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Compositional Analysis of Exchange Rates

In: Advances in Contemporary Statistics and Econometrics

Author

Listed:
  • Wilfredo L. Maldonado

    (University of São Paulo. Av. Professor Luciano Gualberto, Faculty of Economics, Management and Accounting)

  • Juan José Egozcue

    (Technical University of Catalonia, Department of Civil and Environmental Engineering)

  • Vera Pawlowsky-Glahn

    (University of Girona, Department of Computer Science, Applied Mathematics and Statistics)

Abstract

Triangular arbitrage in the foreign exchange market of a group of countries exists whenever it is possible to make profit by buying and selling their currencies using the spot exchange rates. Working in the framework of the Aitchison geometry, and using characterizations of the absence of triangular arbitrage, we present two applications to the currencies of Brazil (Real), the European Union (Euro), Great Britain (Pound Sterling), and the United States of America (US Dollar). The first application refers to the Special Drawing Rights, an asset created by the International Monetary Fund to provide liquidity to the member countries. The exchange rates matrix is projected onto the subspace of no-arbitrage exchange rate matrices, and its only eigenvector, associated with a non-null eigenvalue, is demonstrated to be compositional and close to the Special Drawing Rights. The second application studies the relative exchange rate bubbles among the countries. It uses the closest no-arbitrage matrix of an exchange rate matrix and the purchasing power parity values for the fundamental exchange rates to analyze the dynamics of those bubbles. These applications show the potential the compositional approach has for the matrices of exchange rates.

Suggested Citation

  • Wilfredo L. Maldonado & Juan José Egozcue & Vera Pawlowsky-Glahn, 2021. "Compositional Analysis of Exchange Rates," Springer Books, in: Abdelaati Daouia & Anne Ruiz-Gazen (ed.), Advances in Contemporary Statistics and Econometrics, pages 489-507, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-73249-3_25
    DOI: 10.1007/978-3-030-73249-3_25
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