Weighted Reduced Rank Estimators Under Cointegration Rank Uncertainty

TL;DR

This paper investigates the impact of rank misspecification in cointegration analysis, proposing weighted estimators that improve predictive accuracy under rank uncertainty, with empirical validation on EEG data.

Contribution

It introduces a new class of weighted reduced rank estimators that handle rank uncertainty more flexibly than traditional methods.

Findings

Weighted estimators reduce bias under rank misspecification

Proper weighting improves predictive performance

Empirical EEG data demonstrates estimator effectiveness

Abstract

Cointegration analysis was developed for non-stationary linear processes that exhibit stationary relationships between coordinates. Estimation of the cointegration relationships in a multi-dimensional cointegrated process typically proceeds in two steps. First the rank is estimated, then the cointegration matrix is estimated, conditionally on the estimated rank (reduced rank regression). The asymptotics of the estimator is usually derived under the assumption of knowing the true rank. In this paper, we quantify the asymptotic bias and find the asymptotic distributions of the cointegration estimator in case of misspecified rank. Furthermore, we suggest a new class of weighted reduced rank estimators that allow for more flexibility in settings where rank selection is hard. We show empirically that a proper choice of weights can lead to increased predictive performance when there is rank uncertainty. Finally, we illustrate the estimators on empirical EEG data from a psychological experiment on visual processing.