Testing for non-linearity in an artificial financial market: a recurrence quantification approach

Belaire‐Franch, Jorge

doi:10.1016/j.jebo.2003.05.001

Cited by 21 publications

(27 citation statements)

References 29 publications

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“…Since its introduction in 1987 by Eckmann et al [1987], and the development of different quantification approaches, recurrence plots (RPs) have been widely used for the investigation of complex systems in a variety of different disciplines, as physiology, ecology, finance or earth sciences [e.g., Marwan, 2008;Schinkel et al, 2007;Zbilut et al, 2004;Belaire-Franch, 2004;Pecar, 2003;Trauth et al, 2003;Cermák, 2009]. RPs may attract attention because of their ability to produce beautiful or fancy pictures, as in the case of the colourful representations of fractal sets [Mandelbrot, 1982].…”

Section: Introductionmentioning

confidence: 99%

How to Avoid Potential Pitfalls in Recurrence Plot Based Data Analysis

Marwan

2011

Int. J. Bifurcation Chaos

271

236

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Recurrence plots and recurrence quantification analysis have become popular in the last two decades. Recurrence based methods have on the one hand a deep foundation in the theory of dynamical systems and are on the other hand powerful tools for the investigation of a variety of problems. The increasing interest encompasses the growing risk of misuse and uncritical application of these methods. Therefore, we point out potential problems and pitfalls related to different aspects of the application of recurrence plots and recurrence quantification analysis.

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Section: Introductionmentioning

confidence: 99%

How to Avoid Potential Pitfalls in Recurrence Plot Based Data Analysis

Marwan

2011

Int. J. Bifurcation Chaos

271

236

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“…However, the p-value of our test is still very small, so small as to reject the null hypothesis of independence for any usual significance level. Considering that one property of the regression models is that "the residuals have a nonlinear association with X if and only if the original observations of Y have a nonlinear association with X", the conclusion will be that a nonlinear relationship exists between GDP and employment 10 .…”

Section: The Relationship Between Employment and Gdpmentioning

confidence: 99%

An Independence Test Based on Joint Recurrences

Aparicio¹,

Pozo

Saura³

2015

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We propose in this paper a test procedure to determine whether two series proceed from independent systems or not. Our starting point is a multivariate extension of the methodology called Recurrence Quantification Analysis (RQA). We derive the test procedure from the probability distribution of the number of joint recurrences of both series under the null hypothesis of independence. The behavior of the test is evaluated by means of a large set of simulations, carried out with different types of dynamical systems: random, deterministic chaotic, deterministic non-chaotic, systems affected by noise and coupled systems. We obtain satisfactory results in all cases. Finally, the methodology is used to study two questions, on which the bulk of the existing economic literature agrees: 1) the relationship between the nominal interest rate and the inflation rate; and 2) the relationship between the gross domestic product and the employment. The results suggest that our test can be a suitable tool for detecting linear and nonlinear dependence between real series.

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“…From a methodological point of view, the proposed data analysis approach has been found to be particularly effective for highlighting hidden structures of the dynamics of the system under consideration without imposing any pre-defined constraint to the data. Some applications include nonlinear analysis of Electroencephalogram signals and heart rate data (Thomasson et al, 2001, Wessel et al, 2001, financial time series analysis and stock market indices (McKenzie, 2001;Belaire-Franch, 2004;Fabretti and Ausloos, 2005), IP-network traffic (Masugi, 2006), analysis of seismic processes (Matcharashvili et al, 2008), and road traffic analysis (Vlahogianni et al, 2006;Vlahogianni et al, 2007;Vlahogianni et al, 2008).…”

Section: Visualizing and Quantifying Dynamics In The Phase-spacementioning

confidence: 99%

Nonlinear dynamics and recurrence analysis of extreme precipitation for observed and general circulation model generated climates

Panagoulia

Vlahogianni

2013

Hydrological Processes

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A statistical framework based on nonlinear dynamics theory and recurrence quantification analysis of dynamical systems is proposed to quantitatively identify the temporal characteristics of extreme (maximum) daily precipitation series. The methodology focuses on both observed and general circulation model (GCM) generated climates for present (1961–2000) and future (2061–2100) periods which correspond to 1xCO2 and 2xCO2 simulations. The daily precipitation has been modelled as a stochastic process coupled with atmospheric circulation. An automated and objective classification of daily circulation patterns (CPs) based on optimized fuzzy rules was used to classify both observed CPs and ECHAM4 GCM‐generated CPs for 1xCO2 and 2xCO2 climate simulations (scenarios). The coupled model ‘CP‐precipitation’ was suitable for precipitation downscaling. The overall methodology was applied to the medium‐sized mountainous Mesochora catchment in Central‐Western Greece. Results reveal substantial differences between the observed maximum daily precipitation statistical patterns and those produced by the two climate scenarios. A variable nonlinear deterministic behaviour characterizes all climate scenarios examined. Transitions’ patterns differ in terms of duration and intensity. The 2xCO2 scenario contains the strongest transitions highlighting an unusual shift between floods and droughts. The implications of the results to the predictability of the phenomenon are also discussed. Copyright © 2013 John Wiley & Sons, Ltd.

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Testing for non-linearity in an artificial financial market: a recurrence quantification approach

Cited by 21 publications

References 29 publications

How to Avoid Potential Pitfalls in Recurrence Plot Based Data Analysis

How to Avoid Potential Pitfalls in Recurrence Plot Based Data Analysis

An Independence Test Based on Joint Recurrences

Nonlinear dynamics and recurrence analysis of extreme precipitation for observed and general circulation model generated climates

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