Spectral representation of random processes and time series

Author(s):  
Hisashi Kobayashi ◽  
Brian L. Mark ◽  
William Turin
2021 ◽  
pp. 30-36
Author(s):  

The use of the analysis methodology and forecasting of time series of indicators of the effectiveness of maintaining airworthiness of aircraft of civil aviation made it possible to present the dynamics of indicators as a combination of the regular component, harmonic components with oscillation periods of 12 months and more, and a random component, which represents random processes developing under the influence of groups of factors affecting the airworthiness maintenance process. The results obtained are aimed at improving the safety and effectiveness of aircraft use. Keywords: aircraft, airworthiness, effectiveness of airworthiness maintenance, analysis methodology, forecasting, time series of effectiveness indicators. [email protected]


2019 ◽  
Vol 34 (4) ◽  
pp. 187-196
Author(s):  
Alexander B. Medvinsky ◽  
Alexey V. Rusakov ◽  
Boris V. Adamovich ◽  
Tamara M. Mikheyeva ◽  
Nailya I. Nurieva

Abstract The quantitative analysis of recurrence plots while applied to mathematical models was shown to be an effective tool in recognizing a frontier between deterministic chaos and random processes. In nature, however, unlike mathematical models, deterministic processes are closely intertwined with random influences. As a result, the non-structural distributions of points on the recurrence plots, which are typical of random processes, are inevitably superimposed on the aperiodic structures characteristic of chaos. Taking into account that the stochastic impacts are an inherent feature of the dynamics of populations in the wild, we present here the results of the analysis of recurrence plots in order to reveal the extent to which irregular phytoplankton oscillations in the Naroch Lakes, Belarus, are susceptible to stochastic impacts. We demonstrate that numerical assessments of the horizon of predictability Tpr of the dynamics under study and the average number Pd of the points that belong to the diagonal segments on the recurrence plots can furnish insights into the extent to which the dynamics of both model and phytoplankton populations are affected by random components. Specifically, a comparative analysis of the values of Tpr and Pd for the time series of phytoplankton and the time series of random processes allows us to conclude that random components of the phytoplankton dynamics in the Naroch Lakes do not prevent recognition of chaotic nature of these dynamics.


2005 ◽  
Vol 16 (11) ◽  
pp. 1733-1743 ◽  
Author(s):  
A. CHAKRABORTI ◽  
M. S. SANTHANAM

In this paper, we review some of the properties of financial and other spatio-temporal time series generated from coupled map lattices, GARCH(1,1) processes and random processes (for which analytical results are known). We use the Hurst exponent (R/S analysis) and detrended fluctuation analysis as the tools to study the long-time correlations in the time series. We also compare the eigenvalue properties of the empirical correlation matrices, especially in relation to random matrices.


2019 ◽  
Vol 8 (3) ◽  
pp. 246-256
Author(s):  
B. L. Kurilin ◽  
V. Y. Kisselevskaya-Babinina ◽  
N. A. Karasyov ◽  
I. V. Kisselevskaya-Babinina ◽  
E. V. Kislukhkina ◽  
...  

Background The most important part of the state social and economic policy is optimization of the healthcare system, where the loss of public health leads to economic damage. Against this background, forecasting the work of medical institutions is the basis for the successful development of healthcare, despite the fact that the healthcare system, indicators and standards of medical and social welfare are still not stable, and a clear development strategy for the shortand long-term period has not been worked out. Aim of study Determining the most optimal method for predicting the work of a medical institution, based on identification of the main trends in the time series when constructing a model of the dependence of parameters or determining the behavior of data as a stochastic series (i.e. modeling random processes and random events with some random error).Material and methods To predict the main statistical indicators of N.V. Sklifosovsky Research Institute for Emergency Medicine based on a retrospective analysis, data were used that were submitted to the City Bureau of Medical Statistics and entered into official reporting forms (form № 30, approved by Goskomstat of the Russian Federation dated September 10, 2002, № 175): the number of hospitalized patients and mortality rates in inpatient and intensive care units. To select the optimal methodology for the experimental forecast model, data were used for the period from 1991 to 2016. Indicators for 2017 were taken as control values.Results As a result of the comparison of several methods (moving averages, least squares approach, Brown model, Holt–Winters method, autocorrelation model, Box–Jenkins method) as applied to the work of N.V. Sklifosovsky Research Institute for Emergency Medicine, the Holt–Winters model was chosen as the most appropriate one for the data characteristics.Findings 1. When using methods of moving averages, least squares, Box-Jenkins, as well as Brown model and autocorrelation, the forecast result is not always influenced by strictly straight-line indicators of the time series, due to the heterogeneity of the time series and the presence of outliers (often found in a medical institution providing emergency care), which lead to a significant decrease in the reliability of forecasting. 2. The application of the Holt–Winters model, which takes into account the exponential trend (the trend of time series indicators) and additive season (periodic fluctuations observed in the time series), is most suitable for processing statistical data and forecasting for long-term, medium-term and short-term periods taking the specifics of a hospital providing emergency care into account. 3. The choice of the optimal method for predicting the work of a medical institution, based on the identification of the main trends in the time series, taking most of the features in the modeling of random processes and events into account, allowed to reduce the relative forecast error.


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