scholarly journals SELF-SIMILAR EXTRAPOLATION OF ASYMPTOTIC SERIES AND FORECASTING FOR TIME SERIES

2000 ◽  
Vol 14 (22n23) ◽  
pp. 791-800 ◽  
Author(s):  
V. I. YUKALOV
Keyword(s):  
Time Series ◽  
Probability Measure ◽  
Approximation Theory ◽  
Asymptotic Series ◽  
The Self ◽  
Complete Family ◽  
Self Similar ◽  
Similar Approximation

The method of extrapolating asymptotic series, based on the self-similar approximation theory, is developed. Several important questions are answered, which makes the foundation of the method unambiguous and its application straightforward. It is shown how the extrapolation of asymptotic series can be reformulated as forecasting for time series. The probability measure is introduced characterizing the ensemble of forecasted scenarios. The method of choosing the complete family of databases is put forward.

scholarly journals From Asymptotic Series to Self-Similar Approximants

Physics ◽  
2021 ◽  
Vol 3 (4) ◽  
pp. 829-878
Author(s):  
Vyacheslav I. Yukalov ◽  
Elizaveta P. Yukalova
Keyword(s):  
Perturbation Theory ◽  
Approximation Theory ◽  
Good Accuracy ◽  
Asymptotic Series ◽  
Approximate Solutions ◽  
Self Similar ◽  
Similar Approximation ◽  
Physics Problems

The review presents the development of an approach of constructing approximate solutions to complicated physics problems, starting from asymptotic series, through optimized perturbation theory, to self-similar approximation theory. The close interrelation of underlying ideas of these theories is emphasized. Applications of the developed approach are illustrated by typical examples demonstrating that it combines simplicity with good accuracy.

scholarly journals Self-similar extrapolation of nonlinear problems from small-variable to large-variable limit

2020 ◽  
Vol 34 (21) ◽  
pp. 2050208
Author(s):  
V. I. Yukalov ◽  
E. P. Yukalova
Keyword(s):  
Asymptotic Series ◽  
Nonlinear Problems ◽  
Numerical Convergence ◽  
Physical Problems ◽  
Variable Limit ◽  
Small Parameters ◽  
Self Similar ◽  
Similar Approximation ◽  
Similar Factor ◽  
Class Of Functions

Complicated physical problems are usually solved by resorting to perturbation theory leading to solutions in the form of asymptotic series in powers of small parameters. However, finite, and even large values of the parameters, are often of main physical interest. A method is described for predicting the large-variable behavior of solutions to nonlinear problems from the knowledge of only their small-variable expansions. The method is based on self-similar approximation theory resulting in self-similar factor approximants. The latter can well approximate a large class of functions, rational, irrational, and transcendental. The method is illustrated by several examples from statistical and condensed matter physics, where the self-similar predictions can be compared with the available large-variable behavior. It is shown that the method allows for finding the behavior of solutions at large variables when knowing just a few terms of small-variable expansions. Numerical convergence of approximants is demonstrated.

scholarly journals Extrapolation of perturbation-theory expansions by self-similar approximants

2014 ◽  
Vol 25 (5) ◽  
pp. 595-628 ◽  
Author(s):  
S. GLUZMAN ◽  
V.I. YUKALOV
Keyword(s):  
Perturbation Theory ◽  
Approximation Theory ◽  
Asymptotic Expansions ◽  
Applied Mathematics ◽  
Self Similar ◽  
Similar Approximation ◽  
Asymptotic Perturbation

The problem of extrapolating asymptotic perturbation-theory expansions in powers of a small variable to large values of the variable tending to infinity is investigated. The analysis is based on self-similar approximation theory. Several types of self-similar approximants are considered and their use in different problems of applied mathematics is illustrated. Self-similar approximants are shown to constitute a powerful tool for extrapolating asymptotic expansions of different natures.

scholarly journals Renormalization Group Analysis of October Market Crashes

1998 ◽  
Vol 12 (02n03) ◽  
pp. 75-84 ◽  
Author(s):  
S. Gluzman ◽  
V. I. Yukalov
Keyword(s):  
Time Series ◽  
Renormalization Group ◽  
Group Analysis ◽  
The Self ◽  
Main Attention ◽  
Renormalization Group Analysis ◽  
Suggested Approach ◽  
Market Crashes ◽  
Self Similar ◽  
Analysis Of Time Series

The self-similar analysis of time series, suggested earlier by the authors, is applied to the description of market crises. The main attention is payed to the October 1929, 1987 and 1997 stock market crises, which can be successfully treated by the suggested approach. The analogy between market crashes and critical phenomena is emphasized.

scholarly journals Booms and Crashes in Self-Similar Markets

1998 ◽  
Vol 12 (14n15) ◽  
pp. 575-587 ◽  
Author(s):  
S. Gluzman ◽  
V. I. Yukalov
Keyword(s):  
Time Series ◽  
Critical Phenomena ◽  
The Self ◽  
Market Dynamics ◽  
Classi Cation ◽  
Self Similar

Sharp changes in time series representing market dynamics are studied by means of the self-similar analysis suggested earlier by the authors. These sharp changes are market booms and crashes. Such crises phenomena in markets are analogous to critical phenomena in physics. A simple classi cation of the market crisis phenomena is given.

scholarly journals WEIGHTED FIXED POINTS IN SELF-SIMILAR ANALYSIS OF TIME SERIES

1999 ◽  
Vol 13 (12) ◽  
pp. 1463-1476 ◽  
Author(s):  
V. I. YUKALOV ◽  
S. GLUZMAN
Keyword(s):  
Time Series ◽  
Fixed Point ◽  
Standard Deviation ◽  
Stock Market ◽  
Fixed Points ◽  
A Priori ◽  
The Self ◽  
Self Similar ◽  
Analysis Of Time Series

The self-similar analysis of time series is generalized by introducing the notion of scenario probabilities. This makes it possible to give a complete statistical description for the forecast spectrum by defining the average forecast as a weighted fixed point and by calculating the corresponding a priori standard deviation and variance coefficient. Several examples of stock-market time series illustrate the method.

scholarly journals Describing phase transitions in field theory by self-similar approximants

2019 ◽  
Vol 204 ◽  
pp. 02003
Author(s):  
V.I. Yukalov ◽  
E.P. Yukalova
Keyword(s):  
Field Theory ◽  
Phase Transitions ◽  
Coupling Parameter ◽  
Asymptotic Series ◽  
Quantum Field ◽  
Lattice Data ◽  
Borel Summation ◽  
Self Similar ◽  
Similar Approximation ◽  
Good Agreement

Self-similar approximation theory is shown to be a powerful tool for describing phase transitions in quantum field theory. Self-similar approximants present the extrapolation of asymptotic series in powers of small variables to the arbitrary values of the latter, including the variables tending to infinity. The approach is illustrated by considering three problems: (i) The influence of the coupling parameter strength on the critical temperature of the O(N)-symmetric multicomponent field theory. (ii) The calculation of critical exponents for the phase transition in the O(N)-symmetric field theory. (iii) The evaluation of deconfinement temperature in quantum chromodynamics. The results are in good agreement with the available numerical calculations, such as Monte Carlo simulations, Padé-Borel summation, and lattice data.

ON THE SELF-SIMILAR DISTRIBUTION OF THE EMERGENCY WARD ARRIVALS TIME SERIES

Fractals ◽  
2002 ◽  
Vol 10 (04) ◽  
pp. 413-427 ◽  
Author(s):  
ENRIC MONTE ◽  
JOSEP ROCA ◽  
LLUIS VILARDELL
Keyword(s):  
Time Series ◽  
Lognormal Distribution ◽  
The Self ◽  
Similar Distribution ◽  
Hospital Emergency ◽  
Emergency Ward ◽  
Telephone Exchange ◽  
Wide Range ◽  
Self Similar ◽  
High Level

Hospital emergency arrivals are often modeled as Poisson processes because of the similarity of the problem to a telephone exchange model, i.e. applications that involve counting the number of times a random event occurs in a given time, where the interval between individual counts follows the exponential distribution. In this paper, we propose a statistical modeling of hospital emergency ward arrivals, using self-similar processes. This modeling takes into account the fact that it is known empirically that the emergency time series consists of periods marked by "bursts" of high level demand peaks, followed by periods of lower demand. This is explained neither by a Poisson during fixed-lengths intervals nor by a lognormal distribution. We show that a self-similar distribution can model this phenomenon. We also show that the commonly used Poisson models seriously underestimate the "burstiness" of emergency arrivals over a wide range of time scales, and that the emergency time series cannot be modeled by a lognormal distribution. The self-similar distribution was tested by the Hurst parameter, which we have calculated using five different methods, all of which agree on the value of the parameter.

scholarly journals Hausdorff measure and Assouad dimension of generic self-conformal IFS on the line

2020 ◽  
pp. 1-31
Author(s):  
Balázs Bárány ◽  
Károly Simon ◽  
István Kolossváry ◽  
Michał Rams
Keyword(s):  
Hausdorff Measure ◽  
Similar Case ◽  
Iterated Function Systems ◽  
The Self ◽  
Dimensional Hausdorff Measure ◽  
Assouad Dimension ◽  
Iterated Function ◽  
Self Similar ◽  
Weak Separation ◽  
Topological Sense

This paper considers self-conformal iterated function systems (IFSs) on the real line whose first level cylinders overlap. In the space of self-conformal IFSs, we show that generically (in topological sense) if the attractor of such a system has Hausdorff dimension less than 1 then it has zero appropriate dimensional Hausdorff measure and its Assouad dimension is equal to 1. Our main contribution is in showing that if the cylinders intersect then the IFS generically does not satisfy the weak separation property and hence, we may apply a recent result of Angelevska, Käenmäki and Troscheit. This phenomenon holds for transversal families (in particular for the translation family) typically, in the self-similar case, in both topological and in measure theoretical sense, and in the more general self-conformal case in the topological sense.

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