LASSO-driven inference in time and space

Chernozhukov, Victor; Härdle, Wolfgang Karl; Huang, Chen; Wang, Weining

doi:10.1214/20-aos2019

Cited by 26 publications

(10 citation statements)

References 68 publications

(87 reference statements)

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“…Lastly, it is important to study the high-dimensional statistical inference under the proposed model, e.g., hypothesis testing for Granger causality (Chernozhukov et al, 2021;Babii et al, 2022).…”

Section: Conclusion and Discussionmentioning

confidence: 99%

An Interpretable and Efficient Infinite-Order Vector Autoregressive Model for High-Dimensional Time Series

Zheng¹,

Li²

2022

Preprint

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As a special infinite-order vector autoregressive (VAR) model, the vector autoregressive moving average (VARMA) model can capture much richer temporal patterns than the widely used finite-order VAR model. However, its practicality has long been hindered by its non-identifiability, computational intractability, and relative difficulty of interpretation. This paper introduces a novel infinite-order VAR model which, with only a little sacrifice of generality, inherits the essential temporal patterns of the VARMA model but avoids all of the above drawbacks. As another attractive feature, the temporal and cross-sectional dependence structures of this model can be interpreted separately, since they are characterized by different sets of parameters. For high-dimensional time series, this separation motivates us to impose sparsity on the parameters determining the cross-sectional dependence. As a result, greater statistical efficiency and interpretability can be achieved, while no loss of temporal information is incurred by the imposed sparsity. We introduce an ℓ 1 -regularized estimator for the proposed model and derive the corresponding nonasymptotic error bounds. An efficient block coordinate descent algorithm and a consistent model order selection method are developed. The merit of the proposed approach is supported by simulation studies and a real-world macroeconomic data analysis.

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Section: Conclusion and Discussionmentioning

confidence: 99%

An Interpretable and Efficient Infinite-Order Vector Autoregressive Model for High-Dimensional Time Series

Zheng¹,

Li²

2022

Preprint

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“…For instance, Kock and Callot (2015) establish oracle inequalities for the VAR with i.i.d. errors; Wong, Li, and Tewari (2019) consider β-mixing series with exponential tails; Wu and Wu (2016), Han andTsay (2017), andChernozhukov, Härdle, Huang, andWang (2019) allow for polynomial tails under the functional dependence measure of Wu (2005).…”

Section: Introductionmentioning

confidence: 99%

Machine Learning Time Series Regressions with an Application to Nowcasting

Babii¹,

Ghysels²,

Striaukas³

2020

Preprint

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This paper introduces structured machine learning regressions for high-dimensional time series data potentially sampled at different frequencies. The sparse-group LASSO estimator can take advantage of such time series data structures and outperforms the unstructured LASSO. We establish oracle inequalities for the sparse-group LASSO estimator within a framework that allows for the mixing processes and recognizes that the financial and the macroeconomic data may have heavier than exponential tails. An empirical application to nowcasting US GDP growth indicates that the estimator performs favorably compared to other alternatives and that the text data can be a useful addition to more traditional numerical data.

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“…For instance, Kock and Callot (2015) establish oracle inequalities for VAR with i.i.d. errors, Wong, Li, and Tewari (2019) consider β-mixing series with exponential tails, Wu and Wu (2016), Han and Tsay (2017), and Chernozhukov, Härdle, Huang, and Wang (2019) allow for polynomial tails under the functional dependence measure of Wu (2005). They also develop the partialling-out type inference in systems of regression equations.…”

Section: Introductionmentioning

confidence: 99%

“….31 A.6 Monte Carlo Simulations 31 An alternative, less conservative, but computationally more intensive bootstrap-based algorithm is discussed inChernozhukov, Härdle, Huang, and Wang (2019).…”

mentioning

confidence: 99%