Prediction for Minimum and Nonminimum Phase Models

Abstract

Assume that x _t is a stationary ARMA scheine satisfying the system of equations

$$ {x_{t}} - {\phi _{1}}{x_{{t - 1}}} - \cdots - {\phi _{p}}{x_{{t - p}}} = {\xi _{t}} + {\theta _{1}}{\xi _{{t - 1}}} + \cdots + {\theta _{q}}{\xi _{{t - q}}} $$

where the ξ_t’s are independent and identically distributed with Eξ_t = 0 and Eξ ²_t = σ² > 0. Consider the prediction problem in which one approximates x₁ by a function of x_s, s ≤ 0, in mean square as well as one can.