scholarly journals Ordinal patterns-based methodologies for distinguishing chaos from noise in discrete time series

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Massimiliano Zanin ◽  
Felipe Olivares
Keyword(s):  
Time Series ◽  
Discrete Time ◽  
Real World ◽  
Chaotic Maps ◽  
Computational Cost ◽  
Permutation Patterns ◽  
Discrete Time Series ◽  
Ordinal Patterns ◽  
Theoretical Foundations ◽  
Real World Problems

AbstractOne of the most important aspects of time series is their degree of stochasticity vs. chaoticity. Since the discovery of chaotic maps, many algorithms have been proposed to discriminate between these two alternatives and assess their prevalence in real-world time series. Approaches based on the combination of “permutation patterns” with different metrics provide a more complete picture of a time series’ nature, and are especially useful to tackle pathological chaotic maps. Here, we provide a review of such approaches, their theoretical foundations, and their application to discrete time series and real-world problems. We compare their performance using a set of representative noisy chaotic maps, evaluate their applicability through their respective computational cost, and discuss their limitations.

scholarly journals Combined Games with Randomly Delayed Beginnings

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 534
Author(s):  
F. Thomas Bruss
Keyword(s):  
Discrete Time ◽  
Real World ◽  
Optimal Stopping ◽  
Random Variables ◽  
Approximate Solutions ◽  
Real World Problems

This paper presents two-person games involving optimal stopping. As far as we are aware, the type of problems we study are new. We confine our interest to such games in discrete time. Two players are to chose, with randomised choice-priority, between two games G1 and G2. Each game consists of two parts with well-defined targets. Each part consists of a sequence of random variables which determines when the decisive part of the game will begin. In each game, the horizon is bounded, and if the two parts are not finished within the horizon, the game is lost by definition. Otherwise the decisive part begins, on which each player is entitled to apply their or her strategy to reach the second target. If only one player achieves the two targets, this player is the winner. If both win or both lose, the outcome is seen as “deuce”. We motivate the interest of such problems in the context of real-world problems. A few representative problems are solved in detail. The main objective of this article is to serve as a preliminary manual to guide through possible approaches and to discuss under which circumstances we can obtain solutions, or approximate solutions.

Determination of chaotic attractors in short discrete time series

2019 ◽  
pp. 339-360
Author(s):  
A. Celletti ◽  
C. Froeschlé ◽  
I.V. Tetko ◽  
A.E.P. Villa
Keyword(s):  
Time Series ◽  
Discrete Time ◽  
Chaotic Attractors ◽  
Discrete Time Series

Regression derivatives and their application for registration of a tsunami wave arrival by sea-level records

2019 ◽  
pp. 28-41
Author(s):  
Сергей Мартикович Агаян ◽  
Шамиль Рафекович Богоутдинов ◽  
Ольга Васильевна Иванченко ◽  
Дмитрий Альфредович Камаев
Keyword(s):  
Time Series ◽  
Data Processing ◽  
Sea Level ◽  
Discrete Time ◽  
Mathematical Analysis ◽  
Visual Analysis ◽  
Tsunami Wave ◽  
Information Support ◽  
Discrete Time Series ◽  
Wave Arrival

Структура дискретного временного ряда тесно связана со свойствами процесса, который он описывает. В рамках дискретного математического анализа имеется несколько подходов к анализу структуры дискретных рядов: геометрические меры, динамические коридоры и концепция тренда. Для дискретного временного ряда, заданного в общем случае на нерегулярной сетке, с характером тренда тесным образом связана регрессионная производная: области ее положительного (отрицательного) значения соответствуют возрастающим (убывающим) трендам, а границы между ними - экстремумам. В настоящей работе исследуются возможности применения методов дискретного математического анализа для разработки процедуры регистрации вступления волны цунами по оперативным данным измерения уровня моря. The research addresses the possibility of application of the methods of discrete mathematical analysis to develop a procedure for recording tsunami wave arrival on the base of the operational data for measuring sea level. As a basis for constructing a tsunami wave registration procedure, this research uses a schematization of the actions of the oceanographer on-duty during visual analysis of the sea level records. The task of automatic registration of a tsunami wave by sea level recording arises in various situations of information support of the oceanographer on duty. Requirements for the processing of sea level records depend on the situation. The structure of a discrete time series is closely related to the properties of the described process. As part of the discrete mathematical analysis, there are several approaches to the analysis of the structure of discrete series: geometric measures, dynamic corridors and the trend concept. For a discrete time series, given in the general case on an irregular grid, the regression derivative is closely related to the nature of the trend: the areas of its positive (negative) values correspond to the increasing (decreasing) trends, and the boundaries between them are extremes. The content of this research is a presentation of data processing techniques using regression derivatives, constructing data processing procedures based on derivatives, as well as a demonstration of their applicability to the problem of recording tsunami wave arrival according to the measuring of sea level.

TESTING TIME-SERIES STATIONARITY AGAINST AN ALTERNATIVE WHOSE MEAN IS PERIODIC

2001 ◽  
Vol 5 (3) ◽  
pp. 380-412 ◽  
Author(s):  
Melvin A. Hinich ◽  
Phillip Wild
Keyword(s):  
Time Series ◽  
Fourier Transform ◽  
Real World ◽  
Null Hypothesis ◽  
Data Sets ◽  
Testing Time ◽  
Economic Data ◽  
The Mean ◽  
Important Form ◽  
Real World Problems

We develop a test of the null hypothesis that an observed time series is a realization of a strictly stationary random process. Our test is based on the result that the kth value of the discrete Fourier transform of a sample frame has a zero mean under the null hypothesis. The test that we develop will have considerable power against an important form of nonstationarity hitherto not considered in the mainstream econometric time-series literature, that is, where the mean of a time series is periodic with random variation in its periodic structure. The size and power properties of the test are investigated and its applicability to real-world problems is demonstrated by application to three economic data sets.

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