Cointegrated Solutions of Unit-Root VARs: An Extended Representation Theorem

TL;DR

This paper introduces an extended representation theorem for unit-root VARs, providing algebraic methods to recover stationarity and deriving explicit results for integrated processes up to the 4th order.

Contribution

It presents a novel algebraic approach to analyze cointegrated solutions of unit-root VARs, extending the theory to higher-order processes through induction.

Findings

Derived closed-form solutions for integrated processes up to the 4th order

Developed an algebraic technique for stationarity recovery in unit-root VARs

Extended the representation theorem to higher-order processes

Abstract

This paper establishes an extended representation theorem for unit-root VARs. A specific algebraic technique is devised to recover stationarity from the solution of the model in the form of a cointegrating transformation. Closed forms of the results of interest are derived for integrated processes up to the 4-th order. An extension to higher-order processes turns out to be within the reach on an induction argument.