Person: Escot Mangas, Lorenzo
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First Name
Lorenzo
Last Name
Escot Mangas
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Estudios estadísticos
Department
Economía Aplicada, Pública y Política
Area
Economía Aplicada
Identifiers
4 results
Search Results
Now showing 1 - 4 of 4
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 Detecting Structural Changes in Time Series by Using the BDS Test Recursively: An Application to COVID-19 Effects on International Stock Markets(Mathematics, 2023) Escot Mangas, Lorenzo; Sandubete, Julio E. ; Pietrych, ŁukaszStructural change tests aim to identify evidence of a structural break or change in the underlying generating process of a time series. The BDS test has its origins in chaos theory and seeks to test, using the correlation integral, the hypothesis that a time series is generated by an identically and independently distributed (IID) stochastic process over time. The BDS test is already widely used as a powerful tool for testing the hypothesis of white noise in the residuals of time series models. In this paper, we illustrate how the BDS test can be implemented also in a recursive manner to evaluate the hypothesis of structural change in a time series, taking advantage of its ability to test the IID hypothesis. We apply the BDS test repeatedly, starting with a sub-sample of the original time series and incrementally increasing the number of observations until it is applied to the full sample time series. A structural change in the unknown underlying generator model is detected when a change in the trend shown by this recursively computed BDS statistic is detected. The strength of this recursive BDS test lies in the fact that it does not require making any assumptions about the underlying time series generator model. We ilustrate the power and potential of this recursive BDS test through an application to real economic data. In this sense, we apply the test to assess the structural changes caused by the COVID-19 pandemic in international financial markets. Using daily data from the world’s top stock indices, we have detected strong and statistically significant evidence of two major structural changes during the period from June 2018 to June 2022. The first occurred in March 2020, coinciding with the onset of economic restrictions in the main Western countries as a result of the pandemic. The second occurred towards the end of August 2020, with the end of the main economic restrictions and the beginning of a new post-pandemic economic scenario. This methodology to test for structural changes in a time series is easy to implement and can detect changes in any system or process behind the time series even when this generating system is not known, and without the need to specify or estimate any a priori generating model. In this sense, the recursive BDS test could be incorporated as an initial preliminary step to any exercise of time series modeling. If a structural change is detected in a time series, rather than estimating a single predictive model for the full-sample time series, efforts should be made to estimate different predictive models, one for the time before and one for the time after the detected structural change.Item 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.