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 financial time series. An efficient block coordinate descent algorithm is further introduced to search for estimates, and a Bayesian information criterion 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：本文考虑了最近提出的可扩展ARMA模型（一种参数化的无穷阶向量自回归模型）的最小二乘估计和拟极大似然估计，并建立了它们的渐近正态性。这使得对该计算高效模型的推断成为可能，尤其适用于金融时间序列分析。本文进一步引入了一种高效的块坐标下降算法以求解估计量，并提出了贝叶斯信息准则用于模型选择。通过模拟实验展示了它们在有限样本下的表现，同时对六个宏观经济指标的实际应用说明了所提方法的有效性。