On LASSO for predictive regression

By Ji Hyung Lee, Zhentao Shi, Zhan Gao. Journal of Econometrics, 2018

108 citations recorded by the source corpus.

A typical predictive regression employs a multitude of potential regressors with various degrees of persistence while their signal strength in explaining the dependent variable is often low. Variable selection in such context is of great importance. In this paper, we explore the pitfalls and possibilities of LASSO methods in this predictive regression framework with mixed degrees of persistence. In the presence of stationary, unit root and cointegrated predictors, we show that the adaptive LASSO asymptotically breaks cointegrated groups although it cannot wipe out all inactive cointegrating variables. This new finding motivates a simple but novel post-selection adaptive LASSO, which we call the twin adaptive LASSO (TAlasso), to fix variable selection inconsistency. TAlasso's penalty scheme accommodates the system of heterogeneous regressors, and it recovers the well-known oracle property that implies variable selection consistency and optimal rate of convergence for all three types of regressors. On the contrary, conventional LASSO fails to attain coefficient estimation consistency and variable screening in all components simultaneously, since its penalty is imposed according to the marginal behavior of each individual regressor only. We demonstrate the theoretical properties via extensive Monte Carlo simulations. These LASSO-type methods are applied to evaluate short- and long-horizon predictability of S&P 500 excess return.

Subfields: Artificial Intelligence, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/879687132131275e2b897548c797e052d743aa5c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Marcelo C. Medeiros
2. Eduardo F. Mendes
3. Ricardo P. Masini

In Management Science and Operations Research

1. Marcelo C. Medeiros
2. Eduardo F. Mendes
3. Ricardo P. Masini
4. James W. Taylor

In Statistics and Probability

1. Ricardo P. Masini
2. Marcelo C. Medeiros
3. Eduardo F. Mendes
4. Tetsuya Takaishi

Citations in the corpus

• Machine Learning Advances for Time Series Forecasting (2020, background): “In sparse, high-dimensional, integrated time-series settings, Lee and Shi (2020) and Koo et al. (2020) show model selection consistency and derive the asymptotic distributions of LASSO estimators and some variants.”