Journal articles: 'Time-series analysis – Mathematical models'

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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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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 may differ only in nomenclature. ARMA-Transfer Function models can be used for systems which are linear or can be linearized such as typical BOD or suspended solids influent-effluent relationships for which the type of model is known. For systems which are highly nonlinear, and/or the input-output model is unknown, neural network models can be used. Both ARMA-TF models and neural network models can be made self-learning, that is, the performance of the model can be periodically improved manually or in an automated mode as new information is collected by monitoring. Application examples are included.

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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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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 time series. Thus, for the stiffness degrading systems and bilinear systems, the metrics of hysteretic energy demand and displacement ductility demand during displacement are used. The applicability of artificially generated acceleration time series for the qualitative description of information was shown. More specifically, ARMA (2,2) showed the best results in the study for three accelerated time series through nonlinear response analysis. In addition, as a result, normalized hysteretic energy demand, empirically valid displacement ductility relationships, and model parameters were proposed.

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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 of silk are also in the theoretic confidence interval, which can also verify the degree of accuracy and precision of the established model.

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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-propagation neural network (BPNN) model, and the data from July to December 2019 was used for validation. Results: A total of 30,083 rubella cases were reported in this study, with a significantly higher average annual incidence before the nationwide introduction of rubella-containing vaccine (RCV). The peak of rubella notification was from April to June annually. Both SARIMA and BPNN models were capable of predicting the expected incidence of rubella. However, the linear SARIMA model fits and predicts better than the nonlinear BPNN model. Conclusions: Based on the results, rubella incidence in Chongqing has an obvious seasonal trend, and SARIMA (2,1,1) × (1,1,1) 12 model can predict the incidence of rubella well. The SARIMA model is a feasible tool for producing reliable rubella forecasts in Chongqing.

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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, you should use the time series, which is influenced by the following factors: • Emerging trends of the series (the trend in cumulative long-term effects of many factors on the dynamics of the phenomenon under study - ascending or descending); • forming a series of cyclical fluctuations related to the seasonality of the disease; • random factors. In our study, we conducted a study to identify cyclical time series of long-term dynamics of morbidity of HFRS and autumn bank vole population. This study was performed using the autocorrelation coefficient. As a result of time-series studies of incidence of HFRS, indicators autumn bank vole population revealed no recurrence, and these figures are random variables, which is confirmed by three tests: nonrepeatability of time series, the assessment increase and decrease time-series analysis of the sum of squares. This shows that a number of indicators of the time series are random variables, contains a strong non-linear trend, to identify which need further analysis, for example by means of regression analysis.

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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 obtained results will help the decision makers to avoid unnecessary risk and correctly make a decision.

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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) model are connected with the ARIMA(p, d, q) orders of the describing each series separately. This step makes the set of the investigated ADL(p, q) models much smaller. In the previous papers it was also shown that the ARIMA(p, d, q) automatical fitting functions in popular packages use limitations on the p, q orders of the time series process: q ≤ 5, p ≤ 5. The wish to use the simplest models is also built in the structure of the Akaike (AIC) and Bayes (BIC) informational criteria. In the paper the maximal values of the ADL(p, q) model orders are supposed to be the orders of the appropriate ARIMA(p, d, q) series. In the previous work it was shown that using high order ARIMA(p, d, q) it is possible to fit the models better. In this paper the experiments on the ADL(p, q) models construction are presented. The wage index and money income index time series pair is researched, and also the gas, water and energy production and consumption index/real agricultural production index pair is investigated. The data in the 2000–2018 time period is taken from the dynamic series of macroeconomic statistics of the Russian Federation.

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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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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 asymptotically strictly stationary if {mt} is a Markov chain satisfying a certain condition on its transition kernel. Also, we find the limit distribution of st for some message processes {mt}. These results show that a joint method of probability theory, linear and non-linear time series analysis can yield fruitful results. They also have significance for FM modulation and demodulation in communications.

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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 } is asymptotically strictly stationary if {m t } is a Markov chain satisfying a certain condition on its transition kernel. Also, we find the limit distribution of st for some message processes {mt }. These results show that a joint method of probability theory, linear and non-linear time series analysis can yield fruitful results. They also have significance for FM modulation and demodulation in communications.

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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, to date, sufficient information has yet to be published for many cases. In addition, experimental observations are expensive. A new mathematical approach that is applicable to small sample data, and that requires no detailed reaction information, is strongly needed. S-system is one such model that can use smaller samples than other ordinary differential equation models. We propose a simplified S-system to apply minimal quantities of samples for a dynamic analysis of the metabolic pathways. We applied the model to the phenyl lactate production pathway of Escherichia coli. The model obtained suggests that actually activated reaction steps and feedback are inhibitions within the pathway.

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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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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 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.

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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, using the data on daily confirmed cases. To validate the predictions, these models were compared through data tests. The test results show that the CART regression model outperformed the ARIMA model in terms of accuracy, leading to a fast growth in the number of confirmed COVID-19 cases. The research findings help governments to make proper decisions on how the prepare for the outbreak. Besides, our analysis reveals the lack of quarantine wards in Nigeria, in addition to the insufficiency of medications, medical staff, lockdown decisions, volunteer training, and economic preparation.

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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 chain embedded in continuous noise can be synthesized as values obtained from an autoregressive moving-average data generating mechanism. We then use this realization result to motivate the construction of a procedure for identifying the state dimension of the hidden Markov chain. The identification technique is based on a new approach to the estimation of the order of an autoregressive moving-average process. Conditions for the method to produce strongly consistent estimates of the state dimension are given. The asymptotic distribution of the statistic underlying the identification process is also presented and shown to yield critical values commensurate with the requirements for strong consistency.

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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 measures dissimilarity in dynamical operators and another that measures dissimilarity in noise covariances. Under suitable assumptions, these statistics are independent and can be tested separately for significance. If a term is significant, then the linear combination of variables that maximizes that term is obtained. The resulting indices contain all relevant information about differences between data sets. These techniques are applied to diagnose how the variability of annual-mean North Atlantic sea surface temperature differs between climate models and observations. For most models, differences in both noise processes and dynamics are important. Over 40 % of the differences in noise statistics can be explained by one or two discriminant components, though these components can be model dependent. Maximizing dissimilarity in dynamical operators identifies situations in which some climate models predict large-scale anomalies with the wrong sign.

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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 forecasting model, the source of time series analysis, and the status of research development at home and abroad are given, and the purpose and significance of the research topic and the research content are summarized. Then, the paper gives the relevant theories about the ARIMA model and the basic principles of model recognition and explains the method of time series smoothing. Finally, the paper uses the ARIMA model to identify and fit the time series data and then the gray forecast model to fit and predict the time series data. Finally, by assigning reasonable weights and combining these methods, a combined forecasting model is proposed and carried out.

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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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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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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 given to show the application in a lighting lamp system and a hi-fi system.

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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 to find underlying factors of load consumption and predict the behavior of customers based on different parameters. On evaluating the accuracy of the prediction models, it is observed that ARIMA models with the (P, D, Q) values as (1, 1, 1) were most accurate compared to other values.

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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 known in the literature as multi-nomenclature) that minimises only the cost of inventory management. The cost of inventory is not included. Methods: The article used the methods of mathematical optimisation, the method of least squares, and regression analysis. The scope of the models in the article is inventory management, with a limited number of stock keeping units. Time series data for the delivered quantities and time series data for the costs of stock management are used. Both time series use the same time period. Results: The constructed specific nonlinear mathematical models for optimising the total cost of stock management are approbated based on sample data and the results obtained are analysed. Conclusions: The created mathematical models and methods for optimising the total cost of stock management may be used by logistics managers to minimise the total costs of inventory management.

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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 widely employed ensemble learning strategies: ensemble-averaging, bagging and stacking with advanced deep learning models for forecasting major cryptocurrency hourly prices. The proposed ensemble models were evaluated utilizing state-of-the-art deep learning models as component learners, which were comprised by combinations of long short-term memory (LSTM), Bi-directional LSTM and convolutional layers. The ensemble models were evaluated on prediction of the cryptocurrency price on the following hour (regression) and also on the prediction if the price on the following hour will increase or decrease with respect to the current price (classification). Additionally, the reliability of each forecasting model and the efficiency of its predictions is evaluated by examining for autocorrelation of the errors. Our detailed experimental analysis indicates that ensemble learning and deep learning can be efficiently beneficial to each other, for developing strong, stable, and reliable forecasting models.

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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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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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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 relevance. To validate the model and estimate the parameters to predict the disease spread, we consider the special case for COVID-19 to study the real cases of infected cases from [2] for Russia and India. For better insight, in addition to mathematical model, a history based LSTM model is trained to learn temporal patterns in COVID-19 time series and predict future trends. In the end, the future predictions from mathematical model and the LSTM based model are compared to generate reliable results.

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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 in pathological tremor shows a specific difference between orthostatic and all other forms of tremor. An investigation of EEG and tremor in patients suffering from Parkinson's disease reveals the tremor-correlated cortical activity. Finally, the general issue of interpreting the results of methods designed for the analysis of bivariate processes when applied to multivariate processes is considered. We discuss and apply partial cross-spectral analysis in the frame of graphical models as an extention of bivariate cross-spectral analysis for the multivariate case.

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Лузянина, Т., and T. Luzyanina. "Численный бифуркационный анализ математических моделей с запаздыванием по времени с использованием пакета программ DDE-BIFTOOL." Mathematical Biology and Bioinformatics 12, no. 2 (December 13, 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 so on. Due to an infinite-dimensional nature of DDEs, analytical studies of the corresponding mathematical models can only give limited results. Therefore, a numerical analysis is the major way to achieve both a qualitative and quantitative understanding of the model dynamics. A bifurcation analysis of a dynamical system is used to understand how solutions and their stability change as the parameters in the system vary. The package DDE-BIFTOOL is the first general-purpose package for bifurcation analysis of DDEs. This package can be used to compute and analyze the local stability of steady-state (equilibria) and periodic solutions of a given system as well as to study the dependence of these solutions on system parameters via continuation. Further one can compute and continue several local and global bifurcations: fold and Hopf bifurcations of steady states; folds, period doublings and torus bifurcations of periodic orbits; and connecting orbits between equilibria. In this paper we describe the structure of DDE-BIFTOOL, numerical methods implemented in the package and we illustrate the use of the package using a certain DDE system.

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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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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 the data series and moving average technical analysis are used in both models. Explanatory factors were used as indicators, and the prediction performance was assessed using a variety of commonly known statistical metrics. These statistical metrics suggested the presence of conditional heteroscedasticity. Thus, the process turns to capture the volatility effect of conditional heteroscedasticity through GARCH modeling. It may be inferred based on the results of tentative models; that the ARCH model outperforms the GARCH model in terms of predicting the USD/PKR exchange rate.

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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 noise and a compound Poisson noise is presented. The method is applied to financial time series data (dollar-yen exchange rate data), and illustrated via six models.

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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 detection tools for nonlinear time series modelling, such as Radial Basis Functions and Multivariate State Estimation Technique, allow one to build models representing a healthy state in individuals. We illustrate these methods on an experimental dataset of 306 Collaborative Cross mice challenged with Salmonella typhimurium and show how interruption in circadian patterns and severity of infection can be revealed directly from these time series within 3 days of the infection event.

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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 from the indicators of identifying sufficient data to solve problems and implementing strategies to solve problems, is quite high, but the indicators of making mathematical models are classified as moderate, and checking the correctness of results and answers still relatively low.</em></p>

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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 verification of the model can only be ensured by conducting long-term experimental studies using a multistage load program.

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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 same time, the use of the shape coefficient - the agreement coefficient in the differential equation system leads to "rough" mathematical models, which does not allow to adequately describe the projectile flight trajectory and its individual elements. The solution to this problem is especially relevant during developing and implementing procedures, technical solutions in the interest of achieving the necessary level of interoperability with NATO forces, the gradual abandonment of the standard functions of air resistance, the transition to individual functions and mathematical models of projectile motion, which are currently accepted in the member states of the Alliance. The conducted analysis of modern mathematical models showed that their construction is based on an approximate approach, which was called the small-angle approximation, in which, for an axisymmetric rotating projectile, it is considered that the nutation angles are sufficiently small, the aerodynamic forces (moments) depend only on the speed of its flight and the nutation angle, and only the linear terms of their Taylor series expansion are used in the calculations. The nutation-precessional behavior of the projectile was considered and the nonlinear dependencies of the coefficients of the aerodynamic forces (moments) of the projectile on the angles of nutation were revealed.

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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 to analyze long-term groundwater trends, the average water fluctuation range and to determine the most probable date of peak groundwater level. The one which takes advantage of the knowledge of expected groundwater changes, clearly over performed the purely mathematical model, and it is selected for the construction of a spatiotemporal trend. Model fitting error values are considered as a set of stochastic time series which expresses short-term anomalies of the groundwater, and they are modelled as joint space-time distribution. The resulting spatiotemporal residual field is added to the trend field, thus resulting 125 simulated realizations, which are evaluated probabilistically. The high number of joint spatiotemporal realizations provides alternative groundwater datasets as boundary conditions for a wide variety of environmental models, while the presented procedure behaves more robust over non-complete datasets.

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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 artificial intelligence tools, to measure the relationships between sequences by grey relational analysis (GRA). This paper contributes to propose an unsupervised method to detect possible change points in time series by GRA. Change-point analysis of the proposed method was performed on S&P100 stock returns. Experimental results from evaluating the recognition accuracy rate show that the proposed method performs well compared to other methods considered for change-point detection.

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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 advantages and disadvantages of each method. The need to improve the existing methodology and develop a new approach is formulated.

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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 intelligence (AI) powered data analytics for predictions, anomaly detection, event correlations and root cause analysis. Time series metrics, logs and traces are the three pillars of observability and the valuable source of information for IT operations. Accurate, scalable and robust time series forecasting and anomaly detection are the requested capabilities of the analytics. Approaches based on neural networks (NN) and deep learning gain an increasing popularity due to their flexibility and ability to tackle complex nonlinear problems. However, some of the disadvantages of NN-based models for distributed cloud applications mitigate expectations and require specific approaches. We demonstrate how NN-models, pretrained on a global time series database, can be applied to customer specific data using transfer learning. In general, NN-models adequately operate only on stationary time series. Application to nonstationary time series requires multilayer data processing including hypothesis testing for data categorization, category specific transformations into stationary data, forecasting and backward transformations. We present the mathematical background of this approach and discuss experimental results based on implementation for Wavefront by VMware (an APM software) while monitoring real customer cloud environments.

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

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