Spurious relationships in high-dimensional systems with strong or mild persistence
Spurious relationships in high-dimensional systems with strong or mild persistence
This paper is concerned with the interactions of persistence and dimensionality in the context of the eigenvalue estimation problem of large covariance matrices arising in cointegration and principal component analysis. Following a review of the early and more recent developments in this area, we investigate the behaviour of these eigenvalues in a vector autoregression setting that blends pure unit root, local to unit root and mildly integrated components. Our results highlight the seriousness of spurious relationships that may arise in such big data environments even when the degree of persistence of the variables involved is mild and affects only a small proportion of a large data matrix, with important implications for forecasts based on principal component regressions and related methods. We argue that, prior to principal component analysis, first-differencing may be suitable even in stationary or nearly stationary environments.
Spurious cointegration, spurious factors, persistence, high dimensional covariances, principal components
1480-1497
Pitarakis, Jean-Yves
ee5519ae-9c0f-4d79-8a3a-c25db105bd51
Gonzalo, Jesús
48015f9d-eef0-4ebd-8f2b-cbe7aa0cf667
31 December 2021
Pitarakis, Jean-Yves
ee5519ae-9c0f-4d79-8a3a-c25db105bd51
Gonzalo, Jesús
48015f9d-eef0-4ebd-8f2b-cbe7aa0cf667
Pitarakis, Jean-Yves and Gonzalo, Jesús
(2021)
Spurious relationships in high-dimensional systems with strong or mild persistence.
International Journal of Forecasting, 37 (4), .
Abstract
This paper is concerned with the interactions of persistence and dimensionality in the context of the eigenvalue estimation problem of large covariance matrices arising in cointegration and principal component analysis. Following a review of the early and more recent developments in this area, we investigate the behaviour of these eigenvalues in a vector autoregression setting that blends pure unit root, local to unit root and mildly integrated components. Our results highlight the seriousness of spurious relationships that may arise in such big data environments even when the degree of persistence of the variables involved is mild and affects only a small proportion of a large data matrix, with important implications for forecasts based on principal component regressions and related methods. We argue that, prior to principal component analysis, first-differencing may be suitable even in stationary or nearly stationary environments.
Text
GonzaloPitarakis-IJF-Accepted-November2020
- Accepted Manuscript
More information
Accepted/In Press date: 13 November 2020
Published date: 31 December 2021
Keywords:
Spurious cointegration, spurious factors, persistence, high dimensional covariances, principal components
Identifiers
Local EPrints ID: 445210
URI: http://eprints.soton.ac.uk/id/eprint/445210
ISSN: 0169-2070
PURE UUID: a22a362e-590e-4cc7-9783-37c4f4ff7954
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Date deposited: 25 Nov 2020 17:31
Last modified: 17 Mar 2024 06:05
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Author:
Jesús Gonzalo
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