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Journal articles on the topic 'Unstable time series'

Author: Grafiati

Published: 28 May 2022

Last updated: 31 July 2025

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1

Grillenzoni, Carlo. "Forecasting unstable and nonstationary time series." International Journal of Forecasting 14, no. 4 (1998): 469–82. http://dx.doi.org/10.1016/s0169-2070(98)00039-9.

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2

Neamah, Kawther Abood. "Mathematical Model for Handling Unstable Time Series by Using a Linear Approximation Technique." Webology 19, no. 1 (2022): 2835–52. http://dx.doi.org/10.14704/web/v19i1/web19189.

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Time series are typically built on basic assumptions that include stationarity, linearity and normality. The three characteristics are crucial for estimating and building time series models. Studies on time series include these assumptions. To deal with unstable time series that are based on its basis, mathematical models that are suitable for such series are adopted in this study. A nonlinear self-regression model, called the rational model, is proposed. This model is a fraction in which the numerator is the complete sine function and the denominator is an exponential self-regression model. T

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3

Carroll, T. L. "Approximating chaotic time series through unstable periodic orbits." Physical Review E 59, no. 2 (1999): 1615–21. http://dx.doi.org/10.1103/physreve.59.1615.

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4

Dhamala, Mukeshwar, Ying-Cheng Lai, and Eric J. Kostelich. "Detecting unstable periodic orbits from transient chaotic time series." Physical Review E 61, no. 6 (2000): 6485–89. http://dx.doi.org/10.1103/physreve.61.6485.

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5

So, Paul, Edward Ott, Tim Sauer, Bruce J. Gluckman, Celso Grebogi, and Steven J. Schiff. "Extracting unstable periodic orbits from chaotic time series data." Physical Review E 55, no. 5 (1997): 5398–417. http://dx.doi.org/10.1103/physreve.55.5398.

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6

Zoldi, Scott M. "Unstable Periodic Orbit Analysis of Histograms of Chaotic Time Series." Physical Review Letters 81, no. 16 (1998): 3375–78. http://dx.doi.org/10.1103/physrevlett.81.3375.

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7

Chan, Ngai Hang, and Wei Wei Liu. "Residual empirical processes for nearly unstable long-memory time series." Journal of the Korean Statistical Society 39, no. 3 (2010): 337–45. http://dx.doi.org/10.1016/j.jkss.2010.03.001.

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8

Chan, Ngai Hang. "Asymptotic inference for unstable auto- regressive time series with drifts." Journal of Statistical Planning and Inference 23, no. 3 (1989): 301–12. http://dx.doi.org/10.1016/0378-3758(89)90074-8.

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9

Zhuravka, Fedir, Hanna Filatova, Petr Šuleř, and Tomasz Wołowiec. "State debt assessment and forecasting: time series analysis." Investment Management and Financial Innovations 18, no. 1 (2021): 65–75. http://dx.doi.org/10.21511/imfi.18(1).2021.06.

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One of the pressing problems in the modern development of the world financial system is an excessive increase in state debt, which has many negative consequences for the financial system of any country. At the same time, special attention should be paid to developing an effective state debt management system based on its forecast values. The paper is aimed at determining the level of persistence and forecasting future values of state debt in the short term using time series analysis, i.e., an ARIMA model. The study covers the time series of Ukraine’s state debt data for the period from Decembe

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10

Kaplan, D. T. "Time Series and the Dynamics of Demand Pacing." Methods of Information in Medicine 39, no. 02 (2000): 114–17. http://dx.doi.org/10.1055/s-0038-1634284.

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Abstract:Motivated by a common practice in cardiology, we analyze the dynamics of a demand paced system where one seeks to create a stable periodic response. By using techniques originally developed for controlling chaotic systems, one can enhance the information contained in time series regarding hidden, unstable periodic orbits. This makes it possible, for example, to track drifts in a system‘s dynamics.

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11

Gel, Yulia R., and Vladimir N. Fomin. "Identification of an unstable ARMA equation." Mathematical Problems in Engineering 7, no. 1 (2001): 97–112. http://dx.doi.org/10.1155/s1024123x01001557.

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Usually the coefficients in a stochastic time series model are partially or entirely unknown when the realization of the time series is observed. Sometimes the unknown coefficients can be estimated from the realization with the required accuracy. That will eventually allow optimizing the data handling of the stochastic time series.Here it is shown that the recurrent least-squares (LS) procedure provides strongly consistent estimates for a linear autoregressive (AR) equation of infinite order obtained from a minimal phase regressive (ARMA) equation. The LS identification algorithm is accomplish

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12

Lai, Ying-Cheng, and Nong Ye. "Recent Developments in Chaotic Time Series Analysis." International Journal of Bifurcation and Chaos 13, no. 06 (2003): 1383–422. http://dx.doi.org/10.1142/s0218127403007308.

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In this paper, two issues are addressed: (1) the applicability of the delay-coordinate embedding method to transient chaotic time series analysis, and (2) the Hilbert transform methodology for chaotic signal processing.A common practice in chaotic time series analysis has been to reconstruct the phase space by utilizing the delay-coordinate embedding technique, and then to compute dynamical invariant quantities of interest such as unstable periodic orbits, the fractal dimension of the underlying chaotic set, and its Lyapunov spectrum. As a large body of literature exists on applying the techni

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13

MAEHARA, Takaaki, Kenji ITO, and Mikio NAKAI. "Topological Procedures for Finding Unstable Fixed Points from Time Series Data." Transactions of the Japan Society of Mechanical Engineers Series C 70, no. 693 (2004): 1277–84. http://dx.doi.org/10.1299/kikaic.70.1277.

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14

MÜLLER, ULRICH K., and PHILIPPE-EMMANUEL PETALAS. "Efficient Estimation of the Parameter Path in Unstable Time Series Models." Review of Economic Studies 77, no. 4 (2010): 1508–39. http://dx.doi.org/10.1111/j.1467-937x.2010.00603.x.

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15

Schwartz, Ira B., and Ioana Triandaf. "Controlling unstable states in reaction-diffusion systems modeled by time series." Physical Review E 50, no. 4 (1994): 2548–52. http://dx.doi.org/10.1103/physreve.50.2548.

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16

YAGASAKI, KAZUYUKI, and MASATOSHI KOUYAMA. "EXCLUSION OF FALSE PERIODIC ORBITS DETECTED FROM CHAOTIC TIME SERIES." International Journal of Bifurcation and Chaos 15, no. 02 (2005): 659–65. http://dx.doi.org/10.1142/s0218127405012272.

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Some techniques based on delay coordinates embedding for detecting unstable periodic orbits from chaotic time series work successfully in several applications but frequently yield false periodic orbits. We present a simple method for excluding false ones from candidates of periodic orbits obtained from chaotic time series. We demonstrate our method in numerical simulations for the Ikeda map and experiments for periodically forced, single and coupled pendula.

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17

Wu, Yuhan. "Financial and Economic Sequence Forecasting Based on Time Slot Allocation Algorithm." Security and Communication Networks 2022 (May 16, 2022): 1–13. http://dx.doi.org/10.1155/2022/2340521.

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Financial and economic series prediction was very important for the study of economic time series. Because the traditional time series analysis method was mainly suitable for stable data and cannot be applied to unstable economic variables, this paper proposed a knowledge model of financial and economic series prediction time slot algorithm, which provided the basis for solving unstable financial data. Firstly, based on the analysis of relevant financial and economic series prediction methods at home and abroad, this paper applied the time slot allocation algorithm to economic series analysis

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18

Rajilić, Zoran, Dragana Malivuk Gak, and Enes Škrgić. "Unstable oscillation of a particle described by digits of pi." Journal of Physics: Conference Series 2930, no. 1 (2024): 012003. https://doi.org/10.1088/1742-6596/2930/1/012003.

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Abstract We ćonsider 3, 1, 4, 1, 5, 9, … as a time series desćribing osćillation of a partićle. The level of instability is defined using two of ten forće parameters assigned to the time series. Irrationality of the number p ćan then be seen through instability of motion, using Newton’s sećond law. If we intervene in digits, making a rational number, with termination or a repeating sequenće, level of instability slumps to zero. New rules for digits of p are found out. High instability is ćonnećted with strong damping and driving forćes. Tendenćy to a moderate instability is observed. Unrealise

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19

Petrov, Valery, Eugene Mihaliuk, Stephen K. Scott, and Kenneth Showalter. "Stabilizing and characterizing unstable states in high-dimensional systems from time series." Physical Review E 51, no. 5 (1995): 3988–96. http://dx.doi.org/10.1103/physreve.51.3988.

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20

Bhaskaran, Anil, and A. Seshagiri Rao. "Predictive control of unstable time delay series cascade processes with measurement noise." ISA Transactions 99 (April 2020): 403–16. http://dx.doi.org/10.1016/j.isatra.2019.08.065.

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21

Youns, Anas S., and Salim M. Ahmad. "Stability Conditions for a Nonlinear Time Series Model." International Journal of Mathematics and Mathematical Sciences 2023 (May 8, 2023): 1–10. http://dx.doi.org/10.1155/2023/5575771.

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This research aims to determine whether the proposed time series model is stable or not. To achieve this, Ozaki’s approximation method was utilized, where the nonlinear part is a function that approaches zero, similar to Ozaki’s imposed function. The study produced examples of both stable and unstable models, and it was discovered that the stability and instability of the model are affected by the enforced optional constants. The researchers used the approximation method to obtain an asymptotic linear model that satisfied the singular point of the proposed model. The study first identified the

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Jalil, Andrés M., Cristian A. Ferreyra, Mauricio Balla, Fabián J. Castellán, and Pablo S. Mancini. "Unstable osteoarthritis genu varum. Our experience." Orthopaedic Journal of Sports Medicine 5, no. 1_suppl (2017): 2325967117S0000. http://dx.doi.org/10.1177/2325967117s00003.

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Background: The natural evolution of chronic anterior cruciate ligament (ACL) failure is the progressive deterioration of articular cartilage of the knee, which consequences are the arthrosis and the secondary misalignment. This is an increasingly common in middle-aged patients (30-50 years). Also, these patients are demanding reinstatement expectation of sporting activity, claiming that refund promptly and at the same level prior to the injury. Objectives: Communicate the experience in our service, of treatment implement in young adults patients with misalignment., osteoarthritis and instabil

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23

Zhou, Hao, Keren Dai, Xiaochuan Tang, et al. "Time-Series InSAR with Deep-Learning-Based Topography-Dependent Atmospheric Delay Correction for Potential Landslide Detection." Remote Sensing 15, no. 22 (2023): 5287. http://dx.doi.org/10.3390/rs15225287.

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Synthetic aperture radar interferometry (InSAR) has emerged as an effective technique for monitoring potentially unstable landslides and has found widespread application. Nevertheless, in mountainous reservoir regions, the precision of time-series InSAR outcomes is often constrained by topography-dependent atmospheric delay (TDAD) effects. To address this limitation, we propose a novel InSAR time-series method that integrates TDAD correction. This approach employs advanced deep learning algorithms to individually model and mitigate TDAD for each interferogram, thereby enhancing the accuracy of

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24

Qin, Rui, and Yong Wang. "ImputeGAN: Generative Adversarial Network for Multivariate Time Series Imputation." Entropy 25, no. 1 (2023): 137. http://dx.doi.org/10.3390/e25010137.

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Since missing values in multivariate time series data are inevitable, many researchers have come up with methods to deal with the missing data. These include case deletion methods, statistics-based imputation methods, and machine learning-based imputation methods. However, these methods cannot handle temporal information, or the complementation results are unstable. We propose a model based on generative adversarial networks (GANs) and an iterative strategy based on the gradient of the complementary results to solve these problems. This ensures the generalizability of the model and the reasona

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25

Wang, Zhihua, Yongbo Zhang, and Huimin Fu. "Autoregressive Prediction with Rolling Mechanism for Time Series Forecasting with Small Sample Size." Mathematical Problems in Engineering 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/572173.

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Reasonable prediction makes significant practical sense to stochastic and unstable time series analysis with small or limited sample size. Motivated by the rolling idea in grey theory and the practical relevance of very short-term forecasting or 1-step-ahead prediction, a novel autoregressive (AR) prediction approach with rolling mechanism is proposed. In the modeling procedure, a new developed AR equation, which can be used to model nonstationary time series, is constructed in each prediction step. Meanwhile, the data window, for the next step ahead forecasting, rolls on by adding the most re

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26

Yamamoto, Keiichi, Masahiko Sakaguchi, Akira Onishi, et al. "Energy landscape analysis and time-series clustering analysis of patient state multistability related to rheumatoid arthritis drug treatment: The KURAMA cohort study." PLOS ONE 19, no. 5 (2024): e0302308. http://dx.doi.org/10.1371/journal.pone.0302308.

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Rheumatoid arthritis causes joint inflammation due to immune abnormalities, resulting in joint pain and swelling. In recent years, there have been considerable advancements in the treatment of this disease. However, only approximately 60% of patients achieve remission. Patients with multifactorial diseases shift between states from day to day. Patients may remain in a good or poor state with few or no transitions, or they may switch between states frequently. The visualization of time-dependent state transitions, based on the evaluation axis of stable/unstable states, may provide useful inform

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27

Bobrov, Konstantin, та Aleksandr Iskoldsky. "Stability оf numerical estimations of time series characteristics". Izvestiya VUZ. Applied Nonlinear Dynamics 10, № 1-2 (2002): 127–36. http://dx.doi.org/10.18500/0869-6632-2002-10-1-127-136.

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The numerical methods of a data analysis (finite ordered sequences of natural binary codes), corresponding to fragments оf trajectories, obtained by the numerical solving of а finite number of nonlinear ordinary differential equations are discussed. These equations represent the determined dissipative chaotic dynamic systems. Measuring properties of such sequences are characterized by the estimation which assumes the code, obtained as a result of processing of source sequence of data by given algorithm, realized on the computer and not supposing the participation of the expert. The concept оf

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28

Ivan, Cosmin, and Mihai Catalin Arva. "Nonlinear Time Series Analysis in Unstable Periodic Orbits Identification-Control Methods of Nonlinear Systems." Electronics 11, no. 6 (2022): 947. http://dx.doi.org/10.3390/electronics11060947.

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The main purpose of this paper is to present a solution to the well-known problems generated by classical control methods through the analysis of nonlinear time series. Among the problems analyzed, for which an explanation has been sought for a long time, we list the significant reduction in control power and the identification of unstable periodic orbits (UPOs) in chaotic time series. To accurately identify the type of behavior of complex systems, a new solution is presented that involves a method of two-dimensional representation specific to the graphical point of view, and in particular the

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29

Zhang, Hu-Ming. "A log log law for unstable ARMA models with applications to time series analysis." Journal of Multivariate Analysis 40, no. 2 (1992): 173–204. http://dx.doi.org/10.1016/0047-259x(92)90021-7.

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30

Liu, L., F. Hu, and X. L. Cheng. "Extreme fluctuations of vertical velocity in the unstable atmospheric surface layer." Nonlinear Processes in Geophysics 21, no. 2 (2014): 463–75. http://dx.doi.org/10.5194/npg-21-463-2014.

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Abstract. In this paper, we propose a new method to extract the extreme fluctuations of vertical velocity in the unstable atmospheric surface layer. Unlike the commonly used conditional sampling analysis, this method defines a threshold by using a systematical method and tries to reduce the artificiality in this process. It defines threshold as the position where the types of probability density functions (PDFs) of vertical velocity fluctuations begin to change character from stable distributions to truncated stable distributions. Absolute values of fluctuations greater than the threshold are

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31

Tarasova, S. A. "Information Value Factor in Adaptive Time Series Forecasting." Informacionnye Tehnologii 28, no. 4 (2022): 219–24. http://dx.doi.org/10.17587/it.28.219-224.

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The article considers the task of forecasting time series with unstable dynamics. Adaptive forecasting methods are usually used to solve such tasks, but there is a problem of using adaptive forecasting methods, which consists of choosing an adequate adaptation parameter, in science. The purpose of the study is to construct and test an adaptive forecasting model, in which the adaptation parameter is calculated based on the information value. The discount factor is calculated as the ratio of the measure of the information value in the current period to the measure of the information value in the

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Van Vliet, David, and Marcos Mortensen Steagall. "Time and postphotography." Revista 2i: Estudos de Identidade e Intermedialidade 3, no. 4 (2021): 49–60. http://dx.doi.org/10.21814/2i.3434.

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This article presents a practice-led research project that asks how experienced time can be perceived through manipulated photographic images. The investigation is carried out by a series of digital images whose content is renegotiated over time, while the subject of the photograph remains within the frame. The artwork evidences an unstable space between a photographic composition and a moving image employed to question the power conventions in visualization and to expand the way we can conceive of time as duration in digital photographic images. It contributes to the discourse about practice-

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Musaev, Alexander A., and Maksim A. Kolosov. "CHANGE POINT DETECTION IN NON-STATIONARY TIME SERIES: REVIEW AND CRITICAL ANALYSIS." Bulletin of the Saint Petersburg State Institute of Technology (Technical University) 70 (2024): 75–87. http://dx.doi.org/10.36807/1998-9849-2024-70-96-75-87.

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A critical analysis of modern mathematical technologies used to solve the problem of nonstationary time series change point, taking into account the chaotic nature of the observed processes, is considered. The known methods of the quickest change point detection in nonstationary time series described by traditional models of random processes are considered as initial assumptions. The discrepancy between the known time series observation models and the real processes occurring in unstable immersion environments described by the concept of stochastic chaos is shown. Time series segmentation tech

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Zhang, Jian-Zhi, and Xiao-Ping Zhou. "AE event rate characteristics of flawed granite: from damage stress to ultimate failure." Geophysical Journal International 222, no. 2 (2020): 795–814. http://dx.doi.org/10.1093/gji/ggaa207.

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SUMMARY Uniaxial compression tests with combined acousto-optical monitoring techniques are conducted on flawed granite specimens, with the aim of investigating the fracture-related acoustic emission (AE) event rate characteristics at the unstable cracking phase in flawed rocks. The interevent time (IET) function F(τ) is adopted to interpret the AE time-series from damage stress (σcd) to ultimate failure, and photographic data are used to evaluate unstable cracking behaviours in flawed granite. The results show that a high AE event rate is always registered but intermittently interrupted by mac

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35

Bonsall, M. B., S. M. A. Wallace-Hadrill, J. R. Geddes, G. M. Goodwin, and E. A. Holmes. "Nonlinear time-series approaches in characterizing mood stability and mood instability in bipolar disorder." Proceedings of the Royal Society B: Biological Sciences 279, no. 1730 (2011): 916–24. http://dx.doi.org/10.1098/rspb.2011.1246.

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Bipolar disorder is a psychiatric condition characterized by episodes of elevated mood interspersed with episodes of depression. While treatment developments and understanding the disruptive nature of this illness have focused on these episodes, it is also evident that some patients may have chronic week-to-week mood instability. This is also a major morbidity. The longitudinal pattern of this mood instability is poorly understood as it has, until recently, been difficult to quantify. We propose that understanding this mood variability is critical for the development of cognitive neuroscience-

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36

Van de Wouw, N., G. Verbeek, and D. H. Van Campen. "Nonlinear Parametric Identification Using Chaotic Data." Journal of Vibration and Control 1, no. 3 (1995): 291–305. http://dx.doi.org/10.1177/107754639500100303.

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The subject of this paper is the development of a nonlinear parametric identification method using chaotic data. In former research, the main problem in using chaotic data in parameter estimation appeared to be the numerical computation of the chaotic trajectories. This computational problem is due to the highly unstable character of the chaotic orbits. The method proposed in this paper is based on assumed physical models and has two important components. First, the chaotic time series is characterized by a "skeleton" of unstable periodic orbits. Second, these unstable periodic orbits are used

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Sun, Yao Jie, Li Qing Tong, and Yan Dan Lin. "Stability Analysis of the Series-In Series Hybrid Active Power Filter." Applied Mechanics and Materials 58-60 (June 2011): 601–7. http://dx.doi.org/10.4028/www.scientific.net/amm.58-60.601.

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For the important characteristic of the system stability, a state-space averaging model of the series-in series hybrid active power filter (SHAPF) is constructed to analyze its system stability by traditional control strategy taking into account the effect of the time delay in the digital control system, inverter, low pass filter and second-order carrier-wave filter. Based on the analysis of the close-loop control model, the traditional control strategy of the series-in SHAPF is an unstable system. A new control strategy is proposed to reduce the impact of the high frequency current interferen

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Zhang, Xiuxian, Hongwei Zhao, Weishan Zhang, Shaohua Cao, Haoyun Sun, and Baoyu Zhang. "FedSW-TSAD: SWGAN-Based Federated Time Series Anomaly Detection." Sensors 25, no. 13 (2025): 4014. https://doi.org/10.3390/s25134014.

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As distributed sensing technologies evolve, the collection of time series data is becoming increasingly decentralized, which introduces serious challenges for both model training and data privacy protection. In response to this trend, federated time series anomaly detection enables collaborative analysis across distributed sensing nodes without exposing raw data. However, federated anomaly detection experiences issues with unstable training and poor generalization due to client heterogeneity and the limited expressiveness of single-path detection methods. To address these challenges, this stud

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Morales, Raffaello, T. Di Matteo, Ruggero Gramatica, and Tomaso Aste. "Dynamical generalized Hurst exponent as a tool to monitor unstable periods in financial time series." Physica A: Statistical Mechanics and its Applications 391, no. 11 (2012): 3180–89. http://dx.doi.org/10.1016/j.physa.2012.01.004.

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Avalos, Lyndsay A., G. Thomas Ray, Stacey E. Alexeeff, et al. "Association of the COVID-19 Pandemic With Unstable and/or Unsafe Living Situations and Intimate Partner Violence Among Pregnant Individuals." JAMA Network Open 6, no. 2 (2023): e230172. http://dx.doi.org/10.1001/jamanetworkopen.2023.0172.

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ImportanceThe social, behavioral, and economic consequences of the COVID-19 pandemic may be associated with unstable and/or unsafe living situations and intimate partner violence (IPV) among pregnant individuals.ObjectiveTo investigate trends in unstable and/or unsafe living situations and IPV among pregnant individuals prior to and during the COVID-19 pandemic.Design, Setting, and ParticipantsA cross-sectional population-based interrupted time-series analysis was conducted among Kaiser Permanente Northern California members who were pregnant and screened for unstable and/or unsafe living situ

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Hayder, Lanja Assi, and Journal of International University of Erbil Academic. "Time Series Models to Forecast Barley Crop Production in The Kurdistan Region of Iraq." Academic Journal of International University of Erbil 02, no. 02 (2025): 186–201. https://doi.org/10.5281/zenodo.15306452.

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Time series are important methods in analyzing phenomena and events during specific time periods and predicting future values that contribute to giving an estimated picture of the phenomenon. Therefore, the study aimed to use the Box Jenkins methodology to forecasting barley production in the Kurdistan Region of Iraq for the period (2024-2030) based on the time series of barley production in Kurdistan for the period (1981-2023). It was found through studying the time series of barley production quantities for the period (1981-2023) that the time series is unstable in the mean and variance; aft

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42

Zhu, Qunxi, Xin Li, and Wei Lin. "Leveraging neural differential equations and adaptive delayed feedback to detect unstable periodic orbits based on irregularly sampled time series." Chaos: An Interdisciplinary Journal of Nonlinear Science 33, no. 3 (2023): 031101. http://dx.doi.org/10.1063/5.0143839.

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Detecting unstable periodic orbits (UPOs) based solely on time series is an essential data-driven problem, attracting a great deal of attention and arousing numerous efforts, in nonlinear sciences. Previous efforts and their developed algorithms, though falling into a category of model-free methodology, dealt with the time series mostly with a regular sampling rate. Here, we develop a data-driven and model-free framework for detecting UPOs in chaotic systems using the irregularly sampled time series. This framework articulates the neural differential equations (NDEs), a recently developed and

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Liu, Banteng, Wei Chen, Meng Han, et al. "Nonlinear time series prediction algorithm based on AD-SSNET for artificial intelligence–powered Internet of Things." International Journal of Distributed Sensor Networks 17, no. 3 (2021): 155014772110041. http://dx.doi.org/10.1177/15501477211004112.

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Time series have broad usage in the wireless Internet of Things. This article proposes a nonlinear time series prediction algorithm based on the Small-World Scale-Free Network after the AIC-Optimized Subtractive Clustering Algorithm (AIC-DSCA-SSNET, AD-SSNET) to predict the nonlinear and unstable time series, which improves the prediction accuracy. The AD-SSNET is introduced as a reservoir based on the echo state network to improve the predictive capability of nonlinear time series, and combined with artificial intelligence method to construct the prediction model training samples. First, the

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Kumar, Ajay. "A Review of Time Series forecasting Techniques: Predicting Solar energy using AI and Statistics Techniques." International Scientific Journal of Engineering and Management 03, no. 05 (2024): 1–9. http://dx.doi.org/10.55041/isjem01832.

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The overuse of fossil fuels and their detrimental effects on the environment must be considered in the current electrical energy crisis scenario. This promotes sustainable development by encouraging the use of renewable resources. The overall capacity of the energy systems was enhanced by adding such unpredictable renewable energy sources; however, the design of these hybrid systems is extremely important, which is why many academics have come to trust this area. Normally, in order to advance sustainable growth in the current electrical market, renewable resources like solar energy have been i

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Lv, Pin, Qinjuan Wu, Jia Xu, and Yating Shu. "Stock Index Prediction Based on Time Series Decomposition and Hybrid Model." Entropy 24, no. 2 (2022): 146. http://dx.doi.org/10.3390/e24020146.

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The stock index is an important indicator to measure stock market fluctuation, with a guiding role for investors’ decision-making, thus being the object of much research. However, the stock market is affected by uncertainty and volatility, making accurate prediction a challenging task. We propose a new stock index forecasting model based on time series decomposition and a hybrid model. Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) decomposes the stock index into a series of Intrinsic Mode Functions (IMFs) with different feature scales and trend term. The Augmente

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Jiang, Meihui, Xiangyun Gao, Haizhong An, Xiaoliang Jia, and Xiaoqi Sun. "Multiscale Fluctuation Features of the Dynamic Correlation between Bivariate Time Series." Mathematical Problems in Engineering 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/4742060.

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The fluctuation of the dynamic correlation between bivariate time series has some special features on the time-frequency domain. In order to study these fluctuation features, this paper built the dynamic correlation network models using two kinds of time series as sample data. After studying the dynamic correlation networks at different time-scales, we found that the correlation between time series is a dynamic process. The correlation is strong and stable in the long term, but it is weak and unstable in the short and medium term. There are key correlation modes which can effectively indicate

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Chancellor, R. S., R. M. Alexander, and S. T. Noah. "Detecting Parameter Changes Using Experimental Nonlinear Dynamics and Chaos." Journal of Vibration and Acoustics 118, no. 3 (1996): 375–83. http://dx.doi.org/10.1115/1.2888193.

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A method of detecting parameter changes using analytical and experimental nonlinear dynamics and chaos is applied to a piecewise-linear oscillator. Experimental data show the chaotic nature of the system through phase portraits, Poincare´ maps, frequency spectra and bifurcation diagrams. Unstable periodic orbits were extracted from each chaotic time series obtained from the system with six different parameter values. Movement of the unstable periodic orbits in phase space is used to detect parameter changes in the system.

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LEFRANC, MARC, and PIERRE GLORIEUX. "TOPOLOGICAL ANALYSIS OF CHAOTIC SIGNALS FROM A CO2 LASER WITH MODULATED LOSSES." International Journal of Bifurcation and Chaos 03, no. 03 (1993): 643–50. http://dx.doi.org/10.1142/s0218127493000544.

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Unstable periodic orbits have been extracted from chaotic time series coming from a CO 2 laser with modulated losses. Topological analysis of their organization reveals that chaos in this laser occurs through the formation of a Smale’s horseshoe.

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Stacer, R. G., and F. N. Kelley. "Criteria for Unstable Tearing of Elastomers." Rubber Chemistry and Technology 58, no. 5 (1985): 924–38. http://dx.doi.org/10.5254/1.3536104.

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Abstract 1. Unstable, or stick-slip, tearing has been evaluated in a series of unfilled elastomers. It was found that unstable tearing in these materials occurs only in well defined regions of temperature and rate. The behavior of the material in these regions follows a definite time-dependent pattern, suggesting the existence of simple time-temperature correspondence. This has been demonstrated by showing that the same shift factors that superpose other viscoelastic functions also describe the time-dependent nature of unstable tearing. Previous work showed that the magnitude of unstable teari

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Sugiura, Nozomi, Shuhei Masuda, Yosuke Fujii, Masafumi Kamachi, Yoichi Ishikawa, and Toshiyuki Awaji. "A Framework for Interpreting Regularized State Estimation." Monthly Weather Review 142, no. 1 (2014): 386–400. http://dx.doi.org/10.1175/mwr-d-12-00231.1.

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Abstract Four-dimensional variational data assimilation (4D-Var) on a seasonal-to-interdecadal time scale under the existence of unstable modes can be viewed as an optimization problem of synchronized, coupled chaotic systems. The problem is tackled by adjusting initial conditions to bring all stable modes closer to observations and by using a continuous guide to direct unstable modes toward a reference time series. This interpretation provides a consistent and effective procedure for solving problems of long-term state estimation. By applying this approach to an ocean general circulation mode

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