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Entropy 2019, 21(4), 376; https://doi.org/10.3390/e21040376

Between Nonlinearities, Complexity, and Noises: An Application on Portfolio Selection Using Kernel Principal Component Analysis

1
Campus Universitário Darcy Ribeiro-Brasília, University of Brasilia, Brasilia 70910-900, Brazil
2
Federal Institute of Piauí, Rua Álvaro Mendes, 94-Centro (Sul), Teresina-PI 64001-270, Brazil
*
Author to whom correspondence should be addressed.
Received: 22 February 2019 / Revised: 29 March 2019 / Accepted: 4 April 2019 / Published: 7 April 2019
(This article belongs to the Section Multidisciplinary Applications)
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Abstract

This paper discusses the effects of introducing nonlinear interactions and noise-filtering to the covariance matrix used in Markowitz’s portfolio allocation model, evaluating the technique’s performances for daily data from seven financial markets between January 2000 and August 2018. We estimated the covariance matrix by applying Kernel functions, and applied filtering following the theoretical distribution of the eigenvalues based on the Random Matrix Theory. The results were compared with the traditional linear Pearson estimator and robust estimation methods for covariance matrices. The results showed that noise-filtering yielded portfolios with significantly larger risk-adjusted profitability than its non-filtered counterpart for almost half of the tested cases. Moreover, we analyzed the improvements and setbacks of the nonlinear approaches over linear ones, discussing in which circumstances the additional complexity of nonlinear features seemed to predominantly add more noise or predictive performance. View Full-Text
Keywords: nonlinearity; regularization; high dimensionality; portfolio allocation; machine learning; covariance estimation; random matrix theory; kernel methods nonlinearity; regularization; high dimensionality; portfolio allocation; machine learning; covariance estimation; random matrix theory; kernel methods
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Peng, Y.; Albuquerque, P.H.M.; do Nascimento, I.F.; Machado, J.V.F. Between Nonlinearities, Complexity, and Noises: An Application on Portfolio Selection Using Kernel Principal Component Analysis. Entropy 2019, 21, 376.

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