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A New Parametrization of Correlation Matrices

Ilya Archakov, Peter Reinhard Hansen

arXiv 4 Dec 2020 · Econometrics · publishedEconometrica (2021) · 3 citations (OpenAlex)

arXiv:2012.02395 · PDF · DOI · OpenAlex · Extracted main text

Abstract

We introduce a novel parametrization of the correlation matrix. The reparametrization facilitates modeling of correlation and covariance matrices by an unrestricted vector, where positive definiteness is an innate property. This parametrization can be viewed as a generalization of Fisther's Z-transformation to higher dimensions and has a wide range of potential applications. An algorithm for reconstructing the unique n x n correlation matrix from any d-dimensional vector (with d = n(n-1)/2) is provided, and we derive its numerical complexity.

Citation extraction

31
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appendix boundary found by appendix_command · 66% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Archakov, Hansen \ Lunde (2020) `A Multivariate Realized GARCH Model', Working Paper0.84333100%
2Linton \ McCrorie (1995) `Differentiation of an exponential matrix function: Solution', Econometric Theory 11, 1182–11850.5112250%
3Archakov \ Hansen (2020) `Web-appendix for: A New Parametrization of Correlation Matrices', https://sites.google.com/site/peterreinhardhansen/0.40511100%
4Asai \ So (2015) `Long memory and asymmetry for matrix-exponential dynamic correlation processes', Journal of Time Series Econometrics 7, 69–740.40511100%
5Bauer \ Vorkink (2011) `Forecasting multivariate realized stock market volatility', Journal of Econometrics 160, 93–1010.40511100%
6Bauwens, Storti \ Violante (2012) `Dynamic conditional correlation models for realized covariance matrices', Working Paper (2012060)0.40511100%
7Bollerslev (1990) `Modelling the coherence in short-run nominal exchange rates: A multivariate generalized ARCH model', The Review of Economics an…0.40511100%
8Browne \ Shapiro (1986) `The asymptotic covariance matrix of sample correlation coefficients under general conditions', Linear Algebra and its Applicati…0.40511100%
9Chiriac \ Voev (2011) `Modelling and forecasting multivariate realized volatility', Journal of Applied Econometrics 26, 922–9470.40511100%
10Chiu, Leonard \ Tsui (1996) `The matrix-logarithmic covariance model', Journal of the American Statistical Association 91, 198–2100.40511100%

Showing the top 10 of 33 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Cluster GARCH0.96195
2Dynamic Factor Correlation Model0.95073
3The Generalized Fisher Transformation: Finite-Sample Properties and Inference0.92853
4Split-Session Cluster GARCH for Overnight and Intraday Returns: The Role of Tail Heterogeneity0.84343
5A Multivariate Realized GARCH Model0.73743
6Characterizing Correlation Matrices that Admit a Clustered Factor Representation0.64422
7A Robust Similarity Estimator0.64422
8Bayesian modelling of VAR precision matrices using stochastic block networks\@thefnmark\@footnotetextWe would like to thank Luca Barbaglia, Sune Karlsson, James Mitchell, Luca Onorante, Michael Smith, Mike West as well as participants of the 13th European Seminar on Bayesian Econometrics (Glasgow, 2023), the yearly meeting of the Austrian Economic Association 2023 (Salzburg, 2023), the 6th Annual Workshop on Financial Econometrics (Örebro, 2023) and the 17th International Conference on Computational and Financial Econometrics (Berlin, 2023) for helfpul comments and suggestions. Huber and Scheckel gratefully acknowledge funding from the Austrian Science Fund (FWF, grant no. ZK-35) and the Jubiläumsfond of the Oesterreischische Nationalbank (OeNB, grant no. JF-18740 and JF-18763)0.51121
9Spectral Dynamics and Regularization for High-Dimensional Copulas0.51121
10Dynamic factor, leverage and realized covariances in multivariate stochastic volatility0.40511