A Consistent ICM-based $\chi^2$ Specification Test

TL;DR

This paper introduces a new ICM-based $\\chi^2$ test that is consistent, computationally efficient, robust to heteroskedasticity, and suitable for large samples, improving upon existing bootstrap methods.

Contribution

It proposes a novel ICM-based specification test with asymptotic $\\chi^2$ distribution, robustness, and enhanced computational efficiency compared to traditional bootstrap schemes.

Findings

Exhibits good size control in simulations

Demonstrates competitive power with classical tests

Robust to heteroskedasticity of unknown form

Abstract

In spite of the omnibus property of Integrated Conditional Moment (ICM) specification tests, they are not commonly used in empirical practice owing to features such as the non-pivotality of the test and the high computational cost of available bootstrap schemes, especially in large samples. This paper proposes specification and mean independence tests based on ICM metrics. The proposed test exhibits consistency, asymptotic $\chi^2$-distribution under the null hypothesis, and computational efficiency. Moreover, it demonstrates robustness to heteroskedasticity of unknown form and can be adapted to enhance power towards specific alternatives. A power comparison with classical bootstrap-based ICM tests using Bahadur slopes is also provided. Monte Carlo simulations are conducted to showcase the excellent size control and competitive power of the proposed test.