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Journal articles on the topic 'Time-series analysis – Mathematical models'

Author: Grafiati

Published: 4 June 2021

Last updated: 31 January 2023

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1

Petrusevich, D. A. "ANALYSIS OF MATHEMATICAL MODELS USED FOR ECONOMETRICAL TIME SERIES FORECASTING." Russian Technological Journal 7, no. 2 (May 16, 2019): 61–73. http://dx.doi.org/10.32362/2500-316x-2019-7-2-61-73.

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2

Novotny, V., H. Jones, X. Feng, and A. Capodaglio. "Time Series Analysis Models of Activated Sludge Plants." Water Science and Technology 23, no. 4-6 (February 1, 1991): 1107–16. http://dx.doi.org/10.2166/wst.1991.0562.

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Time series models of the activated sludge process are very useful in design and real time operation of wastewater treatment systems which deal with variable influent flows and pollution loads. In contrast to common deterministic dynamic mathematical models which require knowledge of a large number of coefficients, the time series models can be developed from input and output monitoring data series. In order to avoid “black box” approaches, time series models can be made compatible and identical in principle, with their dynamic mass balance model equivalents. In fact, these two types of models

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3

Ray, Bonnie K. "Regression Models for Time Series Analysis." Technometrics 45, no. 4 (November 2003): 364. http://dx.doi.org/10.1198/tech.2003.s166.

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4

Brahimi, Tahar, and Tahar Smain. "A Nonstationary Mathematical Model for Acceleration Time Series." Mathematical Modelling of Engineering Problems 8, no. 2 (April 28, 2021): 246–52. http://dx.doi.org/10.18280/mmep.080211.

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The choice of nonstationary stochastic models for the study is fully justified by the limitation of acceleration time series number. The three acceleration time series under consideration are used to generate a new, artificial series of ten per historical one using autoregressive moving average model. Subsequently, the average of nonlinear is utilized for the ten acceleration time series in order to obtain the spectral response of a system with single degree of freedom. Modeling of acceleration time series involves critical estimation of metrics that characterize nonstationary acceleration tim

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5

Yang, Xi, Bo Nie, Bing Di Liu, Hai Liu, and Lun Bai. "Time Series Modeling and Analysis on the Silk Crape Satin Product." Advanced Materials Research 175-176 (January 2011): 412–17. http://dx.doi.org/10.4028/www.scientific.net/amr.175-176.412.

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Empirical analysis on typical product categories, product series and Price Index of every level of single species is made by using classical ARMA models as well as ARCH models, which based on the actual data sampling and network. This study sets up AR models with ARCH effect of timing of product operations Index that judged by LM test used as model identification, and then establishes corresponding mathematical quantitative model for prediction. All of these are carried out by the Metrical Economics and the Eviews software. With time series, the fitting and prediction for running change-trend

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Chen, Qi, Han Zhao, Hongfang Qiu, Qiyin Wang, Dewei Zeng, and Mengliang Ye. "Time series analysis of rubella incidence in Chongqing, China using SARIMA and BPNN mathematical models." Journal of Infection in Developing Countries 16, no. 08 (August 30, 2022): 1343–50. http://dx.doi.org/10.3855/jidc.16475.

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Introduction: Chongqing is among the areas with the highest rubella incidence rates in China. This study aimed to analyze the temporal distribution characteristics of rubella and establish a forecasting model in Chongqing, which could provide a tool for decision-making in the early warning system for the health sector. Methodology: The rubella monthly incidence data from 2004 to 2019 were obtained from the Chongqing Center of Disease and Control. The incidence from 2004 to June 2019 was fitted using the seasonal autoregressive integrated moving average (SARIMA) model and the back-propaga

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7

Gluhovsky, Alexander, and Kevin Grady. "Effective low-order models for atmospheric dynamics and time series analysis." Chaos: An Interdisciplinary Journal of Nonlinear Science 26, no. 2 (February 2016): 023119. http://dx.doi.org/10.1063/1.4942586.

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Евстегнеева, V. Evstegneeva, Честнова, Tatyana Chestnova, Смольянинова, and O. Smolyaninova. "Time series analysis in forecasting pririrodno focal infections." Journal of New Medical Technologies. eJournal 9, no. 4 (December 8, 2015): 0. http://dx.doi.org/10.12737/17087.

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Mathematical methods and models used in forecasting problems may relate to a wide variety of topics: from the regression analysis, time series analysis, formulation and evaluation of expert opinions, simulation, systems of simultaneous equations, discriminant analysis, logit and probit models, logical unit decision functions, variance or covariance analysis, rank correlation and contingency tables, etc. In the analysis of the phenomenon over a long timeperiod, for example, the incidence of long-term dynamics with a forecast of further development of the process, y

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Sidorova, N. Р., and D. S. Demina. "Comparison of results of forecasting of time series based on autoregression analysis and model trends." Informacionno-technologicheskij vestnik 13, no. 3 (September 30, 2017): 118–26. http://dx.doi.org/10.21499/2409-1650-2017-3-118-126.

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At the moment, there are various forecasting models. Model tendencies are based on the key technical analysis techniques: smoothing data using a mathematical average, the allocation trend. Attempt selecting optimal models, are showing the minimum average error of prediction. On the basis of autoregressive models, based on the sample maximum likelihood, and model trends based on the methods of technical analysis based forecast for a sufficiently long period. Thus, the proposed models give a forecast with minimum average error, and its values are in the interval allowed for the researcher. The o

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10

Kalugin, T. R., A. K. Kim, and D. A. Petrusevich. "Analysis of the high order ADL(p, q) models used to describe connections between time series." Russian Technological Journal 8, no. 2 (April 14, 2020): 7–22. http://dx.doi.org/10.32362/2500-316x-2020-8-2-7-22.

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In the paper the mathematical models describing connection between two time series are researched. At first each of them is investigated separately, and the ARIMA(p, d, q) model is constructed. These models are based on the time series characteristics obtained during the analysis stage. The connection between two time series is confirmed with the aid of cointegration statistical tests. Then the mathematical model of the connection between series is constructed. The ADL(p, q) model describes this dependence. It’s shown that for the time series under investigation the orders p, q of the ADL(p, q

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11

Tong, Howell. "Threshold models in time series analysis — 30 years on." Statistics and Its Interface 4, no. 2 (2011): 107–18. http://dx.doi.org/10.4310/sii.2011.v4.n2.a1.

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12

Huang, D. "Stochastic fm models and non-linear time series analysis." Advances in Applied Probability 29, no. 4 (December 1997): 986–1003. http://dx.doi.org/10.2307/1427850.

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An important model in communications is the stochastic FM signal st = A cos , where the message process {mt} is a stochastic process. In this paper, we investigate the linear models and limit distributions of FM signals. Firstly, we show that this non-linear model in the frequency domain can be converted to an ARMA (2, q + 1) model in the time domain when {mt} is a Gaussian MA (q) sequence. The spectral density of {St} can then be solved easily for MA message processes. Also, an error bound is given for an ARMA approximation for more general message processes. Secondly, we show that {St} is as

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Huang, D. "Stochastic fm models and non-linear time series analysis." Advances in Applied Probability 29, no. 04 (December 1997): 986–1003. http://dx.doi.org/10.1017/s0001867800047984.

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An important model in communications is the stochastic FM signal st = A cos , where the message process {m t} is a stochastic process. In this paper, we investigate the linear models and limit distributions of FM signals. Firstly, we show that this non-linear model in the frequency domain can be converted to an ARMA (2, q + 1) model in the time domain when {mt } is a Gaussian MA (q) sequence. The spectral density of {St } can then be solved easily for MA message processes. Also, an error bound is given for an ARMA approximation for more general message processes. Secondly, we show that {St } i

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Tominaga, Daisuke, Hideo Kawaguchi, Yoshimi Hori, Tomohisa Hasunuma, Chiaki Ogino, and Sachiyo Aburatani. "Mathematical Model for Small Size Time Series Data of Bacterial Secondary Metabolic Pathways." Bioinformatics and Biology Insights 12 (January 1, 2018): 117793221877507. http://dx.doi.org/10.1177/1177932218775076.

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Measuring the concentrations of metabolites and estimating the reaction rates of each reaction step consisting of metabolic pathways are significant for an improvement in microorganisms used in maximizing the production of materials. Although the reaction pathway must be identified for such an improvement, doing so is not easy. Numerous reaction steps have been reported; however, the actual reaction steps activated vary or change according to the conditions. Furthermore, to build mathematical models for a dynamical analysis, the reaction mechanisms and parameter values must be known; however,

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15

Wang, Yi-Fu, and Tsai-Hung Fan. "A Bayesian analysis on time series structural equation models." Journal of Statistical Planning and Inference 141, no. 6 (June 2011): 2071–78. http://dx.doi.org/10.1016/j.jspi.2010.12.017.

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16

Haughton, Dominique, Jonathan Haughton, and Alan J. Izenman. "Information criteria and harmonic models in time series analysis." Journal of Statistical Computation and Simulation 35, no. 3-4 (April 1990): 187–207. http://dx.doi.org/10.1080/00949659008811243.

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Medvinsky, Alexander B., Alexey V. Rusakov, Boris V. Adamovich, Tamara M. Mikheyeva, and Nailya I. Nurieva. "Determinism versus randomness in plankton dynamics: The analysis of noisy time series based on the recurrence plots." Russian Journal of Numerical Analysis and Mathematical Modelling 34, no. 4 (August 27, 2019): 187–96. http://dx.doi.org/10.1515/rnam-2019-0016.

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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 th

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18

Adedotun, Adedayo F. "Hybrid Neural Network Prediction for Time Series Analysis of COVID-19 Cases in Nigeria." Journal of Intelligent Management Decision 1, no. 1 (September 30, 2022): 46–55. http://dx.doi.org/10.56578/jimd010106.

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The lethal coronavirus illness (COVID-19) has evoked worldwide discussion. This contagious, sometimes fatal illness, is caused by the severe acute respiratory syndrome coronavirus 2. So far, COVID-19 has quickly spread to other countries, sickening millions across the globe. To predict the future occurrences of the disease, it is important to develop mathematical models with the fewest errors. In this study, classification and regression tree (CART) models and autoregressive integrated moving averages (ARIMAs) are employed to model and forecast the one-month confirmed COVID-19 cases in Nigeria

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19

Poskitt, D. S., and Shin-Ho Chung. "Markov chain models, time series analysis and extreme value theory." Advances in Applied Probability 28, no. 2 (June 1996): 405–25. http://dx.doi.org/10.2307/1428065.

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Markov chain processes are becoming increasingly popular as a means of modelling various phenomena in different disciplines. For example, a new approach to the investigation of the electrical activity of molecular structures known as ion channels is to analyse raw digitized current recordings using Markov chain models. An outstanding question which arises with the application of such models is how to determine the number of states required for the Markov chain to characterize the observed process. In this paper we derive a realization theorem showing that observations on a finite state Markov

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20

DelSole, Timothy, and Michael K. Tippett. "Comparing climate time series – Part 3: Discriminant analysis." Advances in Statistical Climatology, Meteorology and Oceanography 8, no. 1 (May 16, 2022): 97–115. http://dx.doi.org/10.5194/ascmo-8-97-2022.

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Abstract. In parts I and II of this paper series, rigorous tests for equality of stochastic processes were proposed. These tests provide objective criteria for deciding whether two processes differ, but they provide no information about the nature of those differences. This paper develops a systematic and optimal approach to diagnosing differences between multivariate stochastic processes. Like the tests, the diagnostics are framed in terms of vector autoregressive (VAR) models, which can be viewed as a dynamical system forced by random noise. The tests depend on two statistics, one that measu

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21

Xu, Lu, and Weijie Chen. "Construction and Simulation of Economic Statistics Measurement Model Based on Time Series Analysis and Forecast." Complexity 2021 (June 23, 2021): 1–9. http://dx.doi.org/10.1155/2021/5963516.

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Time series follow the basic principles of mathematical statistics and can provide a set of scientifically based dynamic data processing methods. Using this method, various types of data can be approximated by corresponding mathematical models, and then, the internal structure and complex characteristics of the data can be understood essentially, so as to achieve the purpose of predicting its development trend. This paper mainly studies the combined forecasting model based on the time series model and its application. First, the application prospects and research status of the combined forecas

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22

Robinzonov, Nikolay, Gerhard Tutz, and Torsten Hothorn. "Boosting techniques for nonlinear time series models." AStA Advances in Statistical Analysis 96, no. 1 (June 30, 2011): 99–122. http://dx.doi.org/10.1007/s10182-011-0163-4.

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23

Taniguchi, Masanobu, Kousuke Maeda, and Madan L. Puri. "Statistical analysis of a class of factor time series models." Journal of Statistical Planning and Inference 136, no. 7 (July 2006): 2367–80. http://dx.doi.org/10.1016/j.jspi.2005.08.018.

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24

Liu, Ying, Xiaozhong Li, and Jianbin Li. "Reliability Analysis of Random Fuzzy Unrepairable Systems." Discrete Dynamics in Nature and Society 2014 (2014): 1–15. http://dx.doi.org/10.1155/2014/625985.

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The lifetimes of components in unrepairable systems are considered as random fuzzy variables since randomness and fuzziness are often merged with each other. Then we establish the fundamental mathematical models of random fuzzy unrepairable systems, including series systems, parallel systems, series-parallel systems, parallel-series systems, and cold standby systems with absolutely reliable conversion switches. Furthermore, the expressions of reliability and mean time to failure (MTTF) are given for the above five random fuzzy unrepairable systems, respectively. Finally, numerical examples are

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25

Cho, D. W., K. F. Eman, and S. M. Wu. "A New Time Domain Multiple Input Modal Analysis Method." Journal of Engineering for Industry 109, no. 4 (November 1, 1987): 377–84. http://dx.doi.org/10.1115/1.3187142.

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A time domain approach for multiple input modal analysis of oscillatory systems is proposed. The mathematical foundation for the approach is given along with its applications to a simulated lumped parameter system and the structural dynamics analysis of a milling machine. It has been shown that the proposed multivariate time series models are able to identify the complex mode shapes from multiple input structural test data. The advantages of the proposed method in comparison to existing methods are also highlighted.

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Bratčikovienė, Nomeda. "Adapted SETAR model for lithuanian HCPI time series." Nonlinear Analysis: Modelling and Control 17, no. 1 (January 25, 2012): 27–46. http://dx.doi.org/10.15388/na.17.1.14076.

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We present adapted SETAR (self-exciting threshold autoregressive) model, which enables simultaneous estimation of nonlinearity and unobserved time series components. This model was tested on real Lithuanian harmonised consumer price index (HCPI) time series, covering the period from January 1996 to December 2009. The results show that adapted SETAR model is able to capture features of the real time series with complex nature. ARIMA model has also been used for the same time series for the comparison. Evaluated models and results of the comparison are presented in this work.

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Shaukat, Muhammad Arslan, Haafizah Rameeza Shaukat, Zakria Qadir, Hafiz Suliman Munawar, Abbas Z. Kouzani, and M. A. Parvez Mahmud. "Cluster Analysis and Model Comparison Using Smart Meter Data." Sensors 21, no. 9 (May 2, 2021): 3157. http://dx.doi.org/10.3390/s21093157.

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Load forecasting plays a crucial role in the world of smart grids. It governs many aspects of the smart grid and smart meter, such as demand response, asset management, investment, and future direction. This paper proposes time-series forecasting for short-term load prediction to unveil the load forecast benefits through different statistical and mathematical models, such as artificial neural networks, auto-regression, and ARIMA. It targets the problem of excessive computational load when dealing with time-series data. It also presents a business case that is used to analyze different clusters

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Vasilev, Julian, and Tanka Milkova. "Optimisation Models for Inventory Management with Limited Number of Stock Items." Logistics 6, no. 3 (August 1, 2022): 54. http://dx.doi.org/10.3390/logistics6030054.

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Background: Stocks of raw materials and finished products are found in all units of logistics systems and require significant financial means of management. For this reason, scientifically justified approaches to stock management and cost minimisation must be explored. Despite the existence of many such approaches in literature and practice, each case has its own specificities and specificities to which stock management models should be adapted. In this article, the aim of the authors is to propose an approach to determine optimal supply sizes from different types of stocks (more than one is k

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Livieris, Ioannis E., Emmanuel Pintelas, Stavros Stavroyiannis, and Panagiotis Pintelas. "Ensemble Deep Learning Models for Forecasting Cryptocurrency Time-Series." Algorithms 13, no. 5 (May 10, 2020): 121. http://dx.doi.org/10.3390/a13050121.

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Nowadays, cryptocurrency has infiltrated almost all financial transactions; thus, it is generally recognized as an alternative method for paying and exchanging currency. Cryptocurrency trade constitutes a constantly increasing financial market and a promising type of profitable investment; however, it is characterized by high volatility and strong fluctuations of prices over time. Therefore, the development of an intelligent forecasting model is considered essential for portfolio optimization and decision making. The main contribution of this research is the combination of three of the most wi

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Chan, W. S., S. H. Cheung, L. X. Zhang, and K. H. Wu. "Temporal aggregation of equity return time-series models." Mathematics and Computers in Simulation 78, no. 2-3 (July 2008): 172–80. http://dx.doi.org/10.1016/j.matcom.2008.01.010.

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31

Brockwell, Peter. "Discussion of “Threshold models in time series analysis — 30 years on”." Statistics and Its Interface 4, no. 2 (2011): 129–30. http://dx.doi.org/10.4310/sii.2011.v4.n2.a5.

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32

Tyagi, Swati, Shaifu Gupta, Syed Abbas, Krishna Pada Das, and Baazaoui Riadh. "Analysis of infectious disease transmission and prediction through SEIQR epidemic model." Nonautonomous Dynamical Systems 8, no. 1 (January 1, 2021): 75–86. http://dx.doi.org/10.1515/msds-2020-0126.

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Abstract In literature, various mathematical models have been developed to have a better insight into the transmission dynamics and control the spread of infectious diseases. Aiming to explore more about various aspects of infectious diseases, in this work, we propose conceptual mathematical model through a SEIQR (Susceptible-Exposed-Infected-Quarantined-Recovered) mathematical model and its control measurement. We establish the positivity and boundedness of the solutions. We also compute the basic reproduction number and investigate the stability of equilibria for its epidemiological relevanc

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33

TIMMER, J., M. LAUK, S. HÄUßLER, V. RADT, B. KÖSTER, B. HELLWIG, B. GUSCHLBAUER, C. H. LÜCKING, M. EICHLER, and G. DEUSCHL. "CROSS-SPECTRAL ANALYSIS OF TREMOR TIME SERIES." International Journal of Bifurcation and Chaos 10, no. 11 (November 2000): 2595–610. http://dx.doi.org/10.1142/s0218127400001663.

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We discuss cross-spectral analysis and report applications for the investigation of human tremors. For the physiological tremor in healthy subjects, the analysis enables to determine the resonant contribution to the oscillation and allows to test for a contribution of reflexes to this tremor. Comparing the analysis of the relation between the tremor of both hands in normal subjects and subjects with a rare abnormal organization of certain neural pathways proves the involvement of central structures in enhanced physiological tremor. The relation between the left and the right side of the body i

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34

Лузянина, Т., та T. Luzyanina. "Численный бифуркационный анализ математических моделей с запаздыванием по времени с использованием пакета программ DDE-BIFTOOL". Mathematical Biology and Bioinformatics 12, № 2 (13 грудня 2017): 496–520. http://dx.doi.org/10.17537/2017.12.496.

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Mathematical modeling with delay differential equations (DDEs) is widely used for analysis and making predictions in various areas of the life sciences, e.g., population dynamics, epidemiology, immunology, physiology, neural networks. The time delays in these models take into account a dependence of the present state of the modeled system on its past history. The delay can be related to the duration of certain hidden processes like the stages of the life cycle, the time between infection of a cell and the production of new viruses, the duration of the infectious period, the immune period and s

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35

Dickman, Ronald. "Nonequilibrium lattice models: Series analysis of steady states." Journal of Statistical Physics 55, no. 5-6 (June 1989): 997–1026. http://dx.doi.org/10.1007/bf01041076.

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36

Akhtar, Sohail, Maham Ramzan, Sajid Shah, Iftikhar Ahmad, Muhammad Imran Khan, Sadique Ahmad, Mohammed A. El-Affendi, and Humera Qureshi. "Forecasting Exchange Rate of Pakistan Using Time Series Analysis." Mathematical Problems in Engineering 2022 (August 24, 2022): 1–11. http://dx.doi.org/10.1155/2022/9108580.

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Exchange rates are crucial in regulating the foreign exchange market's dynamics. Because of the unpredictability and volatility of currency rates, the exchange rate prediction has become one of the most challenging applications of financial time series forecasting. This study aims to build and compare the accuracy of various methods. The time series model Auto-Regressive Integrated Moving Average (ARIMA) and Generalized Auto-Regressive Conditional Heteroscedasticity (GARCH) are utilized to forecast the daily US dollar to Pakistan rupee currency exchange rates (USD/PKR). Lagged observations of

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Ozaki, Tohru, and Mitsunori Iino. "An innovation approach to non-Gaussian time series analysis." Journal of Applied Probability 38, A (2001): 78–92. http://dx.doi.org/10.1239/jap/1085496593.

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The paper shows that the use of both types of random noise, white noise and Poisson noise, can be justified when using an innovations approach. The historical background for this is sketched, and then several methods of whitening dependent time series are outlined, including a mixture of Gaussian white noise and a compound Poisson process: this appears as a natural extension of the Gaussian white noise model for the prediction errors of a non-Gaussian time series. A statistical method for the identification of non-linear time series models with noise made up of a mixture of Gaussian white nois

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Недорезов, Л. В., and L. V. Nedorezov. "Analysis of Pine Looper Population Dynamics Using Discrete Time Mathematical Models." Mathematical Biology and Bioinformatics 5, no. 2 (November 30, 2010): 114–23. http://dx.doi.org/10.17537/2010.5.114.

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Aminian, Manuchehr, Helene Andrews-Polymenis, Jyotsana Gupta, Michael Kirby, Henry Kvinge, Xiaofeng Ma, Patrick Rosse, Kristin Scoggin, and David Threadgill. "Mathematical methods for visualization and anomaly detection in telemetry datasets." Interface Focus 10, no. 1 (December 13, 2019): 20190086. http://dx.doi.org/10.1098/rsfs.2019.0086.

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Recent developments in both biological data acquisition and analysis provide new opportunities for data-driven modelling of the health state of an organism. In this paper, we explore the evolution of temperature patterns generated by telemetry data collected from healthy and infected mice. We investigate several techniques to visualize and identify anomalies in temperature time series as temperature relates to the onset of infectious disease. Visualization tools such as Laplacian Eigenmaps and Multidimensional Scaling allow one to gain an understanding of a dataset as a whole. Anomaly detectio

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Chan, W. S., S. H. Cheung, and K. H. Wu. "Multiple forecasts with autoregressive time series models: case studies." Mathematics and Computers in Simulation 64, no. 3-4 (February 2004): 421–30. http://dx.doi.org/10.1016/s0378-4754(03)00108-3.

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Maryati, Iyam, and Dila Nurhayati Fadhilah. "Sequence and Series: An Analysis of Mathematical Problem Solving Ability." IndoMath: Indonesia Mathematics Education 4, no. 2 (August 23, 2021): 95. http://dx.doi.org/10.30738/indomath.v4i2.3.

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<p><em>This study aims to analyze the level of mathematical problem solving abilities of students in one of the high schools in Garut City on the material of sequence and series. The method used in this research is descriptive qualitative research method. The sample in this study was conducted on 5 students in class XI at one of the public high schools in Garut City. The instruments given to the students were 4 questions on the sequence and series material. The conclusion of this study is the mathematical problem solving ability of class XI high school students in Garut City, seen

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Socha, Tomasz, Krzysztof Kula, and Arkadiusz Denisiewicz. "Relaxation of Chipboard Beams – Analysis of Results of Exploratory Research." Civil and Environmental Engineering Reports 28, no. 2 (June 1, 2018): 196–203. http://dx.doi.org/10.2478/ceer-2018-0030.

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Abstract The paper presents results of experimental tests and a theoretical analysis of the phenomenon of relaxation of chipboard beams. Three linearly viscoelastic rheological models were used for mathematical modeling of the rheology of the studied material. The constants of models were determined using experimental tests and the method of least squares. Through analyses of the obtained results it was found that the rheological behavior of the beam in the specified time is best described by a five-parameter model, consisting of standard and Kelvin-Voigt models connected in series. The final

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Cetinkaya, Suleyman, Ali Demir, and Dumitru Baleanu. "Analysis of fractional Fokker-Planck equation with Caputo and Caputo-Fabrizio derivatives." Annals of the University of Craiova - Mathematics and Computer Science Series 48, no. 1 (June 30, 2021): 334–48. http://dx.doi.org/10.52846/ami.v48i1.1473.

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This research focus on the determination of the numerical solution for the mathematical model of Fokker-Planck equations utilizing a new method, in which Sumudu transformation and homotopy analysis method (SHAM) are used together. By SHAM analytical series solution of any mathematical model including fractional derivative can be obtained. By this method, we constructed the solution of fractional Fokker-Planck equations in Caputo and Caputo-Fabrizio senses. The results show that this method is advantageous and applicable to form the series resolution of the fractional mathematical models.

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Мaidaniuk, V. "Analysis of problems of small-angle approximation in mathematical models of projectile flight." Military Technical Collection, no. 27 (November 30, 2022): 19–26. http://dx.doi.org/10.33577/2312-4458.27.2022.19-26.

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The article deals with the topical issue of developing mathematical models of projectile flight, which accurately describe the projectile motion in the air. It is shown that the nature of the mathematical models presentation varies depending on the required reliability degree of the real physical projectile flight process representation by the mathematical model, the adequate consideration of certain forces (moments) acting on the projectile, as well as the level of information about the external flight conditions which include the parameters of the air in which the projectile moves.At the sam

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Fehér, Zsolt Zoltán. "A Spatiotemporal Stochastic Framework Of Groundwater Fluctuation Analysis On The South - Eastern Part Of The Great Hungarian Plain." Journal of Environmental Geography 8, no. 3-4 (December 1, 2015): 41–52. http://dx.doi.org/10.1515/jengeo-2015-0011.

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Abstract The current study was performed on a Hungarian area where the groundwater has been highly affected in the past 40 years by climate change. The stochastic estimation framework of groundwater as a spatiotemporally varying dynamic phenomenon is proposed. The probabilistic estimation of the water depth is performed as a joint realization of spatially correlated hydrographs, where parametric temporal trend models are fitted to the measured time series thereafter regionalized in space. Two types of trend models are evaluated. Due to its simplicity the purely mathematical trend can be used t

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Hu, Yi-Chung, Shu-hen Chiang, and Yu-Jing Chiu. "Applying Grey Relational Analysis to Detect Change Points in Time Series." Journal of Mathematics 2022 (September 30, 2022): 1–10. http://dx.doi.org/10.1155/2022/9242773.

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The goal of detecting change points is to recognize abrupt changes in time series data. This is suitable, for instance, to find events that characterize the financial market or to inspect data streams of stock returns. Regression models categorized as supervised methods have played a significant role in change-point detection. However, since change points might not be available beforehand to train the model, and because the series data might be statistically atypical, the applicability of regression models is limited. To avoid statistical assumptions, this study uses the grey theory, a kind of

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Belas, Oleg, and Andrii Belas. "General methods of forecasting nonlinear nonstationary processes based on mathematical models using statistical data." System research and information technologies, no. 1 (July 11, 2021): 79–86. http://dx.doi.org/10.20535/srit.2308-8893.2021.1.06.

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The article considers the problem of forecasting nonlinear nonstationary processes, presented in the form of time series, which can describe the dynamics of processes in both technical and economic systems. The general technique of analysis of such data and construction of corresponding mathematical models based on autoregressive models and recurrent neural networks is described in detail. The technique is applied on practical examples while performing the comparative analysis of models of forecasting of quantity of channels of service of cellular subscribers for a given station and revealing

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Poghosyan, Arnak, Ashot Harutyunyan, Naira Grigoryan, Clement Pang, George Oganesyan, Sirak Ghazaryan, and Narek Hovhannisyan. "An Enterprise Time Series Forecasting System for Cloud Applications Using Transfer Learning." Sensors 21, no. 5 (February 25, 2021): 1590. http://dx.doi.org/10.3390/s21051590.

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The main purpose of an application performance monitoring/management (APM) software is to ensure the highest availability, efficiency and security of applications. An APM software accomplishes the main goals through automation, measurements, analysis and diagnostics. Gartner specifies the three crucial capabilities of APM softwares. The first is an end-user experience monitoring for revealing the interactions of users with application and infrastructure components. The second is application discovery, diagnostics and tracing. The third key component is machine learning (ML) and artificial inte

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Roberts, S., M. Osborne, M. Ebden, S. Reece, N. Gibson, and S. Aigrain. "Gaussian processes for time-series modelling." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1984 (February 13, 2013): 20110550. http://dx.doi.org/10.1098/rsta.2011.0550.

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In this paper, we offer a gentle introduction to Gaussian processes for time-series data analysis. The conceptual framework of Bayesian modelling for time-series data is discussed and the foundations of Bayesian non-parametric modelling presented for Gaussian processes . We discuss how domain knowledge influences design of the Gaussian process models and provide case examples to highlight the approaches.

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Zaitri, Mohamed A., Cristiana J. Silva, and Delfim F. M. Torres. "Stability Analysis of Delayed COVID-19 Models." Axioms 11, no. 8 (August 13, 2022): 400. http://dx.doi.org/10.3390/axioms11080400.

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We analyze mathematical models for COVID-19 with discrete time delays and vaccination. Sufficient conditions for the local stability of the endemic and disease-free equilibrium points are proved for any positive time delay. The stability results are illustrated through numerical simulations performed in MATLAB.

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