Cointegration


In a system with two or more non-stationary variables there may exist a linear combination that is stationary. Such relations are cointegration relations and the non-stationary variables are said to be cointegrated in this case.
A note with more details: Cointegration

Structural Changes in the Cointegrated Vector Autoregressive Model

 Journal of Econometrics, vol. 114, pp. 261-295 (2003)

An empirical contribution of this paper was to show that an empirical “puzzle” – the apparent violation of the expectation hypothesis in the US term structure of interest rates – can be attributed to structural changes. The standard cointegrated vector autoregressive model assumes constant volatility, causing the model to be seriously misspecified when applied to US term structure data. A flexible specification of the variance, which is particularly important over the volatile period, 1979-1982, resolves the “puzzle”. A theoretical contribution of this paper was a novel estimation method – generalized reduced rank regression – that enables estimation of cointegration models under a large class of parameter restrictions.

Granger’s Representation Theorem: A Closed-Form Expression for I(1) Processes

 Econometrics Journal, vol. 8, pp. 23-38 (2005)

The Granger representation is the moving-average representation of processes that belong to class of cointegrated vector autoregressive processes. The main contribution of this paper was to establish a closed-form expression for the Granger representation. The closed-form expression yields new insight about the dynamics of unit root processes and the result has been utilized in the analysis of impulse response functions and “price discovery” in financial markets.

Reduced-Rank Regression: A Useful Determinant Identity

 Journal of Statistical Planning and Inference. Vol. 138, pp. 2688-2697 (2008)

This paper established an identity for the determinant of a product involving non-squared matrices. The identity can be used to derive the maximum likelihood estimator in reduced-rank regressions with Gaussian innovations. Furthermore, the identity sheds light on the structure of the estimation problem that arises when the reduced-rank parameters are subject to additional constraints, which is known to be a rather complex estimation problem.