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International Workshop on Compositional Data Analysis

CoDaWork 2015: Compositional Data Analysis pp 145–165Cite as

Relationship Between the Popularity of Key Words in the Google Browser and the Evolution of Worldwide Financial Indices

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 187))

Abstract

The purpose of this contribution is to evaluate whether there is enough statistical basis to establish a relationship between the popularity of certain terms in the Google browser and the evolution of several worldwide economic indices the subsequent week. A linear model trying to predict the evolution of 19 financial indices from all over the world with the information of how many times a selected group of 200 key words are looked up online the previous week is proposed. The linear model that is proposed takes a compositional approach due to two reasons. First, the information contained in the values of the financial indices has a compositional nature. The strongest proof supporting this idea is that in case all values for the indices on a certain week were multiplied by a factor, the information would remain unchanged. In fact, the value for a certain index is irrelevant by itself, since it is its evolution with respect to the rest of indices that indicates whether it is performing well. Therefore, this idea suggests that the numerical values of the 19 indices for a certain week can be understood as a vector of the simplex and be analyzed accordingly. Second, the explanatory variable has to be understood as a vector of the simplex as well, for a similar reason as before. For instance, let us imagine that the number of times the words are looked up online in a certain week was multiplied by a factor. Indeed, the information contained in this vector would be exactly the same. Moreover, it seems intuitive as well how the absolute value for the number of searches is irrelevant by itself, since we will be interested in the relationships amongst variables. For the reasons we have just set, a compositional approach seems necessary in order to address the problem successfully, since both the explanatory and predicted variables present a compositional nature. In other words, despite not adding up to a constant, the components of the vectors of both the explanatory and predicted variables seem to be closely related in terms of giving information of a part of a whole, so tackling the problem through a compositional perspective seems appropriate. The analysis consists of an exploratory analysis of both response (indices) and explanatory (searches) variables and a compositional linear multiple regression between both sets of variables.

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Notes

  1. 1.

    The information on the searches of different words is provided by Google Trends, subsidiary of Google, Inc. From now on, we will refer to Google Trends simply as Google.

  2. 2.

    It is arguable whether we could have used an ILR transformation, as we have done for the predicted variable. Provided that a principal component analysis will be applied, it is unnecessary to define a binary partition and an ILR transformation. Given that in the end we will work with the orthogonal base that we get from the principal component analysis, we can work directly with a standard CLR procedure.

  3. 3.

    Yahoo Finance, owned by Yahoo!, Inc. Information consulted in 2013.

  4. 4.

    Investing.com, owned by Fusion Media Limited. Information consulted in 2014.

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Acknowledgments

The present research work has been developed during the time that Robert Ortells has benefited from a grant within the program “Becas de Colaboración” of the Spanish Ministerio de Educación, for the development of the project “Correlació entre l’evolució dels mercats financers globals i la popularitat de diferents paraules al buscador Google” during 2014–2015. This project has been developed in the Applied Mathematics III Department of Universitat Politècnica de Catalunya (UPC). This research has been also partially funded by the Spanish Ministerio de Economía y Competitividad under project ‘Metrics’ Ref.MTM2012-33236, and by the Agència de Gestió d’Ajuts Universitaris i de Recerca (AGAUR) of the Generalitat de Catalunya under the project “Compositional and Spatial Analysis” (COSDA) (Ref: 2014SGR551;2014-2016).

Author information

Authors and Affiliations

  1. The London School of Economics and Political Science (LSE), London, SE11 5TA, UK

    R. Ortells

  2. Universitat Politècnica de Catalunya (UPC), Campus Nord. C/ Jordi Girona, 1-3, Edifici C2, Despatx 211B, 08034, Barcelona, Spain

    J. J. Egozcue

  3. Universitat Politècnica de Catalunya (UPC), Campus Nord. C/ Jordi Girona, 1-3, Edifici C2, Despatx 307, 08034, Barcelona, Spain

    M. I. Ortego

  4. Universitat Politècnica de Catalunya (UPC), Campus Nord. C/ Jordi Girona, 1-3, Edifici B1, Despatx 301, 08034, Barcelona, Spain

    A. Garola

Authors
  1. R. Ortells
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  2. J. J. Egozcue
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  3. M. I. Ortego
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  4. A. Garola
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Corresponding author

Correspondence to R. Ortells .

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Editors and Affiliations

  1. Department of Computer Science and Applied Mathematics, University of Girona, Girona, Spain

    Josep Antoni Martín-Fernández

  2. Department of Computer Science and Applied Mathematics, University of Girona, Girona, Spain

    Santiago Thió-Henestrosa

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Ortells, R., Egozcue, J.J., Ortego, M.I., Garola, A. (2016). Relationship Between the Popularity of Key Words in the Google Browser and the Evolution of Worldwide Financial Indices. In: Martín-Fernández, J., Thió-Henestrosa, S. (eds) Compositional Data Analysis. CoDaWork 2015. Springer Proceedings in Mathematics & Statistics, vol 187. Springer, Cham. https://doi.org/10.1007/978-3-319-44811-4_10

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