remaining idiosyncratic dependence between the variables is modelled by a sparse VAR process. Network estimation of fnets consists of three steps: (i) factor-adjustment via dynamic principal component analysis, (ii) estimation of the parameters of the latent VAR process by means of 1 -regularised Yule-Walker estimators, and (iii) estimation of partial correlation and long-run partial correlation matrices. In doing so, we learn three networks underpinning the latent VAR process, namely a directed network representing the Granger causal linkages between the variables, an undirected one embedding their contemporaneous relationships and finally, an undirected network that summarises both lead-lag and contemporaneous linkages. In addition, fnets provides a suite of methods for separately forecasting the factor-driven and the VAR processes. Under general conditions permitting heavy tails and weak factors, we derive the consistency of fnets in both network estimation and forecasting. Simulation studies and real data applications confirm the good performance of fnets.

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Section: 3mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

FNETS: Factor-adjusted network estimation and forecasting for high-dimensional time series

Barigozzi¹,

Cho²,

Owens³

2022

Preprint

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“…The last two papers also consider regularization procedures applied not only locally, i.e., to each frequency, but also globally and group-wise, that is applied to all frequencies in the interval [0, 2π]. An alternative, semi parametric approach to estimate f −1 is to use sparse vector autoregressive models; see for instance and Krampe and Margaritella (2021) for details.…”

Section: Asymptotic Properties Of Estimatorsmentioning

confidence: 99%

“…In this case, the inverse spectral density matrix can be estimated using, for instance, graphical lasso. However, if the data possesses a factor structure, then spectral density estimators which are designed for lowrank plus sparse structures can be applied; see Barigozzi and Farnè (2021) and Krampe and Margaritella (2021).…”

Section: Implementation Issuesmentioning

confidence: 99%

“…An alternative approach is to use high-dimensional time series models in order to estimate the spectral density matrix or its inverse. Time series models used in this context are dynamic factor models or other types of low rank models, (Forni et al, 2000;Bai and Ng, 2019); sparse vector autoregressive (VAR) models, (Basu and Michailidis, 2015;; as well as combinations thereof, (Basu, Li and Michailidis, 2019;Krampe and Margaritella, 2021). It should be stressed here that a sparse inverse spectral density matrix does not necessarily imply a sparse spectral density matrix, a sparse autocovariance structure, or more general, a sparse time-domain representation of the underlying high-dimensional process.…”

Section: Introductionmentioning

confidence: 99%

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Frequency Domain Statistical Inference for High-Dimensional Time Series

Krampe¹,

Paparoditis²

2022

Preprint

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Analyzing time series in the frequency domain enables the development of powerful tools for investigating the second-order characteristics of multivariate stochastic processes. Parameters like the spectral density matrix and its inverse, the coherence or the partial coherence, encode comprehensively the complex linear relations between the component processes of the multivariate system. In this paper, we develop inference procedures for such parameters in a high-dimensional, time series setup. In particular, we first focus on the derivation of consistent estimators of the coherence and, more importantly, of the partial coherence which possess manageable limiting distributions that are suitable for testing purposes.Statistical tests of the hypothesis that the maximum over frequencies of the coherence, respectively, of the partial coherence, do not exceed a prespecified threshold value are developed. Our approach allows for testing hypotheses for individual coherences and/or partial coherences as well as for multiple testing of large sets of such parameters. In the latter case, a consistent procedure to control the false discovery rate is developed. The finite sample performance of the inference procedures proposed is investigated by means of simulations and applications to the construction of graphical interaction models for brain connectivity based on EEG data are presented.

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Factor Models with Sparse VAR Idiosyncratic Components

Cited by 2 publications

References 0 publications

FNETS: Factor-adjusted network estimation and forecasting for high-dimensional time series

FNETS: Factor-adjusted network estimation and forecasting for high-dimensional time series

Frequency Domain Statistical Inference for High-Dimensional Time Series

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