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Keywords = cointegration for singular vectors

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23 pages, 361 KB  
Article
Cointegration and Error Correction Mechanisms for Singular Stochastic Vectors
by Matteo Barigozzi, Marco Lippi and Matteo Luciani
Econometrics 2020, 8(1), 3; https://doi.org/10.3390/econometrics8010003 - 4 Feb 2020
Cited by 16 | Viewed by 6882
Abstract
Large-dimensional dynamic factor models and dynamic stochastic general equilibrium models, both widely used in empirical macroeconomics, deal with singular stochastic vectors, i.e., vectors of dimension r which are driven by a q-dimensional white noise, with q < r . The present paper [...] Read more.
Large-dimensional dynamic factor models and dynamic stochastic general equilibrium models, both widely used in empirical macroeconomics, deal with singular stochastic vectors, i.e., vectors of dimension r which are driven by a q-dimensional white noise, with q < r . The present paper studies cointegration and error correction representations for an I ( 1 ) singular stochastic vector y t . It is easily seen that y t is necessarily cointegrated with cointegrating rank c r q . Our contributions are: (i) we generalize Johansen’s proof of the Granger representation theorem to I ( 1 ) singular vectors under the assumption that y t has rational spectral density; (ii) using recent results on singular vectors by Anderson and Deistler, we prove that for generic values of the parameters the autoregressive representation of y t has a finite-degree polynomial. The relationship between the cointegration of the factors and the cointegration of the observable variables in a large-dimensional factor model is also discussed. Full article
(This article belongs to the Special Issue Celebrated Econometricians: Katarina Juselius and Søren Johansen)
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