 Tests of Common Stochastic TrendsJukka Nyblom and Andrew Harvey Cambridge Working Papers in Economics from Faculty of Economics, University of Cambridge Abstract: This paper is concerned with tests in multivariate time series models made up of random walk (with drift) and stationary components. When the stationary component is white noise, a Lagrange multiplier test of the hypothesis that the covariance matrix of the disturbances driving the multivariate random walk is null is shown to be locally best invariant, something which does not automatically follow in the multivariate case. The main contribution of the paper is to propose a test of the validity of a specified value for the rank of the covariance matrix of the disturbances driving the multi-variate random walk. This rank is equal to the number of common trends, or levels, in the series. The test is very simple insofar as it does not require any models to be estimated, even if serial correlation is present. Its use with real data is illustrated in the context of a stochastic volatility model and the relationship with tests in the co-integration literature is discussed. Keywords: Co-integration; Cramer-von Mises distribution; Locally best invariant test; Multivariate time series; Stochastic volatility; Structural time-series models; Unobserved components (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:cam:camdae:9902 Access Statistics for this paper More papers in Cambridge Working Papers in Economics from Faculty of Economics, University of Cambridge |
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