Model Selection Consistency for Cointegrating Regressions

TL;DR

This paper demonstrates that the adaptive Lasso can consistently select the correct variables in cointegration regressions with weakly exogenous covariates, achieving oracle properties under classical conditions, and provides an algorithm with finite sample validation.

Contribution

It establishes the asymptotic variable selection consistency and oracle property of the adaptive Lasso in cointegration models with specific sample size conditions.

Findings

Adaptive Lasso correctly identifies the true model asymptotically.

The estimator's distribution matches the oracle OLS distribution.

Numerical results confirm finite sample effectiveness.

Abstract

We study the asymptotic properties of the adaptive Lasso in cointegration regressions in the case where all covariates are weakly exogenous. We assume the number of candidate I(1) variables is sub-linear with respect to the sample size (but possibly larger) and the number of candidate I(0) variables is polynomial with respect to the sample size. We show that, under classical conditions used in cointegration analysis, this estimator asymptotically chooses the correct subset of variables in the model and its asymptotic distribution is the same as the distribution of the OLS estimate given the variables in the model were known in beforehand (oracle property). We also derive an algorithm based on the local quadratic approximation and present a numerical study to show the adequacy of the method in finite samples.