Academic literature on the topic 'Nonlinear time series models'

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Journal articles on the topic "Nonlinear time series models"

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Andel, Jiri. "On nonlinear models for time series." Statistics 20, no. 4 (January 1989): 615–32. http://dx.doi.org/10.1080/02331888908802217.

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Mills, Terence C. "NONLINEAR TIME SERIES MODELS IN ECONOMICS." Journal of Economic Surveys 5, no. 3 (September 1991): 215–42. http://dx.doi.org/10.1111/j.1467-6419.1991.tb00133.x.

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Hollkamp, Joseph J., and Stephen M. Batill. "Time‐Series Models for Nonlinear Systems." Journal of Aerospace Engineering 3, no. 4 (October 1990): 271–84. http://dx.doi.org/10.1061/(asce)0893-1321(1990)3:4(271).

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Tjøstheim, Dag. "Estimation in nonlinear time series models." Stochastic Processes and their Applications 21, no. 2 (February 1986): 251–73. http://dx.doi.org/10.1016/0304-4149(86)90099-2.

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Ngatchou-Wandji, Joseph. "Checking nonlinear heteroscedastic time series models." Journal of Statistical Planning and Inference 133, no. 1 (July 2005): 33–68. http://dx.doi.org/10.1016/j.jspi.2004.03.013.

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Harvey, Andrew C. "Score-Driven Time Series Models." Annual Review of Statistics and Its Application 9, no. 1 (March 7, 2022): 321–42. http://dx.doi.org/10.1146/annurev-statistics-040120-021023.

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The construction of score-driven filters for nonlinear time series models is described, and they are shown to apply over a wide range of disciplines. Their theoretical and practical advantages over other methods are highlighted. Topics covered include robust time series modeling, conditional heteroscedasticity, count data, dynamic correlation and association, censoring, circular data, and switching regimes.
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Hagemann, Andreas. "Stochastic equicontinuity in nonlinear time series models." Econometrics Journal 17, no. 1 (January 21, 2014): 188–96. http://dx.doi.org/10.1111/ectj.12013.

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Öcal, Nadir. "Nonlinear Models for U.K. Macroeconomic Time Series." Studies in Nonlinear Dynamics and Econometrics 4, no. 3 (September 1, 2000): 123–35. http://dx.doi.org/10.1162/108118200750387982.

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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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Judd, Kevin, and Alistair Mees. "On selecting models for nonlinear time series." Physica D: Nonlinear Phenomena 82, no. 4 (May 1995): 426–44. http://dx.doi.org/10.1016/0167-2789(95)00050-e.

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Dissertations / Theses on the topic "Nonlinear time series models"

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Dupré, la Tour Tom. "Nonlinear models for neurophysiological time series." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLT018/document.

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Dans les séries temporelles neurophysiologiques, on observe de fortes oscillations neuronales, et les outils d'analyse sont donc naturellement centrés sur le filtrage à bande étroite.Puisque cette approche est trop réductrice, nous proposons de nouvelles méthodes pour représenter ces signaux.Nous centrons tout d'abord notre étude sur le couplage phase-amplitude (PAC), dans lequel une bande haute fréquence est modulée en amplitude par la phase d'une oscillation neuronale plus lente.Nous proposons de capturer ce couplage dans un modèle probabiliste appelé modèle autoregressif piloté (DAR). Cette modélisation permet une sélection de modèle efficace grâce à la mesure de vraisemblance, ce qui constitue un apport majeur à l'estimation du PAC.%Nous présentons différentes paramétrisations des modèles DAR et leurs algorithmes d'inférence rapides, et discutons de leur stabilité.Puis nous montrons comment utiliser les modèles DAR pour l'analyse du PAC, et démontrons l'avantage de l'approche par modélisation avec trois jeux de donnée.Puis nous explorons plusieurs extensions à ces modèles, pour estimer le signal pilote à partir des données, le PAC sur des signaux multivariés, ou encore des champs réceptifs spectro-temporels.Enfin, nous proposons aussi d'adapter les modèles de codage parcimonieux convolutionnels pour les séries temporelles neurophysiologiques, en les étendant à des distributions à queues lourdes et à des décompositions multivariées. Nous développons des algorithmes d'inférence efficaces pour chaque formulations, et montrons que l'on obtient de riches représentations de façon non-supervisée
In neurophysiological time series, strong neural oscillations are observed in the mammalian brain, and the natural processing tools are thus centered on narrow-band linear filtering.As this approach is too reductive, we propose new methods to represent these signals.We first focus on the study of phase-amplitude coupling (PAC), which consists in an amplitude modulation of a high frequency band, time-locked with a specific phase of a slow neural oscillation.We propose to use driven autoregressive models (DAR), to capture PAC in a probabilistic model. Giving a proper model to the signal enables model selection by using the likelihood of the model, which constitutes a major improvement in PAC estimation.%We first present different parametrization of DAR models, with fast inference algorithms and stability discussions.Then, we present how to use DAR models for PAC analysis, demonstrating the advantage of the model-based approach on three empirical datasets.Then, we explore different extensions to DAR models, estimating the driving signal from the data, PAC in multivariate signals, or spectro-temporal receptive fields.Finally, we also propose to adapt convolutional sparse coding (CSC) models for neurophysiological time-series, extending them to heavy-tail noise distribution and multivariate decompositions. We develop efficient inference algorithms for each formulation, and show that we obtain rich unsupervised signal representations
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Li, Dao. "Common Features in Vector Nonlinear Time Series Models." Doctoral thesis, Högskolan Dalarna, Statistik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:du-13253.

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This thesis consists of four manuscripts in the area of nonlinear time series econometrics on topics of testing, modeling and forecasting nonlinear common features. The aim of this thesis is to develop new econometric contributions for hypothesis testing and forecasting in these area. Both stationary and nonstationary time series are concerned. A definition of common features is proposed in an appropriate way to each class. Based on the definition, a vector nonlinear time series model with common features is set up for testing for common features. The proposed models are available for forecasting as well after being well specified. The first paper addresses a testing procedure on nonstationary time series. A class of nonlinear cointegration, smooth-transition (ST) cointegration, is examined. The ST cointegration nests the previously developed linear and threshold cointegration. An Ftypetest for examining the ST cointegration is derived when stationary transition variables are imposed rather than nonstationary variables. Later ones drive the test standard, while the former ones make the test nonstandard. This has important implications for empirical work. It is crucial to distinguish between the cases with stationary and nonstationary transition variables so that the correct test can be used. The second and the fourth papers develop testing approaches for stationary time series. In particular, the vector ST autoregressive (VSTAR) model is extended to allow for common nonlinear features (CNFs). These two papers propose a modeling procedure and derive tests for the presence of CNFs. Including model specification using the testing contributions above, the third paper considers forecasting with vector nonlinear time series models and extends the procedures available for univariate nonlinear models. The VSTAR model with CNFs and the ST cointegration model in the previous papers are exemplified in detail,and thereafter illustrated within two corresponding macroeconomic data sets.
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黃鎮山 and Chun-shan Wong. "Statistical inference for some nonlinear time series models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1998. http://hub.hku.hk/bib/B31239444.

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Wong, Chun-shan. "Statistical inference for some nonlinear time series models /." Hong Kong : University of Hong Kong, 1998. http://sunzi.lib.hku.hk/hkuto/record.jsp?B20715316.

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Sando, Simon Andrew. "Estimation of a class of nonlinear time series models." Thesis, Queensland University of Technology, 2004. https://eprints.qut.edu.au/15985/1/Simon_Sando_Thesis.pdf.

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The estimation and analysis of signals that have polynomial phase and constant or time-varying amplitudes with the addititve noise is considered in this dissertation.Much work has been undertaken on this problem over the last decade or so, and there are a number of estimation schemes available. The fundamental problem when trying to estimate the parameters of these type of signals is the nonlinear characterstics of the signal, which lead to computationally difficulties when applying standard techniques such as maximum likelihood and least squares. When considering only the phase data, we also encounter the well known problem of the unobservability of the true noise phase curve. The methods that are currently most popular involve differencing in phase followed by regression, or nonlinear transformations. Although these methods perform quite well at high signal to noise ratios, their performance worsens at low signal to noise, and there may be significant bias. One of the biggest problems to efficient estimation of these models is that the majority of methods rely on sequential estimation of the phase coefficients, in that the highest-order parameter is estimated first, its contribution removed via demodulation, and the same procedure applied to estimation of the next parameter and so on. This is clearly an issue in that errors in estimation of high order parameters affect the ability to estimate the lower order parameters correctly. As a result, stastical analysis of the parameters is also difficult. In thie dissertation, we aim to circumvent the issues of bias and sequential estiamtion by considering the issue of full parameter iterative refinement techniques. ie. given a possibly biased initial estimate of the phase coefficients, we aim to create computationally efficient iterative refinement techniques to produce stastically efficient estimators at low signal to noise ratios. Updating will be done in a multivariable manner to remove inaccuracies and biases due to sequential procedures. Stastical analysis and extensive simulations attest to the performance of the schemes that are presented, which include likelihood, least squares and bayesian estimation schemes. Other results of importance to the full estimatin problem, namely when there is error in the time variable, the amplitude is not constant, and when the model order is not known, are also condsidered.
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Sando, Simon Andrew. "Estimation of a class of nonlinear time series models." Queensland University of Technology, 2004. http://eprints.qut.edu.au/15985/.

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The estimation and analysis of signals that have polynomial phase and constant or time-varying amplitudes with the addititve noise is considered in this dissertation.Much work has been undertaken on this problem over the last decade or so, and there are a number of estimation schemes available. The fundamental problem when trying to estimate the parameters of these type of signals is the nonlinear characterstics of the signal, which lead to computationally difficulties when applying standard techniques such as maximum likelihood and least squares. When considering only the phase data, we also encounter the well known problem of the unobservability of the true noise phase curve. The methods that are currently most popular involve differencing in phase followed by regression, or nonlinear transformations. Although these methods perform quite well at high signal to noise ratios, their performance worsens at low signal to noise, and there may be significant bias. One of the biggest problems to efficient estimation of these models is that the majority of methods rely on sequential estimation of the phase coefficients, in that the highest-order parameter is estimated first, its contribution removed via demodulation, and the same procedure applied to estimation of the next parameter and so on. This is clearly an issue in that errors in estimation of high order parameters affect the ability to estimate the lower order parameters correctly. As a result, stastical analysis of the parameters is also difficult. In thie dissertation, we aim to circumvent the issues of bias and sequential estiamtion by considering the issue of full parameter iterative refinement techniques. ie. given a possibly biased initial estimate of the phase coefficients, we aim to create computationally efficient iterative refinement techniques to produce stastically efficient estimators at low signal to noise ratios. Updating will be done in a multivariable manner to remove inaccuracies and biases due to sequential procedures. Stastical analysis and extensive simulations attest to the performance of the schemes that are presented, which include likelihood, least squares and bayesian estimation schemes. Other results of importance to the full estimatin problem, namely when there is error in the time variable, the amplitude is not constant, and when the model order is not known, are also condsidered.
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Ainkaran, Ponnuthurai. "Analysis of Some Linear and Nonlinear Time Series Models." Thesis, The University of Sydney, 2004. http://hdl.handle.net/2123/582.

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Abstract This thesis considers some linear and nonlinear time series models. In the linear case, the analysis of a large number of short time series generated by a first order autoregressive type model is considered. The conditional and exact maximum likelihood procedures are developed to estimate parameters. Simulation results are presented and compare the bias and the mean square errors of the parameter estimates. In Chapter 3, five important nonlinear models are considered and their time series properties are discussed. The estimating function approach for nonlinear models is developed in detail in Chapter 4 and examples are added to illustrate the theory. A simulation study is carried out to examine the finite sample behavior of these proposed estimates based on the estimating functions.
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Ainkaran, Ponnuthurai. "Analysis of Some Linear and Nonlinear Time Series Models." University of Sydney. Mathematics & statistics, 2004. http://hdl.handle.net/2123/582.

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Abstract This thesis considers some linear and nonlinear time series models. In the linear case, the analysis of a large number of short time series generated by a first order autoregressive type model is considered. The conditional and exact maximum likelihood procedures are developed to estimate parameters. Simulation results are presented and compare the bias and the mean square errors of the parameter estimates. In Chapter 3, five important nonlinear models are considered and their time series properties are discussed. The estimating function approach for nonlinear models is developed in detail in Chapter 4 and examples are added to illustrate the theory. A simulation study is carried out to examine the finite sample behavior of these proposed estimates based on the estimating functions.
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Pitrun, Ivet 1959. "A smoothing spline approach to nonlinear inference for time series." Monash University, Dept. of Econometrics and Business Statistics, 2001. http://arrow.monash.edu.au/hdl/1959.1/8367.

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Batten, Douglas James. "Nonlinear time series modeling of some Canadian river flow data." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp01/MQ54860.pdf.

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Books on the topic "Nonlinear time series models"

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Dag, Tjøstheim, and Granger, C. W. J. (Clive William John), 1934-2009, eds. Modelling nonlinear economic time series. Oxford: Oxford University Press, 2010.

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Costas, Milas, and Rothman Philip, eds. Nonlinear time series analysis of business cycles. Boston: Elsevier, 2006.

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Christian, Dunis, and Zhou Bin 1956-, eds. Nonlinear modelling of high frequency financial time series. Chichester [England]: Wiley, 1998.

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Philip, Rothman, ed. Nonlinear time series analysis of economic and financial data. Boston: Kluwer Academic Publishers, 1999.

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1949-, Creedy John, and Martin Vance 1955-, eds. Nonlinear economic models: Cross-sectional, time series and neural network applications. Cheltenham, U.K: E. Elgar, 1997.

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Terdik, György. Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-1552-3.

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Nonlinear time series analysis with applications to foreign exchange rate volatility. Heidelberg: Physica-Verlag, 1997.

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Douc, Randal. Nonlinear times series: Theory, methods and applications with R examples. Boca Raton: CRC Press, 2014.

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Lewis, Peter A. W. Nonlinear modeling of time series using Multivariate Adaptive Regression Splines (MARS). Monterey, Calif: Naval Postgraduate School, 1990.

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Kariya, Takeaki. Hi senkei keizai jikeiretsu bunsekihō to sono ōyō: Gausu-sei kentei to hi senkei moderu. Tōkyō: Iwanami Shoten, 1997.

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Book chapters on the topic "Nonlinear time series models"

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Turkman, Kamil Feridun, Manuel González Scotto, and Patrícia de Zea Bermudez. "Nonlinear Time Series Models." In Non-Linear Time Series, 23–89. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-07028-5_2.

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Turkman, Kamil Feridun, Manuel González Scotto, and Patrícia de Zea Bermudez. "Inference for Nonlinear Time Series Models." In Non-Linear Time Series, 121–97. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-07028-5_4.

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Ahmad, Yamin, and Ming Chien Lo. "Nonlinear Time Series Models and Model Selection." In Recent Advances in Estimating Nonlinear Models, 99–121. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-8060-0_6.

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De Gooijer, Jan G. "Classic Nonlinear Models." In Elements of Nonlinear Time Series Analysis and Forecasting, 29–85. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-43252-6_2.

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Carmona, René. "Nonlinear Time Series: Models and Simulation." In Springer Texts in Statistics, 473–533. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-8788-3_8.

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Baragona, Roberto, Francesco Battaglia, and Irene Poli. "Time Series Linear and Nonlinear Models." In Evolutionary Statistical Procedures, 85–124. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-16218-3_4.

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Chaubal, Aditi. "Typology of Nonlinear Time Series Models." In Recent Econometric Techniques for Macroeconomic and Financial Data, 315–53. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-54252-8_13.

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Tsay, Ruey S. "Nonlinear Time Series Models: Testing and Applications." In Wiley Series in Probability and Statistics, 267–85. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2011. http://dx.doi.org/10.1002/9781118032978.ch10.

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De Gooijer, Jan G. "Vector Parametric Models and Methods." In Elements of Nonlinear Time Series Analysis and Forecasting, 439–93. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-43252-6_11.

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Ozaki, Tohru, and Valerie H. Ozaki. "Statistical Identification of Nonlinear Dynamics in Macroeconomics Using Nonlinear Time Series Models." In Statistical Analysis and Forecasting of Economic Structural Change, 345–65. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-662-02571-0_22.

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Conference papers on the topic "Nonlinear time series models"

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HOLLKAMP, J., and S. BATILL. "Time series models for nonlinear systems." In 30th Structures, Structural Dynamics and Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1989. http://dx.doi.org/10.2514/6.1989-1197.

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Vinayak and Thomas H. Seligman. "Time series, correlation matrices and random matrix models." In LATIN-AMERICAN SCHOOL OF PHYSICS MARCOS MOSHINSKY ELAF: Nonlinear Dynamics in Hamiltonian Systems. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4861704.

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Souza, Roberto Molina de Souza, Jorge Alberto Achcar Achcar, and Glaucia Maria Bressan Bressan. "Correlated time series using mixed models in a Bayesian perspective." In 6th International Conference on Nonlinear Science and Complexity. São José dos Campos, Brazil: INPE Instituto Nacional de Pesquisas Espaciais, 2016. http://dx.doi.org/10.20906/cps/nsc2016-0021.

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Brolin, Magnus Olsson, and Lennart Soder. "Modeling Swedish real-time balancing power prices using nonlinear time series models." In 2010 IEEE 11th International Conference on Probabilistic Methods Applied to Power Systems (PMAPS). IEEE, 2010. http://dx.doi.org/10.1109/pmaps.2010.5526246.

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Yunyan Wang and Mingtian Tang. "Nonergodicity for a class of general nonlinear time series models." In 2011 2nd International Conference on Artificial Intelligence, Management Science and Electronic Commerce (AIMSEC). IEEE, 2011. http://dx.doi.org/10.1109/aimsec.2011.6010299.

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Monbet, Vale´rie, Pierre Ailliot, and Marc Prevosto. "Nonlinear Simulation of Multivariate Sea State Time Series." In ASME 2005 24th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2005. http://dx.doi.org/10.1115/omae2005-67490.

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In this paper, three nonlinear methods are described for artificially generating operational sea state histories. In the first method, referred to as Translated Gaussian Process the observed time series is transformed to a process which is supposed to be Gaussian. This Gaussian process is simulated and back transformed. The second method, called Local Grid Bootstrap, consists in a resampling algorithm for Markov chains within which the transition probabilities are estimated locally. The last models is a Markov Switching Autoregressive model which allows in particular to model different weather types.
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Liu, Xinxia, Shengli Li, Yujie Zhang, Yantao Yang, and Tianyang Chen. "Prediction Model for Nonlinear Deformation Time Series." In 2015 International Symposium on Computers and Informatics. Paris, France: Atlantis Press, 2015. http://dx.doi.org/10.2991/isci-15.2015.299.

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Markusson, O., and H. Hjalmarsson. "Higher order cumulant based parameter estimation in nonlinear time series models." In Proceedings of American Control Conference. IEEE, 2001. http://dx.doi.org/10.1109/acc.2001.945758.

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Tang, Mingtian, and Yunyan Wang. "On nonrecurrence of general nonlinear time series models with random time delay under random environment." In 2011 Seventh International Conference on Natural Computation (ICNC). IEEE, 2011. http://dx.doi.org/10.1109/icnc.2011.6022315.

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Li, Rui, Tai-Peng Tian, and Stan Sclaroff. "Simultaneous Learning of Nonlinear Manifold and Dynamical Models for High-dimensional Time Series." In 2007 IEEE 11th International Conference on Computer Vision. IEEE, 2007. http://dx.doi.org/10.1109/iccv.2007.4409044.

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Reports on the topic "Nonlinear time series models"

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Stock, James, and Mark Watson. A Comparison of Linear and Nonlinear Univariate Models for Forecasting Macroeconomic Time Series. Cambridge, MA: National Bureau of Economic Research, June 1998. http://dx.doi.org/10.3386/w6607.

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Dassanayake, Wajira, Chandimal Jayawardena, Iman Ardekani, and Hamid Sharifzadeh. Models Applied in Stock Market Prediction: A Literature Survey. Unitec ePress, March 2019. http://dx.doi.org/10.34074/ocds.12019.

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Stock market prices are intrinsically dynamic, volatile, highly sensitive, nonparametric, nonlinear, and chaotic in nature, as they are influenced by a myriad of interrelated factors. As such, stock market time series prediction is complex and challenging. Many researchers have been attempting to predict stock market price movements using various techniques and different methodological approaches. Recent literature confirms that hybrid models, integrating linear and non-linear functions or statistical and learning models, are better suited for training, prediction, and generalisation performance of stock market prices. The purpose of this review is to investigate different techniques applied in stock market price prediction with special emphasis on hybrid models.
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Wheat, Jr., Robert M. Chaos in Electronic Circuits: Nonlinear Time Series Analysis. Office of Scientific and Technical Information (OSTI), July 2003. http://dx.doi.org/10.2172/821547.

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Bielinskyi, Andrii O., Oleksandr A. Serdyuk, Сергій Олексійович Семеріков, Володимир Миколайович Соловйов, Андрій Іванович Білінський, and О. А. Сердюк. Econophysics of cryptocurrency crashes: a systematic review. Криворізький державний педагогічний університет, December 2021. http://dx.doi.org/10.31812/123456789/6974.

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Cryptocurrencies refer to a type of digital asset that uses distributed ledger, or blockchain technology to enable a secure transaction. Like other financial assets, they show signs of complex systems built from a large number of nonlinearly interacting constituents, which exhibits collective behavior and, due to an exchange of energy or information with the environment, can easily modify its internal structure and patterns of activity. We review the econophysics analysis methods and models adopted in or invented for financial time series and their subtle properties, which are applicable to time series in other disciplines. Quantitative measures of complexity have been proposed, classified, and adapted to the cryptocurrency market. Their behavior in the face of critical events and known cryptocurrency market crashes has been analyzed. It has been shown that most of these measures behave characteristically in the periods preceding the critical event. Therefore, it is possible to build indicators-precursors of crisis phenomena in the cryptocurrency market.
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Sugihara, George. Applications of Nonlinear Time Series Methods in Marine Ecology. Fort Belvoir, VA: Defense Technical Information Center, September 1998. http://dx.doi.org/10.21236/ada362252.

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Chen, Xiaohong, ., and Yixiao Sun. Sieve inference on semi-nonparametric time series models. Institute for Fiscal Studies, February 2012. http://dx.doi.org/10.1920/wp.cem.2012.0612.

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Kedem, B. A Graphical Similarity Measure for Time Series Models. Fort Belvoir, VA: Defense Technical Information Center, April 1985. http://dx.doi.org/10.21236/ada158869.

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Osborne, A. R. Physics, Nonlinear Time Series Analysis, Data Assimilation and Hyperfast Modeling of Nonlinear Ocean Waves. Fort Belvoir, VA: Defense Technical Information Center, September 2010. http://dx.doi.org/10.21236/ada542499.

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Bernanke, Ben, Henning Bohn, and Peter Reiss. Alternative Nonnested Specification Tests of Time Series Investment Models. Cambridge, MA: National Bureau of Economic Research, June 1985. http://dx.doi.org/10.3386/t0049.

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Eichenbaum, Martin, and Lars Peter Hansen. Estimating Models with Intertemporal Substitution Using Aggregate Time Series Data. Cambridge, MA: National Bureau of Economic Research, March 1987. http://dx.doi.org/10.3386/w2181.

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