Neural networks principal component analysis for estimating the generative multifactor model of returns under a statistical approach to the arbitrage pricing theory: Evidence from the mexican stock exchange

A nonlinear principal component analysis (NLPCA) represents an extension of the standard principal component analysis (PCA) that overcomes the limitation of the PCA’s assumption about the linearity of the model. The NLPCA belongs to the family of nonlinear versions of dimension reduction or the extr...

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Autores: Ladrón de Guevara Cortés, Rogelio, Torra Porras, Salvador, Monte Moreno, Enrique|||0000-0002-4907-0494
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/168380
Acceso en línea:https://hdl.handle.net/2117/168380
https://dx.doi.org/10.13053/CyS-23-2-3193
Access Level:acceso abierto
Palabra clave:Neural networks (Computer science)
Extraction of underlying risk factors
Nonlinear principal component analysis
Arbitrage pricing theory
Mexican stock exchange
Xarxes neuronals (Informàtica)
Àrees temàtiques de la UPC::Informàtica::Intel·ligència artificial
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spelling Neural networks principal component analysis for estimating the generative multifactor model of returns under a statistical approach to the arbitrage pricing theory: Evidence from the mexican stock exchangeLadrón de Guevara Cortés, RogelioTorra Porras, SalvadorMonte Moreno, Enrique|||0000-0002-4907-0494Neural networks (Computer science)Extraction of underlying risk factorsNonlinear principal component analysisArbitrage pricing theoryMexican stock exchangeXarxes neuronals (Informàtica)Àrees temàtiques de la UPC::Informàtica::Intel·ligència artificialA nonlinear principal component analysis (NLPCA) represents an extension of the standard principal component analysis (PCA) that overcomes the limitation of the PCA’s assumption about the linearity of the model. The NLPCA belongs to the family of nonlinear versions of dimension reduction or the extraction techniques of underlying features, including nonlinear factor analysis and nonlinear independent component analysis, where the principal components are generalized from straight lines to curves. The NLPCA can be achieved via an artificial neural network specification where the PCA classic model is generalized to a nonlinear mode, namely, Neural Networks Principal Component Analysis (NNPCA). In order to extract a set of nonlinear underlying systematic risk factors, we estimate the generative multifactor model of returns in a statistical version of the Arbitrage Pricing Theory (APT), in the context of the Mexican Stock Exchange. We used an auto-associative multilayer perceptron neural network or autoencoder, where the ‘bottleneck’ layer represented the nonlinear principal components, or in our context, the scores of the underlying factors of systematic risk. This neural network represents a powerful technique capable of performing a nonlinear transformation of the observed variables into the nonlinear principal components, and to execute a nonlinear mapping that reproduces the original variables. We propose a network architecture capable of generating a loading matrix that enables us to make a first approach to the interpretation of the extracted latent risk factors. In addition, we used a two stage methodology for the econometric contrast of the APT involving first, a simultaneous estimation of the system of equations via Seemingly Unrelated Regression (SUR), and secondly, a cross-section estimation via Ordinary Least Squared corrected by heteroskedasticity and autocorrelation by means of the Newey-West heteroskedasticity and autocorrelation consistent covariances estimates (HEC). The evidence found shows that the reproductions of the observed returns using the estimated components via NNPCA are suitable in almost all cases; nevertheless, the results in an econometric contrast lead us to a partial acceptance of the APT in the samples and periods studied.Peer Reviewed20192019-01-0120192019-09-18journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/168380https://dx.doi.org/10.13053/CyS-23-2-3193reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1683802026-05-27T15:37:01Z
dc.title.none.fl_str_mv Neural networks principal component analysis for estimating the generative multifactor model of returns under a statistical approach to the arbitrage pricing theory: Evidence from the mexican stock exchange
title Neural networks principal component analysis for estimating the generative multifactor model of returns under a statistical approach to the arbitrage pricing theory: Evidence from the mexican stock exchange
spellingShingle Neural networks principal component analysis for estimating the generative multifactor model of returns under a statistical approach to the arbitrage pricing theory: Evidence from the mexican stock exchange
Ladrón de Guevara Cortés, Rogelio
Neural networks (Computer science)
Extraction of underlying risk factors
Nonlinear principal component analysis
Arbitrage pricing theory
Mexican stock exchange
Xarxes neuronals (Informàtica)
Àrees temàtiques de la UPC::Informàtica::Intel·ligència artificial
title_short Neural networks principal component analysis for estimating the generative multifactor model of returns under a statistical approach to the arbitrage pricing theory: Evidence from the mexican stock exchange
title_full Neural networks principal component analysis for estimating the generative multifactor model of returns under a statistical approach to the arbitrage pricing theory: Evidence from the mexican stock exchange
title_fullStr Neural networks principal component analysis for estimating the generative multifactor model of returns under a statistical approach to the arbitrage pricing theory: Evidence from the mexican stock exchange
title_full_unstemmed Neural networks principal component analysis for estimating the generative multifactor model of returns under a statistical approach to the arbitrage pricing theory: Evidence from the mexican stock exchange
title_sort Neural networks principal component analysis for estimating the generative multifactor model of returns under a statistical approach to the arbitrage pricing theory: Evidence from the mexican stock exchange
dc.creator.none.fl_str_mv Ladrón de Guevara Cortés, Rogelio
Torra Porras, Salvador
Monte Moreno, Enrique|||0000-0002-4907-0494
author Ladrón de Guevara Cortés, Rogelio
author_facet Ladrón de Guevara Cortés, Rogelio
Torra Porras, Salvador
Monte Moreno, Enrique|||0000-0002-4907-0494
author_role author
author2 Torra Porras, Salvador
Monte Moreno, Enrique|||0000-0002-4907-0494
author2_role author
author
dc.subject.none.fl_str_mv Neural networks (Computer science)
Extraction of underlying risk factors
Nonlinear principal component analysis
Arbitrage pricing theory
Mexican stock exchange
Xarxes neuronals (Informàtica)
Àrees temàtiques de la UPC::Informàtica::Intel·ligència artificial
topic Neural networks (Computer science)
Extraction of underlying risk factors
Nonlinear principal component analysis
Arbitrage pricing theory
Mexican stock exchange
Xarxes neuronals (Informàtica)
Àrees temàtiques de la UPC::Informàtica::Intel·ligència artificial
description A nonlinear principal component analysis (NLPCA) represents an extension of the standard principal component analysis (PCA) that overcomes the limitation of the PCA’s assumption about the linearity of the model. The NLPCA belongs to the family of nonlinear versions of dimension reduction or the extraction techniques of underlying features, including nonlinear factor analysis and nonlinear independent component analysis, where the principal components are generalized from straight lines to curves. The NLPCA can be achieved via an artificial neural network specification where the PCA classic model is generalized to a nonlinear mode, namely, Neural Networks Principal Component Analysis (NNPCA). In order to extract a set of nonlinear underlying systematic risk factors, we estimate the generative multifactor model of returns in a statistical version of the Arbitrage Pricing Theory (APT), in the context of the Mexican Stock Exchange. We used an auto-associative multilayer perceptron neural network or autoencoder, where the ‘bottleneck’ layer represented the nonlinear principal components, or in our context, the scores of the underlying factors of systematic risk. This neural network represents a powerful technique capable of performing a nonlinear transformation of the observed variables into the nonlinear principal components, and to execute a nonlinear mapping that reproduces the original variables. We propose a network architecture capable of generating a loading matrix that enables us to make a first approach to the interpretation of the extracted latent risk factors. In addition, we used a two stage methodology for the econometric contrast of the APT involving first, a simultaneous estimation of the system of equations via Seemingly Unrelated Regression (SUR), and secondly, a cross-section estimation via Ordinary Least Squared corrected by heteroskedasticity and autocorrelation by means of the Newey-West heteroskedasticity and autocorrelation consistent covariances estimates (HEC). The evidence found shows that the reproductions of the observed returns using the estimated components via NNPCA are suitable in almost all cases; nevertheless, the results in an econometric contrast lead us to a partial acceptance of the APT in the samples and periods studied.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-01-01
2019
2019-09-18
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/168380
https://dx.doi.org/10.13053/CyS-23-2-3193
url https://hdl.handle.net/2117/168380
https://dx.doi.org/10.13053/CyS-23-2-3193
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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