标题： 高维二元变量：非平稳协变量和因子的最大似然估计 显示英文标题

标题： High-Dimensional Binary Variates: Maximum Likelihood Estimation with Nonstationary Covariates and Factors

摘要： 本文介绍了一种高维二元变量模型，该模型可以容纳非平稳的协变量和因子，并研究了它们的渐近理论。这一框架涵盖了单指标非平稳或协整的情形。对于非平稳单指标，当横截面维度 $N$ 和时间跨度 $T$ 趋于无穷时，在条件 $T^{1/2}/N\to0$ 下，系数的最大似然估计量（MLE）具有双重收敛速度且在整体上是一致的。所有非平稳因子的 MLE 在 $T^{\delta}/N\to0$ 成立时是一致的，其中 $\delta$ 取决于链接函数。因子的极限分布依赖于时间 $t$，由 Hessian 矩阵趋于零的收敛性所控制。在单指标协整的情况下，因子和系数的 MLE 以更高的速率 $\min(\sqrt{N},\sqrt{T})$ 收敛。 与非平稳单指标相比，一个显著特征是系数的双重收敛速度从$(T^{1/4},T^{3/4})$增加到$(T^{1/2},T)$。 此外，在协整情况下，因子的极限分布不依赖于$t$。 蒙特卡洛模拟验证了估计的准确性。 在实证应用中，我们利用该模型分析金融市场的跳跃到达，提取跳跃到达因子，并展示了它们在大规模资产定价中的有效性。 显示英文摘要

摘要： This paper introduces a high-dimensional binary variate model that accommodates nonstationary covariates and factors, and studies their asymptotic theory. This framework encompasses scenarios where single indices are nonstationary or cointegrated. For nonstationary single indices, the maximum likelihood estimator (MLE) of the coefficients has dual convergence rates and is collectively consistent under the condition $T^{1/2}/N\to0$, as both the cross-sectional dimension $N$ and the time horizon $T$ approach infinity. The MLE of all nonstationary factors is consistent when $T^{\delta}/N\to0$, where $\delta$ depends on the link function. The limiting distributions of the factors depend on time $t$, governed by the convergence of the Hessian matrix to zero. In the case of cointegrated single indices, the MLEs of both factors and coefficients converge at a higher rate of $\min(\sqrt{N},\sqrt{T})$. A distinct feature compared to nonstationary single indices is that the dual rate of convergence of the coefficients increases from $(T^{1/4},T^{3/4})$ to $(T^{1/2},T)$. Moreover, the limiting distributions of the factors do not depend on $t$ in the cointegrated case. Monte Carlo simulations verify the accuracy of the estimates. In an empirical application, we analyze jump arrivals in financial markets using this model, extract jump arrival factors, and demonstrate their efficacy in large-cross-section asset pricing.