The recently proposed scalable ARMA model preserves the parsimony of traditional VARMA models while achieving greater computational tractability. However, existing studies are limited to regularized least squares estimation (LSE) for high-dimensional settings, which is not only statistically less efficient but also requires the sub-Gaussian assumption for its theoretical guarantees. Moreover, it still lacks inference tool for real applications. To fill this gap, we develop a quasi-maximum likelihood estimation (QMLE) framework for scalable ARMA models. Its asymptotic normality is established under a finite fourth order moment condition, and we formally prove its asymptotic efficiency gain over LSE. We also introduce an efficient block coordinate descent algorithm for computation and a consistent Bayesian information criterion for model selection. Simulation studies validate the finite-sample performance of our methodology, and an empirical application to six macroeconomic indicators demonstrates its practical utility.

翻译：最新提出的可扩展ARMA模型在保持传统VARMA模型简洁性的同时，大幅提升了计算可行性。然而，现有研究主要集中于高维场景下的正则化最小二乘估计，该方法不仅统计效率偏低，而且其理论保证依赖于次高斯分布假设。此外，实际应用中仍缺乏有效的推断工具。为弥补这一不足，我们构建了可扩展ARMA模型的准最大似然估计框架。在有限四阶矩条件下建立了渐近正态性，并严格证明了该估计方法相较于最小二乘估计的渐近效率优势。我们同时提出了高效块坐标下降算法用于计算，以及一致贝叶斯信息准则用于模型选择。仿真实验验证了所提方法在有限样本下的表现，六个宏观经济指标的实证分析展示了其实际应用价值。