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Granger's representation theorem: A closed-form expression for I(1) processes

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  • Peter Reinhard Hansen

Abstract

The Granger representation theorem states that a cointegrated vector autoregressive process can be decomposed into four components: a random walk, a stationary process, a deterministic part, and a term that depends on the initial values. In this paper, we present a new proof of the theorem. This proof enables us to derive closed-form expressions of all terms of the representation and allows a unified treatment of models with different deterministic specifications. The applicability of our results is illustrated by examples. For example, the closed-form expressions are useful for impulse response analyses and facilitate the analysis of cointegration models with structural changes. Copyright 2005 Royal Economic Society

Suggested Citation

  • Peter Reinhard Hansen, 2005. "Granger's representation theorem: A closed-form expression for I(1) processes," Econometrics Journal, Royal Economic Society, vol. 8(1), pages 23-38, March.
    • Handle: RePEc:ect:emjrnl:v:8:y:2005:i:1:p:23-38
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