LASSO-Driven Inference in Time and Space

Abstract

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 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 de-biased 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.JEL classification: C12, C22, C51, C53 IntroductionMany applications in statistics, economics, finance, biology and psychology are concerned with a system of ultra high-dimensional objects that communicate within complex dependency channels. Given a complex system involving many factors, one builds a network model by taking a large set of regressions, i.e. regressing every factor in the system on a large subset of other factors. Examples include analysis of financial systemic risk by quantile predictive graphical * We thank

Forecasting in Blockchain-Based Local Energy Markets

“…The first and most intuitive option is to improve the forecasting accuracy with which the predictions, which serve as the basis of bids and asks, are made. For example, a common approach to reduce the bias of LASSO-based predictions are post-LASSO techniques such as presented by Chernozhukov et al [49]. Another aspect that seems relevant for the improvement of forecasting models is the evaluation method.…”

Estimation and HAC-based Inference for Machine Learning Time Series Regressions

“…Eu 2 , and we take the default choice of parameters c and α for the LASSO model: c = 0.5, α = 0.1, see Chernozhukov, Hansen, and Spindler (2016). 31 A.6 Monte Carlo Simulations 31 An alternative, less conservative, but computationally more intensive bootstrap-based algorithm is discussed in Chernozhukov, Härdle, Huang, and Wang (2019). The table reports simulation results for nowcasting accuracy.…”

“…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.…”

“…We provide a general asymptotic theory framework for parameter estimation using a class of regularized regressions under weaker than mixing and polynomial tail conditions. 1 Chernozhukov, Härdle, Huang, and Wang (2019) consider the HAC estimator with a Bartlett kernel without developing the supporting theory, while Feng, Giglio, and Xiu (2019) look at HAC estimation for a specific application but do not provide a general asymptotic theory. Our paper develops the debiased inference based on the explicit bias correction and considers the HAC-based estimators of the residual long-run variance, characterizing how the optimal choice of the bandwidth parameter depends on the number of regressors, their dependence properties, as well as the tail features of the DGP.…”

IPAD: Stable Interpretable Forecasting with Knockoffs Inference

“…[18] then extended this idea to linear functionals. [17] considered debiased simultaneous inference in a system of high-dimensional regression equations with temporal and cross-sectional dependency based on a uniform robust postselection procedure. [36] proposed Lasso residual-based tests for checking goodness-of-fit in (low-and) high-dimensional linear models.…”