Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDetrending Moving Average Algorithm: Frequency Response and Scaling Performances
272
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The Detrending Moving Average (DMA) algorithm has been widely used in its several variants for characterizing long-range correlations of random signals and sets (one-dimensional sequences or high-dimensional arrays) either over time or space. In this paper, mainly based on analytical arguments, the scaling performances of the centered DMA, including higher-order ones, are investigated by means of a continuous time approximation and a frequency response approach. Our results are also confirmed by numerical tests. The study is carried out for higher-order DMA operating with moving average polynomials of different degree. In particular, detrending power degree, frequency response, asymptotic scaling, upper limit of the detectable scaling exponent and finite scale range behavior will be discussed.
rate research
Read More
We address the problem of defining early warning indicators of critical transition. To this purpose, we fit the relevant time series through a class of linear models, known as Auto-Regressive Moving-Average (ARMA(p,q)) models. We define two indicators representing the total order and the total persistence of the process, linked, respectively, to the shape and to the characteristic decay time of the autocorrelation function of the process. We successfully test the method to detect transitions in a Langevin model and a 2D Ising model with nearest-neighbour interaction. We then apply the method to complex systems, namely for dynamo thresholds and financial crisis detection.
In the canonical framework, we propose an alternative approach for the multifractal analysis based on the detrending moving average method (MF-DMA). We define a canonical measure such that the multifractal mass exponent $tau(q)$ is related to the partition function and the multifractal spectrum $f(alpha)$ can be directly determined. The performances of the direct determination approach and the traditional approach of the MF-DMA are compared based on three synthetic multifractal and monofractal measures generated from the one-dimensional $p$-model, the two-dimensional $p$-model and the fractional Brownian motions. We find that both approaches have comparable performances to unveil the fractal and multifractal nature. In other words, without loss of accuracy, the multifractal spectrum $f(alpha)$ can be directly determined using the new approach with less computation cost. We also apply the new MF-DMA approach to the volatility time series of stock prices and confirm the presence of multifractality.
Some authors have recently argued that a finite-size scaling law for the text-length dependence of word-frequency distributions cannot be conceptually valid. Here we give solid quantitative evidence for the validity of such scaling law, both using careful statistical tests and analytical arguments based on the generalized central-limit theorem applied to the moments of the distribution (and obtaining a novel derivation of Heaps law as a by-product). We also find that the picture of word-frequency distributions with power-law exponents that decrease with text length [Yan and Minnhagen, Physica A 444, 828 (2016)] does not stand with rigorous statistical analysis. Instead, we show that the distributions are perfectly described by power-law tails with stable exponents, whose values are close to 2, in agreement with the classical Zipfs law. Some misconceptions about scaling are also clarified.
Scaling regions -- intervals on a graph where the dependent variable depends linearly on the independent variable -- abound in dynamical systems, notably in calculations of invariants like the correlation dimension or a Lyapunov exponent. In these applications, scaling regions are generally selected by hand, a process that is subjective and often challenging due to noise, algorithmic effects, and confirmation bias. In this paper, we propose an automated technique for extracting and characterizing such regions. Starting with a two-dimensional plot -- e.g., the values of the correlation integral, calculated using the Grassberger-Procaccia algorithm over a range of scales -- we create an ensemble of intervals by considering all possible combinations of endpoints, generating a distribution of slopes from least-squares fits weighted by the length of the fitting line and the inverse square of the fit error. The mode of this distribution gives an estimate of the slope of the scaling region (if it exists). The endpoints of the intervals that correspond to the mode provide an estimate for the extent of that region. When there is no scaling region, the distributions will be wide and the resulting error estimates for the slope will be large. We demonstrate this method for computations of dimension and Lyapunov exponent for several dynamical systems, and show that it can be useful in selecting values for the parameters in time-delay reconstructions.
Fluctuation scaling has been observed universally in a wide variety of phenomena. In time series that describe sequences of events, fluctuation scaling is expressed as power function relationships between the mean and variance of either inter-event intervals or counting statistics, depending on measurement variables. In this article, fluctuation scaling has been formulated for a series of events in which scaling laws in the inter-event intervals and counting statistics were related. We have considered the first-passage time of an Ornstein-Uhlenbeck process and used a conductance-based neuron model with excitatory and inhibitory synaptic inputs to demonstrate the emergence of fluctuation scaling with various exponents, depending on the input regimes and the ratio between excitation and inhibition. Furthermore, we have discussed the possible implication of these results in the context of neural coding.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
