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

Limas, Erick

doi:10.3934/jdg.2019010

Cited by 13 publications

(10 citation statements)

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“…For this reason, the correlation matrix is transformed into the correlation distance matrix according to the Equation 2 which fulfills the three axioms of an Euclidean distance: Subsequently, Prim’s algorithm (Prim, 1957) is applied to adjacency matrix to obtain Minimal Spanning Trees (MST). Being introduced to graph theory by Kruskal (1956) and Prim (1957), MST have been a widely used tool (Limas, 2019; Górski et al, 2008; Kwapień et al, 2009; Rešovský et al, 2013; Wang et al, 2013), mainly because it simplifies network analysis by selecting the most relevant bounds. Indeed, MST are characterized for representing the core information of a complete network with n nodes by selecting the n-1 links that minimize the overall distance.…”

Section: Methodsmentioning

confidence: 99%

Analysis of communities of countries with similar dynamics of the COVID-19 pandemic evolution

Álvarez¹,

Brida²,

Limas

et al. 2021

Preprint

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This work addresses the spread of the coronavirus through a non-parametric approach, with the aim of identifying communities of countries based on how similar their evolution of the disease is. The analysis focuses on the number of daily new COVID-19 cases per ten thousand people during a period covering at least 250 days after the confirmation of the tenth case. Dynamic analysis is performed by constructing Minimal Spanning Trees (MST) and identifying groups of similarity in contagions evolution in 95 time windows of a 150-day amplitude that moves one day at a time. The number of times countries belonged to a similar performance group in constructed time windows was the intensity measure considered. Groups’ composition is not stable, indicating that the COVID-19 evolution needs to be treated as a dynamic problem in the context of complex systems. Three communities were identified by applying the Louvain algorithm. Identified communities analysis according to each country’s socioeconomic characteristics and variables related to the disease sheds light on whether there is any suggested course of action. Even when strong testing and tracing cases policies may be related with a more stable dynamic of the disease, results indicate that communities are conformed by countries with diverse characteristics. The best option to counteract the harmful effects of a pandemic may be having strong health systems in place,with contingent capacity to deal with unforeseen events and available resources capable of a rapid expansion of its capacity.

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Section: Methodsmentioning

confidence: 99%

Analysis of communities of countries with similar dynamics of the COVID-19 pandemic evolution

Álvarez¹,

Brida²,

Limas

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Log-returns and volatilities can obviously be calculated from the price of any financial asset: Foreign exchange [15], [21]; American stocks [1], [7], [13]; Korean stocks [22]; European Government bonds are discussed in [3]; Cryptocurrencies [5], [23]; Oil prices [6]; Furthermore, a single network can represent a market or an economy over a long period of time, but it is also possible to create timevarying graphs for smaller consecutive overlapping or nonoverlapping periods of time [9], [2]. This approach is appropriate when the objective is to analyze how the network changes in response to a financial crisis, and what is the timeevolving behavior of interdependencies between different assets.…”

Section: Marketsmentioning

confidence: 99%

“…The analysis of pairwise relationships between assets, as discussed in Section II, would initially produce a fully connected weighted graph, hence, from this point of view, extracting MSTs can be considered as a filtering procedure [14], which highlights relevant relationships between assets [15]. Weak correlations or causal relationships are simply excluded from the resulting trees, as they correspond to edges with large weights.…”

Section: Topology and Spanning Treesmentioning

confidence: 99%

“…For both (3) and (4), and correspond to two vertices/assets. Weights obtained using (3) can be interpreted as distances, as emphasized in [15] and [1], which means that strongly correlated time series would be represented by vertices which are close to each other, hence retained by the MST filtering procedure (e.g. Kruskal's algorithm).…”

Section: Topology and Spanning Treesmentioning

confidence: 99%

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2021

TUS

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Network based methods are suitable for the analysis of large number of financial time series and the better understanding of their interdependencies. Known approaches to reveal the underlying information about the complex structure of these interdependencies include network-wise and vertexwise measures of the topology, as well as filtering techniques relying on minimum spanning trees, planar graphs, or spectral analysis. The aim of this study is to review relevant graph theoretical and statistical models and techniques for generating and examining the properties of financial networks, obtained by computing time series correlations or causality relationships. In particular, this study reviews literature discussing the time evolution of the observed phenomena from a network perspective, as well as applications in economy and finance, ranging from risk and diversification, through policy making and better understanding crisis impact, to forecasting. The information synthesized in this paper can be useful to gain further insights into this relatively new research area.

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“…Subsequently, Prim's algorithm [26] is applied to adjacency matrix to obtain Minimal Spanning Trees (MST). Being introduced to graph theory by [17] and [26], MST have been a widely used tool [19,15,18,27,33], mainly because it simplifies network analysis by selecting the most relevant bounds. Indeed, MST are characterized by representing the core information of a complete network with n nodes by selecting the n − 1 links that minimize the overall distance.…”

mentioning

confidence: 99%

Analysis of communities of countries with similar dynamics of the COVID-19 pandemic evolution

Álvarez¹,

Brida²,

Rosich³

et al. 2022

JDG

Self Cite

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<p style='text-indent:20px;'>This work addresses the spread of the coronavirus through a non-parametric approach, with the aim of identifying communities of countries based on how similar their evolution of the disease is. The analysis focuses on the number of daily new COVID-19 cases per ten thousand people during a period covering at least 250 days after the confirmation of the tenth case. Dynamic analysis is performed by constructing Minimal Spanning Trees (MST) and identifying groups of similarity in contagions evolution in 95 time windows of a 150-day amplitude that moves one day at a time. The intensity measure considered was the number of times countries belonged to a similar performance group in constructed time windows. Groups' composition is not stable, indicating that the COVID-19 evolution needs to be treated as a dynamic problem in the context of complex systems. Three communities were identified by applying the Louvain algorithm. Identified communities analysis according to each country's socioeconomic characteristics and variables related to the disease sheds light on whether there is any suggested course of action. Even when strong testing and tracing cases policies may be related with a more stable dynamic of the disease, results indicate that communities are conformed by countries with diverse characteristics. The best option to counteract the harmful effects of a pandemic may be having strong health systems in place, with contingent capacity to deal with unforeseen events and available resources capable of a rapid expansion of its capacity.</p>

show abstract

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

Cited by 13 publications

References 35 publications

Analysis of communities of countries with similar dynamics of the COVID-19 pandemic evolution

Analysis of communities of countries with similar dynamics of the COVID-19 pandemic evolution

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Analysis of communities of countries with similar dynamics of the COVID-19 pandemic evolution

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