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April  2019, 6(2): 131-148. doi: 10.3934/jdg.2019010

## An application of minimal spanning trees and hierarchical trees to the study of Latin American exchange rates

 Institute for Latin American Studies, School of Business & Economics, Freie Universität Berlin, Rudesheimer Str. 54, 14197 Berlin, Germany

Received  December 2018 Revised  April 2019 Published  April 2019

Fund Project: Funding by the German Research Foundation (DFG) is gratefully acknowledged

This paper analyzes a group of nine Latin American currencies with the aim of identifying clusters of exchange rates with similar co-movements. In this work the study of currency relationships is formulated as a network problem, where each currency is represented as a node and the relationship between each pair of currencies as a link. The paper combines two methods, Symbolic Time Series Analysis (STSA) and a clustering method based on the Minimal Spanning Tree (MST), from which we obtain a Hierarchical Tree (HT). Symbolic Time Series Analysis consists in the transformation of a given time series into a symbolic sequence with the aim of identifying patterns in the set of data. The Minimal Spanning Tree condenses the core information on the global structure of the network and its main advantage is that it greatly simplifies comparisons by dramatically reducing the number of elements that must be compared. We identify two main clusters in the currency network, as well as specific currencies that function as transmission channels between clusters. Using data regarding the degree of financial liberalization, as well as the distinction between inflation targeting (IT) and non-IT countries, the analysis suggests that the obtained taxonomy is economically relevant.

Citation: Erick Limas. An application of minimal spanning trees and hierarchical trees to the study of Latin American exchange rates. Journal of Dynamics & Games, 2019, 6 (2) : 131-148. doi: 10.3934/jdg.2019010
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Illustration of symbolic encoding: Variation of the exchange rate of the Mexican peso against the U.S. dollar. The horizontal line represents the symbol partition; data below the partition are represented by 0, and data above the partition are represented by 1. In this case, the frontier level is the trend of the series, $\mu = 0.0025$. Then, the original data time series is represented by the symbol sequence S = 100100101
Minimal Spanning Tree (left) and Hierarchical Tree (right). Period: 2007
Minimal Spanning Tree (left) and Hierarchical Tree (right). Period: 2008-2010.
Minimal Spanning Tree (left) and Hierarchical Tree (right). Period: 2011-2014
Minimal Spanning Tree (left) and Hierarchical Tree (right). Period: 2015-2017
Financial openness: the Chinn-Ito index (2007-2016 average). Source: [14]
Countries, currencies and three-letter codes
Monetary Policy Framework. Argentina maintains a de facto exchange rate anchor to the U.S. dollar. Uruguay has an inflation target regime with monetary aggregates control. Source: [28]
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