Diffusion equations and the time evolution of foreign exchange rates

Figueiredo, Annibal; Castro, Márcio T. de; Fonseca, Regina Célia Bueno da; Gleria, Iram

doi:10.1016/j.physleta.2013.04.050

Cited by 2 publications

(1 citation statement)

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“…As an instance, we simulated a long memory (non-linear) process based on an autoregressive fractionally integrated moving average (ARFIMA) model, for which the autocorrelation between θ(t, 1) and θ(t + h, 1) is ρ(h) ∼ h 2d−1 as h increases [17]. We generated 50,000 data points from the ARFIMA model (1 − B) d (1 − φB)θ(t, 1) = ξ(t), where B is the backward shift operator, φ = 0.5, d = 0.4, and ξ(t) is a zero-mean white noise with standard deviation 10 −3 .…”

Section: Applicationsmentioning

confidence: 99%

On the time-homogeneous Ornstein–Uhlenbeck process in the foreign exchange rates

et al. 2015

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Since Gaussianity and stationarity assumptions cannot be fulfilled by financial data, the time-homogeneous Ornstein-Uhlenbeck (THOU) process was introduced as a candidate model to describe time series of financial returns [1]. It is an Ornstein-Uhlenbeck (OU) process in which these assumptions are replaced by linearity and time-homogeneity. We employ the OU and THOU processes to analyze daily foreign exchange rates against the US dollar. We confirm that the OU process does not fit the data, while in most cases the first four cumulants patterns from data can be described by the THOU process. However, there are some exceptions in which the data do not follow linearity or time-homogeneity assumptions.

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Section: Applicationsmentioning

confidence: 99%