Application of nonlinear time series analysis techniques to high-frequency currency exchange data

Towards a non-linear trading strategy for financial time series

“…(6), for values of time delay between 2 and 400 and embedding dimensions between 1 and 15. These values have been selected in agreement with our previous analysis [15] using nonlinear time series methods for the HFDF96 high frequency data set provided by Olsen & Associates [12]. This analysis is reminiscent of a similar approach developed by Zbilut and Webber [19] using RQA analysis to derive embeddings and delays.…”

“…Nonlinear forecasting methodologies try to construct an approximation function of f and they have been applied to financial time series, see for example Lisi and Medio [9] and Cao and Soofi [3]. However, state space reconstruction techniques assume stationarity in the time series which for financial time series does not hold [15]. In the context of nonstationarity, the notion of a ''correct'' embedding or delay is inappropriate as has been demonstrated by Grassberger et al [5].…”

Dynamic characterization and predictability analysis of wind speed and wind power time series in Spain wind farm

“…According to this method, a deterministic dynamics embedded in a sufficiently highdimensional state space should induce a continuous mapping from past to present states and the size of the neighborhoods is increased to investigate the continuity. For deterministic processes, is expected to decrease to zero for decreasing for sufficiently high embedding dimensions [26], but for stochastic processes and processes which are covered by a significant amount of additive observational noise, a nonzero intercept for is expected. Figures 10 (a) and (b) show the results of this method for the wind speed and the wind power time series.…”

“…In order to find out the embedding delay, two methods may be employed. In the first approach, the first zero cross or first cutoff (corresponding to 95%confidence level) of the autocorrelation function (ACF) is the embedding delay [26]. In the second approach, the first minimum of the average mutual information (MI) is the embedding delay [26].…”

Spatiotemporal Time Series Analysis Methods for the Study of Turbulent Magnetohydrodynamic Channel Flows

“…The time series located at the same channel positions with and without magnetic field are studied using phase space reconstruction methods and more specifically the Cross Recurrence Plots (CRPs) method (Eckmann et al 1987;Marwan 2003) and the Cross Recurrence Quantification Analysis (CRQA) (Webber and Zbilut 1994;Marwan et al 2003Marwan et al , 2007 which extracts quantitative information from CRPs. CRQA is the extension of the Recurrence Quantification Analysis method which has been used in the study of various dynamical systems such as proteins (Zbilut et al 2004;Giuliani et al 2002), corrosion (Cazares -Ibanez et al 2005), financial systems (Strozzi et al 2002;Fabretti and Ausloos 2005), physiological systems (Marwan et al 2002a, b;Marwan and Meinke 2004;Riley et al 1999), molecular systems (Karakasidis et al 2007), among many others. The CRP method is applied on climatological and geophysical data (Marwan et al 2002a, b;, financial data (Addoa et al 2013;Crowley and Aaron 2010), engineering data (Nichols et al 2006;Shockley et al 2002;Serrà et al 2009;Wang et al 2012), astronomical data (Deng et al 2013;Ponyavin and Zolotova 2004;Sparavigna 2008), Physics and Mathematics (Ganapathy et al 2007), Biology etc.…”