Person: Sandubete Galán, Julio Emilio
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First Name
Julio Emilio
Last Name
Sandubete Galán
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Estudios estadísticos
Department
Economía Aplicada, Pública y Política
Area
Economía Aplicada
Identifiers
3 results
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Item 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.Item Chaotic signals inside some tick-by-tick financial time series(Chaos, Solitons & Fractals, 2020) Sandubete Galán, Julio Emilio; Escot Mangas, Lorenzo; Boccaletti, StefanoIt has been more than four decades since ideas from chaos began appearing in the literature showing that it is possible to design economic models in regime of chaotic behaviour from a theoretical point of view. However there is no clear evidence that economic time series behave chaotically. So far researchers have found substantial evidence for nonlinearity but relatively weak evidence for chaos. In this paper we propose a possible explanation to this ”chaos model-data paradox”. Our main motivation is that chaos is elusive in financial datasets because of loss of information that occurs when daily quotes are used. This could hinder the detection of chaos in those time series. Chaotic systems are sensitive to initial conditions, so temporal dependence is lost as the chaotic time series are sampled at too long-time intervals, appearing as independent even though they come from a (chaotic) dynamical system. In the case of financial time series, which quotes are continuously traded on markets, the daily sampling may be too long. In order to avoid this problem high-frequency data can be used to detect chaos in financial time series. We have found evidence of chaotic signals inside the 14 tick-by-tick time series considered about some top currency pairs from the Foreign Exchange Market (FOREX). Notice that we do not intend to generalize this finding to all financial series or even to all FOREX series. The main interest of our paper is to illustrate that by choosing a tick-by-tick frequency (instead of a daily one), and with the purpose of preserving the dynamic dependence on the time series, we could find chaos. At least in the 14 specific currency pairs analyzed and during the time intervals considered. Hence we propose take into account all the information available in the financial markets (full sample information on FX rates) instead of daily data. This kind of time series entails several difficulties due to the need to process a huge quantity of information and regarding the reconstruction of the attractor from tick-by-tick time series which are unevenly-spaced. In this sense we have had to implemented new algorithms in order to solve such drawbacks. As far as we know these tick-by-tick financial time series have never been tested for chaos so farItem 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, LorenzoIn 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.