Maximum Likelihood Estimation of Stable ARX Models using Randomized Coordinate Descent

Autoregressive models play an important role in a variety of applications including finance, engineering, sciences, and agriculture. While for some models (e.g., physics-based models) parameters are known, in other domains the parameters may not be available. This paper deals with the estimation of the parameters of an autoregressive model with exogenous variables. A significant body of literature has explored autoregressive model estimation across different estimation criteria, data availability, and parameterization; however, limited attention has been given to the estimation problem under stability constraints. The incorporation of stability constraints often results in increased computational complexity. As an efficient alternative, we propose to estimate stable ARX parameters using randomized coordinate descent. To demonstrate the efficiency of the proposed approach, we present an empirical convergence study and compare our approach to a state-of-the-art alternative.