Determination of cointegrating rank in partially non‐stationary processes via a generalised von‐Neumann criterion

Abstract

In this paper we show that it is possible to characterise the cointegrating structure of a partially non‐stationary, cointegrated, I(1) time series via the canonical correlations between the future and, the present and past, of the first differences of that series. This leads to a consideration of different model free non‐parametric methodologies for identifying the cointegrating rank. An adaptation of existing techniques using a novel method of spectral estimation gives rise to both a new applied tool and an alternative analytical framework that unifies current hypothesis‐testing approaches. An investigation of the eigenstructure of a multivariate version of von‐Neumann's ratio also leads to the development of an entirely new model free cointegrating rank selection criterion. All the procedures considered are easily implemented and the practical relevance of the theoretical results obtained, which are founded on asymptotic arguments, is demonstrated by means of a simulation study.

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