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The nonexplosive solution of explosive autoregressions

Erich Häusler, Harald Luschgy

Abstract

We establish several features of the stationary solution of purely explosive autoregressions of order d based on nonstandard initial values.

The nonexplosive solution of explosive autoregressions

Abstract

We establish several features of the stationary solution of purely explosive autoregressions of order d based on nonstandard initial values.

Paper Structure

This paper contains 3 sections, 12 theorems, 139 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Features of the stationary solution
  3. Central limit theorems via reverse martingale difference sequences

Key Result

Lemma 2.1

The following processes are (strictly) stationary and ergodic: (i) $\left(U_n\right)_{n\geq0}$ , (ii) $\left(Y_{n-d+1}\right)_{n\geq0}$ , (iii) $\left(U_{n-1}Y_n\right)_{n\geq1}$ , (iv) $\left(h\left(U_n\right)Z_n\right)_{n\geq1}$ for some Borel measurable map $h:{\mathbb R}^d\rightarrow{\mathbb R}^

Figures (1)

  • Figure :

Theorems & Definitions (12)

  • Lemma 2.1
  • Lemma 2.2
  • Proposition 2.3
  • Lemma 2.4
  • Lemma 2.5
  • Lemma 2.6
  • Theorem 3.1
  • Proposition 3.2
  • Proposition 3.3
  • Lemma 3.4
  • ...and 2 more