Consistent Selection of the Number of Groups in Panel Models via Cross-Validation

TL;DR

This paper introduces a data-driven cross-validation method for accurately selecting the number of groups in panel data models, ensuring consistency and broad applicability across various models.

Contribution

The paper proposes a novel CV approach for group number selection that is fully data-driven, tuning-free, and adaptable to diverse panel data models.

Findings

The CV method accurately estimates the number of groups in synthetic datasets.

The method demonstrates consistency under theoretical conditions.

Application to Chinese stock data reveals heterogeneous volatility patterns.

Abstract

Group number selection is a key problem for group panel data modeling. In this work, we develop a cross-validation (CV) method to tackle this problem. Specifically, we split the panel data into two data folds on the time span, with group structure preserved for individuals. We first estimate the group memberships and parameters on one data fold, then we plug in the estimates and utilize the other data fold to evaluate a designed criterion. Subsequently, the group number is estimated by minimizing the average criterion across all data folds. The proposed CV method has two advantages compared to existing approaches. First, the method is totally data-driven, thus no further tuning parameters are involved. Second, the method can be flexibly applied to a wide range of panel data models. Theoretically, we establish the estimation consistency by taking advantage of the optimization property of the estimation algorithm. Experiments are carried out with a variety of synthetic datasets and panel models to further illustrate the advantages of the proposed method. Lastly, the CV method is employed to analyze the heterogeneous patterns of stock volatilities in the Chinese stock market through the financial crisis.