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

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

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  • 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.

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

    Citation:

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

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

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

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

    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
     | Show Table
    DownLoad: CSV
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