Quasi-maximum likelihood estimation for scalable ARMA models

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.