Person:
Sandubete Galán, Julio Emilio

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First Name
Julio Emilio
Last Name
Sandubete Galán
URI
https://hdl.handle.net/20.500.14352/86932
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Estudios estadísticos
Department
Economía Aplicada, Pública y Política
Area
Economía Aplicada
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2021 - 20232
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Now showing 1 - 2 of 2
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    Estimating Lyapunov exponents on a noisy environment by global and local Jacobian indirect algorithms
    (Applied Mathematics and Computation, 2023) Escot Mangas, Lorenzo; Sandubete Galán, Julio Emilio; Simos, Theodore E.
    Most of the existing methods and techniques for the detection of chaotic behaviour from empirical time series try to quantify the well-known sensitivity to initial conditions through the estimation of the so-called Lyapunov exponents corresponding to the data generating system, even if this system is unknown. Some of these methods are designed to operate in noise-free environments, such as those methods that directly quantify the separation rate of two initially close trajectories. As an alternative, this paper provides two nonlinear indirect regression methods for estimating the Lyapunov exponents on a noisy environment. We extend the global Jacobian method, by using local polynomial kernel regressions and local neural net kernel models. We apply such methods to several noise-contaminated time series coming from different data generating processes. The results show that in general, the Jacobian indirect methods provide better results than the traditional direct methods for both clean and noisy time series. Moreover, the local Jacobian indirect methods provide more robust and accurate fit than the global ones, with the methods using local networks obtaining more accurate results than those using local polynomials.
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    Solving the chaos model-data paradox in the cryptocurrency market
    (Communications in Nonlinear Science and Numerical Simulation, 2021) Pietrych, Lukasz; Sandubete Galán, Julio Emilio; Escot Mangas, Lorenzo
    In this paper we test for nonlinearity and chaos in some cryptocurrencies returns and volatility. Financial markets are characterized by the so-called chaos model-data paradox, that is, it is relatively easy to design theoretical dynamic financial models that behave chaotically, but it is hard to find robust evidence of this kind of chaotic behaviour in real dataset. In fact, this paradox has been taken as an evidence that support the Efficient Market Hypothesis (EMH). In this paper we apply new robust computational methods based on statistical procedures to reconstruct the underlying attractor and to estimate the Lyapunov exponents based on the Jacobian neural nets. We have tested nonlinearity and chaos in some digital cryptocurrencies (Bitcoin, Ethereum, Ripple and Litecoin). The results show strong evidence against EMH supporting the hypothesis that those time series come from an underlying unknown generating process that behave nonlinear and chaotically. This fact points out that a potential explication to the chaos model-data paradox lies in the methods traditionally used in the literature which are not robust and do not have the capability to find chaos in financial time-series data.