With the increase of wind and solar power plants connected to the grid, frequency stability has become a concern for transmission system operators. The large penetration of these sources reduces the inertia of the system, which naturally reacts to active power perturbations. In this scenario, a method capable of estimating the inertia constant, as perceived by a particular bus, is of practical importance. This paper presents a novel methodology to automatically assess the power system inertial constant using an autoregressive moving average exogenous input (ARMAX) model and demonstrate it using power system disturbance responses measured by a Wide-Area Measurement System (WAMS). The proposed approach can be divided into three parts: (i) Time window selection, which includes the identification of the start of the disturbance as well as the inertial response; (ii) A low-order ARMAX model method to estimate the constant of inertia as perceived by a particular bus; (iii) Accuracy evaluation. The proposed method is evaluated considering simulated signals corrupted with noise and outliers as well as real measurements from the New York transmission system Ver menos