ON THE SIZE CONTROL OF THE HYBRID TEST FOR SUPERIOR PREDICTIVE ABILITY
分析了混合检验在预测能力比较中的理论性质，发现其在常见显著性水平下可能无法控制检验规模，例如在5%名义水平下拒绝率超过11%，并通过蒙特卡洛模拟验证了理论结果。
This article analyzes the theoretical properties of the hybrid test for superior predictive ability. A simple example reveals that the test may not be size-controlled at common significance levels with rejection rates exceeding $11\%$ at a $5\%$ nominal level. Generalizing this observation, the main results show the pointwise asymptotic invalidity of the hybrid test under reasonable conditions. Monte Carlo simulations support these theoretical findings.