Long-range dependence in the volatility of returns in Uruguayan sovereign debt indices

Juan Kalemkerian; Andrés Sosa

doi:10.3934/jdg.2020016

Article Contents

2020, Volume 7, Issue 3: 225-237. Doi: 10.3934/jdg.2020016

This issue Previous Article Financial liquidity: An emergent phenomena Next Article Network ANOVA random effects models for node attributes

Long-range dependence in the volatility of returns in Uruguayan sovereign debt indices

Juan Kalemkerian^1, and
Andrés Sosa^2,

1.
Centro de Matemática, Facultad de Ciencias, Universidad de la República, Iguá 4225, CP 11400, Montevideo, Uruguay
2.
Instituto de Estadística, Facultad de Ciencias Económicas y de Administración, Universidad de la República, Eduardo Acevedo 1139, CP 11200, Montevideo, Uruguay

We are grateful to the Guest Editors, Viktoriya Semeshenko, Gabriel Brida and Andrea Roventini, and the two anonymous referees for helpful comments and suggestions.

Received: January 31, 2020

Revised: March 31, 2020

Published: July 2020

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Abstract

One consequence of the fact that a large number of agents with different behaviors operate in financial systems is the emergence of certain statistical properties in some time series. Some of these properties contradict the hypotheses that are established in the traditional models of efficient market and portfolio optimization. Among them is the long-range dependence that is the objective of this work. The approach is proposed by fractional calculus, as a generalization of the classic approach to financial markets through semi-martingales. This paper study the existence of this property in variables dependent on the term structure curves of Uruguayan sovereign debt after the 2002 economic crisis.

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Mathematics Subject Classification: Primary:91G30;Secondary:60G22.

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Figure 1. Log-returns index of ITLUP (top) and UBI (bottom)

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Figure 2. Autocorrelation Function (left) and Partial Autocorrelation Function (right) in ITLUP returns. Top to bottom: log returns index, absolute returns, square returns

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Figure 3. Autocorrelation Function (left) and Partial Autocorrelation Function (right) in UBI returns. Top to bottom: log-returns index, absolute returns, square returns

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Figure 4. Time-lagged relations between absolute and squared returns in the indices

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Table 1. ITLUP index

Method Estimation	Parameter (square)	Parameter (absolute)
Simple $ R/S $	0.7308	0.7489
Corrected R over S	0.8407	0.8633
Empirical Hurst exponent	0.7703	0.7876
Corrected empirical Hurst	0.7158	0.7342

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Table 2. UBI index

Method Estimation	Parameter (square)	Parameter (absolute)
Simple $ R/S $	0.6987	0.7679
Corrected R over S	0.7887	0.8892
Empirical Hurst exponent	0.7481	0.8304
Corrected empirical Hurst	0.6953	0.7776

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