Review of popular methods of linear time series; Distinguishing features of linear and non-linear time series; Autoregressive integrated moving average models (execution in MATLAB, Python, R);Analysis of chaotic time series for determining time delay and embedding dimension and comparison of different methods; De-trended fluctuation analysis (DFA), Hurst exponent; Grey(1,1) model for non-linear advanced prediction; Horizontal Visibility Graphs (HVG); Lyapunov exponent: different methods of determining maximal Lyapunov exponent for short time series; Z test of chaos; One Step Advance Analysis (OSAA) models for non-linear advanced prediction; Noise reduction in time series; Effect on Lyapunov exponent and phase space; Examples of data based modelling of dynamical systems (students shall be encouraged to bring problems in their specific domain); Construction of phase space and state space diagrams from actual time series data; Application of ANN and ELM to generate surrogate data; Methods of controlling chaotic dynamics: simple proportional feedback (SPF) and OGY method; Application examples to specific dynamical systems including ECG, EEG and FMRI of bio-medical systems; Interfacing model and instruments with process for control in industry; Application of AI techniques for reconstruction of dynamical systems.
Suggested basic books:
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1. H.D.I. Abarbanel, Analysis of Observed Chaotic Data, Springer, Berlin, 1996.
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2. Kantz, H., & Schreiber, T., Preface to the second edition. In Nonlinear Time Series Analysis (pp. Xiii-Xiv). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511755798.002, 2003
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3. C. Diks, Nonlinear Time Series Analysis: Methods and Applications, vol. 4 of Nonlinear Time Series and Chaos, World Scientific, Singapore, 1999.
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4. J. N. Perry, R. H. Smith, I. P. Woiwod, Chaos in Real Data: The Analysis of Non-Linear Dynamics from Short Ecological Time Series, Population and Community Biology Series (Kluwer Academic, Dordrecht, 2000.
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5. Franses, P., & Dijk, D. (2000). Bibliography. In Non-Linear Time Series Models in Empirical Finance (pp. 254-271). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511754067.008, 2000
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6. Camplani, M. (2010). Data Analysis Techniques for Nonlinear Dynamical Systems.
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7. M. Waser, “ Nonlinear dependencies in and between time series,” Master's dissertation Vienna University of Technology, Vienna, 2010.
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