This paper considers both the least squares and quasi-maximum likelihood estimation for the recently proposed scalable ARMA model, a parametric infinite-order vector AR model, and their asymptotic normality is also established. It makes feasible the inference on this computationally efficient model, especially for economic and financial time series. An efficient block coordinate descent algorithm is further introduced to search for estimates, and a Bayesian information criterion with selection consistency is suggested for model selection. Simulation experiments are conducted to illustrate their finite sample performance, and a real application on six macroeconomic indicators illustrates the usefulness of the proposed methodology.

翻译：本文针对最近提出的可扩展ARMA模型（一种参数化无限阶向量自回归模型），同时研究了最小二乘估计与拟极大似然估计方法，并建立了其渐近正态性。这使得对这一计算高效模型进行统计推断成为可能，尤其适用于经济和金融时间序列分析。本文进一步引入了一种高效的块坐标下降算法进行参数估计，并提出具有选择一致性的贝叶斯信息准则用于模型选择。通过模拟实验验证了所提方法在有限样本下的性能，并通过对六个宏观经济指标的实际应用展示了该方法的实用性。