Regularized estimation of high‐dimensional vector autoregressions with weakly dependent innovations

Masini, Ricardo; Medeiros, Marcelo C.; Mendes, Eduardo

doi:10.1111/jtsa.12627

Cited by 15 publications

(11 citation statements)

References 36 publications

(65 reference statements)

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“…Wong et al (2020) derived finite-sample guarantees for the LASSO in a misspecified VAR model involving β-mixing process with sub-Weibull marginal distributions. Masini et al (2019) derive equation-wise error bounds for the LASSO estimator of weakly sparse V AR(p) in mixingale dependence settings, that include models with conditionally heteroscedastic innovations.…”

Section: Theoretical Propertiesmentioning

confidence: 99%

Machine Learning Advances for Time Series Forecasting

Masini¹,

Medeiros²,

Mendes³

2020

Preprint

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In this paper we survey the most recent advances in supervised machine learning and highdimensional models for time series forecasting. We consider both linear and nonlinear alternatives. Among the linear methods we pay special attention to penalized regressions and ensemble of models. The nonlinear methods considered in the paper include shallow and deep neural networks, in their feed-forward and recurrent versions, and tree-based methods, such as random forests and boosted trees. We also consider ensemble and hybrid models by combining ingredients from different alternatives. Tests for superior predictive ability are briefly reviewed. Finally, we discuss application of machine learning in economics and finance and provide an illustration with high-frequency financial data.

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Section: Theoretical Propertiesmentioning

confidence: 99%

Machine Learning Advances for Time Series Forecasting

Masini¹,

Medeiros²,

Mendes³

2020

Preprint

Self Cite

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“…in that case, such that typical m.d.s. assumptions as used for instance in Medeiros and Mendes (2016) and Masini et al (2019) do not allow for dynamic miss-specification. Wong et al (2020) also allow for miss-specification by allowing for mixing errors, which is a subset of the error processes allowed here.…”

Section: The High-dimensional Linear Modelmentioning

confidence: 99%

“…Exceptions are Medeiros and Mendes (2016) Masini et al (2019) and Wong et al (2020). Medeiros and Mendes (2016) consider the adaptive lasso for sparse, high-dimensional time series models and show that it is model selection consistent and has the oracle property, even when the errors are non-Gaussian and conditionally heteroskedastic.…”

Section: Introductionmentioning

confidence: 99%

“…Medeiros and Mendes (2016) consider the adaptive lasso for sparse, high-dimensional time series models and show that it is model selection consistent and has the oracle property, even when the errors are non-Gaussian and conditionally heteroskedastic. Masini et al (2019) derive consistency properties of lasso estimation of high-dimensional approximately sparse vector autoregressions for a class of potentially fat tailed and serially dependent errors, which encompass many multivariate volatility models. Wong et al (2020) consider sparse, potentially misspecified, vector autoregres-sions estimated by the lasso and rely on mixing assumptions to derive nonasymptotic inequalities for estimation error and prediction error of the lasso for sub-Weibull random vectors.…”

Section: Introductionmentioning

confidence: 99%

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Lasso Inference for High-Dimensional Time Series

Adamek¹,

Smeekes²,

Wilms³

2020

Preprint

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The desparsified lasso is a high-dimensional estimation method which provides uniformly valid inference. We extend this method to a time series setting under Near-Epoch Dependence (NED) assumptions allowing for non-Gaussian, serially correlated and heteroskedastic processes, where the number of regressors can possibly grow faster than the time dimension. We first derive an oracle inequality for the (regular) lasso, relaxing the commonly made exact sparsity assumption to a weaker alternative, which permits many small but non-zero parameters. The weak sparsity coupled with the NED assumption means this inequality can also be applied to the (inherently misspecified) nodewise regressions performed in the desparsified lasso. This allows us to establish the uniform asymptotic normality of the desparsified lasso under general conditions. Additionally, we show consistency of a long-run variance estimator, thus providing a complete set of tools for performing inference in high-dimensional linear time series models. Finally, we perform a simulation exercise to demonstrate the small sample properties of the desparsified lasso in common time series settings.

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“…Medeiros and Mendes (2016) studied time series lasso with non-Gaussian and heteroskedastic covariates. Masini et al (2019) derived an oracle inequality for sparse VAR with fat probability tail and various dependent settings. Wong et al (2020) studied time series lasso with general tail probability and dependence by relaxing a restriction in Basu and Michailidis (2015).…”

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confidence: 99%

Benign Overfitting in Time Series Linear Model with Over-Parameterization

Nakakita¹,

Imaizumi²

2022

Preprint

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A. The success of large-scale models in recent years has increased the importance of statistical models with numerous parameters. Several studies have analyzed over-parameterized linear models with high-dimensional data that may not be sparse; however, existing results depend on the independent setting of samples. In this study, we analyze a linear regression model with dependent time series data under over-parameterization settings. We consider an estimator via interpolation and developed a theory for excess risk of the estimator under multiple dependence types. This theory can treat infinite-dimensional data without sparsity and handle long-memory processes in a unified manner. Moreover, we bound the risk in our theory via the integrated covariance and nondegeneracy of autocorrelation matrices. The results show that the convergence rate of risks with short-memory processes is identical to that of cases with independent data, while long-memory processes slow the convergence rate. We also present several examples of specific dependent processes that can be applied to our setting.

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Regularized estimation of high‐dimensional vector autoregressions with weakly dependent innovations

Cited by 15 publications

References 36 publications

Machine Learning Advances for Time Series Forecasting

Machine Learning Advances for Time Series Forecasting

Lasso Inference for High-Dimensional Time Series

Benign Overfitting in Time Series Linear Model with Over-Parameterization

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