Search Results (6)

This paper proposes a deep neural network (DNN) model to estimate the Hurst exponent, a crucial parameter in modelling stock market price movements driven by fractional geometric Brownian motion. We randomly selected 446 indices from the S&P 500 and extracted their price movements over the last 2010 trading days. Using the rescaled range (R/S) analysis and the detrended fluctuation analysis (DFA), we computed the Hurst exponent and related parameters, which serve as the target parameters in the DNN architecture. The DNN model demonstrated remarkable learning capabilities, making accurate predictions even with small sample sizes. This addresses a limitation of R/S analysis, known for biased estimates in such instances. The significance of this model lies in its ability, once trained, to rapidly estimate the Hurst exponent, providing results in a small fraction of a second. Full article

A univariate stochastic system driven by multiplicative Gaussian white noise is considered. The standard method for simulating its Langevin equation of motion involves incrementing the system’s state variable by a biased Gaussian random number at each time step. It is shown that the efficiency of such simulations can be significantly enhanced by incorporating the skewness of the distribution of the updated state variable. A new algorithm based on this principle is introduced, and its superior performance is demonstrated using a model of free diffusion of a Brownian particle with a friction coefficient that decreases exponentially with the kinetic energy. The proposed simulation technique proves to be accurate over time steps that are an order of magnitude longer than those required by standard algorithms. The model used to test the new numerical technique is known to exhibit a transition from normal diffusion to superdiffusion as the environmental temperature rises above a certain critical value. A simple empirical formula for the time-dependent diffusion coefficient, which covers both diffusion regimes, is introduced, and its accuracy is confirmed through comparison with the simulation results. Full article

Are traditional tests of forecast evaluation well behaved when the competing (nested) model is biased? No, they are not. In this paper, we show analytically and via simulations that, under the null hypothesis of no encompassing, a bias in the nested model may severely distort the size properties of traditional out-of-sample tests in economic forecasting. Not surprisingly, these size distortions depend on the magnitude of the bias and the persistency of the additional predictors. We consider two different cases: (i) There is both in-sample and out-of-sample bias in the nested model. (ii) The bias is present exclusively out-of-sample. To address the former case, we propose a modified encompassing test (MENC-NEW) robust to a bias in the null model. Akin to the ENC-NEW statistic, the asymptotic distribution of our test is a functional of stochastic integrals of quadratic Brownian motions. While this distribution is not pivotal, we can easily estimate the nuisance parameters. To address the second case, we derive the new asymptotic distribution of the ENC-NEW, showing that critical values may differ remarkably. Our Monte Carlo simulations reveal that the MENC-NEW (and the ENC-NEW with adjusted critical values) is reasonably well-sized even when the ENC-NEW (with standard critical values) exhibits rejections rates three times higher than the nominal size. Full article

Since the dynamical behavior of chaotic and stochastic systems is very similar, it is sometimes difficult to determine the nature of the movement. One of the best-studied stochastic processes is Brownian motion, a random walk that accurately describes many phenomena that occur in nature, including quantum mechanics. In this paper, we propose an approach that allows us to analyze chaotic dynamics using the Langevin equation describing dynamics of the phase difference between identical coupled chaotic oscillators. The time evolution of this phase difference can be explained by the biased Brownian motion, which is accepted in quantum mechanics for modeling thermal phenomena. Using a deterministic model based on chaotic Rössler oscillators, we are able to reproduce a similar time evolution for the phase difference. We show how the phenomenon of intermittent phase synchronization can be explained in terms of both stochastic and deterministic models. In addition, the existence of phase multistability in the phase synchronization regime is demonstrated. Full article

KIF1A is a kinesin family protein that moves over a long distance along the microtubule (MT) to transport synaptic vesicle precursors in neurons. A single KIF1A molecule can move toward the plus-end of MT in the monomeric form, exhibiting the characteristics of biased Brownian motion. However, how the bias is generated in the Brownian motion of KIF1A has not yet been firmly established. To elucidate this, we conducted a set of molecular dynamics simulations and observed the binding of KIF1A to MT. We found that KIF1A exhibits biased Brownian motion along MT as it binds to MT. Furthermore, we show that the bias toward the plus-end is generated by the ratchet-like energy landscape for the KIF1A-MT interaction, in which the electrostatic interaction and the negatively-charged C-terminal tail (CTT) of tubulin play an essential role. The relevance to the post-translational modifications of CTT is also discussed. Full article

Many signals appear fractal and have self-similarity over a large range of their power spectral densities. They can be described by so-called Hermite processes, among which the first order one is called fractional Brownian motion (fBm), and has a wide range of applications. The fractional Gaussian noise (fGn) series is the successive differences between elements of a fBm series; they are stationary and completely characterized by two parameters: the variance, and the Hurst coefficient (H). From physical considerations, the fGn could be used to model the noise of observations coming from sensors working with, e.g., phase differences: due to the high recording rate, temporal correlations are expected to have long range dependency (LRD), decaying hyperbolically rather than exponentially. For the rigorous testing of deformations detected with terrestrial laser scanners (TLS), the correct determination of the correlation structure of the observations is mandatory. In this study, we show that the residuals from surface approximations with regression B-splines from simulated TLS data allow the estimation of the Hurst parameter of a known correlated input noise. We derive a simple procedure to filter the residuals in the presence of additional white noise or low frequencies. Our methodology can be applied to any kind of residuals, where the presence of additional noise and/or biases due to short samples or inaccurate functional modeling make the estimation of the Hurst coefficient with usual methods, such as maximum likelihood estimators, imprecise. We demonstrate the feasibility of our proposal with real observations from a white plate scanned by a TLS. Full article