Next Article in Journal
Correction: Ardia, D., et al. Return and Risk of Pairs Trading Using a Simulation-Based Bayesian Procedure for Predicting Stable Ratios of Stock Prices. Econometrics 2016, 4, 14.
Previous Article in Journal
Acknowledgement to Reviewers of Econometrics in 2019
Previous Article in Special Issue
Partial Cointegrated Vector Autoregressive Models with Structural Breaks in Deterministic Terms
Open AccessFeature PaperArticle

Cointegration and Error Correction Mechanisms for Singular Stochastic Vectors

1
Università di Bologna, Department of Economics, 40126 Bologna, Italy
2
Einaudi Institute for Economics and Finance, 00187 Roma, Italy
3
Federal Reserve Board of Governors, Washington, DC 20551, USA
*
Author to whom correspondence should be addressed.
Econometrics 2020, 8(1), 3; https://doi.org/10.3390/econometrics8010003
Received: 28 March 2018 / Revised: 30 December 2019 / Accepted: 7 January 2020 / Published: 4 February 2020
(This article belongs to the Special Issue Celebrated Econometricians: Katarina Juselius and Søren Johansen)
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. View Full-Text
Keywords: singular stochastic vectors; cointegration for singular vectors; Granger representation theorem; large-dimensional dynamic factor models) singular stochastic vectors; cointegration for singular vectors; Granger representation theorem; large-dimensional dynamic factor models)
MDPI and ACS Style

Barigozzi, M.; Lippi, M.; Luciani, M. Cointegration and Error Correction Mechanisms for Singular Stochastic Vectors. Econometrics 2020, 8, 3.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop