On Asymptotic Inference in AR and Cointegrated Models With Unit Roots and Heavy Tailed Errors

Abstract

Consider the AR(q) model

$$ {{{\text{X}}}_{i}} = {{\beta }^{{\left( 1 \right)}}}{{{\text{X}}}_{{i - 1}}} + \cdots + {{\beta }^{{\left( q \right)}}}{{{\text{X}}}_{{i - q}}} + {{ \in }_{i}},fori = 1,2, \ldots ,n, $$

(1)

where ∈ _i i ≥ 1, are i.i.d., independent of (X ₀ ,…, X _i-q ). The characteristic polynomial associated with the model (1) is defined by

$$\phi \left( z \right) = 1 - {{\beta }^{{\left( 2 \right)}}}{{z}^{2}} - \cdots - {{\beta }^{{\left( q \right)}}}{{z}^{q}} $$

(2)

.