# American Institute of Mathematical Sciences

July  2020, 7(3): 225-237. doi: 10.3934/jdg.2020016

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

 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  February 2020 Revised  April 2020 Published  July 2020

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.

Citation: Juan Kalemkerian, Andrés Sosa. Long-range dependence in the volatility of returns in Uruguayan sovereign debt indices. Journal of Dynamics & Games, 2020, 7 (3) : 225-237. doi: 10.3934/jdg.2020016
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##### References:
Log-returns index of ITLUP (top) and UBI (bottom)
Autocorrelation Function (left) and Partial Autocorrelation Function (right) in ITLUP returns. Top to bottom: log returns index, absolute returns, square returns
Autocorrelation Function (left) and Partial Autocorrelation Function (right) in UBI returns. Top to bottom: log-returns index, absolute returns, square returns
Time-lagged relations between absolute and squared returns in the indices
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
 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
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
 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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