Explicit Stationarity Regions for AR(4), AR(5), and AR(6) Processes via Unit-Circle Analysis

Autoregressive models have been extensively studied, and computational methods for solving their characteristic equations are well established. This paper aims to systematically derive stationarity conditions through an analytical investigation of solutions based on the unit circle. By combining geometric arguments on the unit circle, we derive stationarity conditions for AR(4), AR(5), and AR(6) processes. For AR(4), the resulting stationarity region coincides with that determined by the classical Schur–Cohn criterion, while admitting a more compact representation. A more precise characterization of stationarity conditions may facilitate research involving stationarity.