Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/247552 
Year of Publication: 
2020
Citation: 
[Journal:] Econometrics [ISSN:] 2225-1146 [Volume:] 8 [Issue:] 1 [Publisher:] MDPI [Place:] Basel [Year:] 2020 [Pages:] 1-23
Publisher: 
MDPI, Basel
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 studies cointegration and error correction representations for an I(1) singular stochastic vector yt . It is easily seen that yt 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 yt 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 yt 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.
Subjects: 
cointegration for singular vectors
Granger representation theorem
large-dimensional dynamic factor models)
singular stochastic vectors
JEL: 
C0
C01
E0
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article

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