AR Characteristic Equation

Definition

By expressing an AR(p) process using the backshift operator: $(1-{\varphi }_{1}B-{\varphi }_2{B}^2-\cdots -{\varphi }_p{B}^p)Z_t=a_t$ The characteristic equation is: $1-{\varphi }_{1}x-{\varphi }_2{x}^2-\cdots -{\varphi }_p{x}^p=0$ The process is stationary if all roots of this equation lie outside the unit circle ($|x|>1$).