Time series formed from the superposition of discrete renewal processes

1989 ◽  
Vol 26 (1) ◽  
pp. 189-195 ◽  
Author(s):  
P. A. Blight
Keyword(s):  
Time Series ◽  
Discrete Time ◽  
Conditional Distribution ◽  
Counting Process ◽  
Correlation Structure ◽  
Renewal Processes ◽  
Discrete Time Series

The superposition of independent, discrete, renewal processes produces a counting process which is also a discrete time series. The conditional distribution and correlation structure of this kind of time series may be obtained. In suitable conditions the conditional distribution has a spectrum which is exactly or approximately rational. When this is so, an ARMA can be found which matches the spectrum of the superposition.

Time series formed from the superposition of discrete renewal processes

1989 ◽  
Vol 26 (01) ◽  
pp. 189-195
Author(s):  
P. A. Blight
Keyword(s):  
Time Series ◽  
Discrete Time ◽  
Conditional Distribution ◽  
Counting Process ◽  
Correlation Structure ◽  
Renewal Processes ◽  
Discrete Time Series

The superposition of independent, discrete, renewal processes produces a counting process which is also a discrete time series. The conditional distribution and correlation structure of this kind of time series may be obtained. In suitable conditions the conditional distribution has a spectrum which is exactly or approximately rational. When this is so, an ARMA can be found which matches the spectrum of the superposition.

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.

Time Series Methods for the Synthesis of Random Vibration Systems

1976 ◽  
Vol 43 (1) ◽  
pp. 159-165 ◽  
Author(s):  
W. Gersch ◽  
R. S-Z. Liu
Keyword(s):  
Differential Equation ◽  
Time Series ◽  
White Noise ◽  
Least Squares ◽  
Discrete Time ◽  
Covariance Function ◽  
Structural System ◽  
Covariance Functions ◽  
Discrete Time Series ◽  
Scalar Output

A least-squares method procedure for synthesizing the discrete time series that is characteristic of the uniform samples of the response of linear structural systems to stationary random excitation is described. The structural system is assumed to be an n-degree-of-freedom system that is representable by a set of ordinary differential equations excited by a vector white noise force. It is known that the discrete time series of uniformly spaced samples of a scalar white noise excited stationary linear differential equation can be represented as an autoregressive-moving average (AR-MA) time series and that the parameters of the AR-MA model can be computed from the covariance function of the differential equation model. The contributions of this paper are (i) the result that a scalar input scalar output AR-MA model duplicates the scalar output covariance function of a regularly sampled linear structural system with a multivariate white noise input, (ii) a computationally efficient method for computing the covariance function of a randomly excited structural system, and (iii) a demonstration of the theory and the numerical details of a two-stage least-squares procedure for the computation of the AR-MA parameters from the output covariance functions data.

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