Reversibility and Identifiability

Abstract

Let us first consider linear stationary sequences. A sequence of independent, identically distributed real random variables ξ_j, j = …, -1,0,1,… is given with Eξ_j = 0, 0 < Eξ ²_j = σ² < ∞. The process x_j is obtained by passing this sequence through a linear filter characterized by the real weights, a _j , ∑a ² _j < ∞,

$$ {x_{t}} = \sum\limits_{{j = - \infty }}^{\infty } {{a_{j}}\xi t - j.} $$

(1.1.1)