Linear Dynamical System

From Ioannis Kourouklides
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This page contains resources about Linear Dynamical Systems, Linear Systems Theory, Dynamic Linear Models, Linear State Space Models and State-Space Representation, including temporal (Time Series) and atemporal Sequential Data.

Subfields and Concepts[edit]

  • Linear SSM
    • Discrete-time LDS
    • Continuous-time LDS
    • Linear Time-Invariant (LTI) system
    • Linear Time-Variant System
  • Parametric models / Time Series models
    • Autoregressive (AR) model / All-Pole model
    • Moving Average (MA) model / All-Zero model
    • ARMA model / Pole-Zero model
    • ARIMA and ARIMAX
    • Seasonal ARIMA (SARIMA) and SARIMAX
    • Autoregressive Conditional Heteroskedasticity (ARCH) model
    • Generalized ARCH (GARCH) model
    • Vector Autoregressive (VAR) model
    • Vector ARMA (VARMA) model
    • Martin Distance (for comparing ARMA processes)
  • Kalman filter / Linear Gaussian SSM
  • Stochastic LDS
  • Structured LDS
  • Bayesian SSM
    • Bayesian Time Series
    • Bayesian LDS
  • SSM with Regime Switching / Jump Markov Linear Systems / Switching LDS / Switching SSM
  • Kernels on Dynamical Systems
  • Computer Vision
    • Linear Dynamic Texture
    • Kernel Dynamic Texture
  • Time Series
    • Univariate Time Series
    • Multivariate Time Series
  • Time Series Forecasting
    • One-step ahead Forecasting
    • Multi-step ahead Forecasting
    • Dynamic Forecasting

Online Courses[edit]

Video Lectures[edit]

Lecture Notes[edit]

Books and Book Chapters[edit]

See also Further Reading.

  • Hyndman, R. J., & Athanasopoulos, G. (2018). Forecasting: Principles and Practice. 2nd Ed. OTexts. (link)
  • Brockett, R. W. (2015). Finite dimensional linear systems. SIAM.
  • Murphy, K. P. (2012). "Chapter 18: State space models". Machine Learning: A Probabilistic Perspective. MIT Press.
  • Barber, D. (2012). "Chapter 24: Continuous-State Markov Models". Bayesian Reasoning and Machine Learning. Cambridge University Press.
  • Barber, D. (2012). "Chapter 25: Switching Linear Dynamical Systems". Bayesian Reasoning and Machine Learning. Cambridge University Press.
  • Durbin, J., & Koopman, S. J. (2012). Time series analysis by state space methods. Oxford University Press.
  • Casti, J. L. (2012). Linear dynamical systems. Academic Press Professional.
  • Prado, R., & West, M. (2010). Time series: modeling, computation, and inference. CRC Press.
  • Tsay, R. S. (2010). Analysis of Financial Time Series. 3rd Ed. John Wiley & Sons.
  • Petris, G., Petrone, S., & Campagnoli, P. (2009). Dynamic Linear Models with R. Springer New York.
  • Hespanha, J. P. (2009). Linear systems theory. Princeton university press.
  • Zadeh, L. A., & Desoer, C. A. (2008). Linear System Theory: The State Space Approach. Dover.
  • Commandeur, J. J., & Koopman, S. J. (2007). An introduction to state space time series analysis. Oxford University Press.
  • Antsaklis, P. J., & Michel, A. N. (2007). A Linear Systems Primer. Springer Science & Business Media.
  • Antsaklis, P. J., & Michel, A. N. (2006). Linear systems. Springer Science & Business Media.
  • Bishop, C. M. (2006). "Chapter 13: Sequential Data". Pattern Recognition and Machine Learning. Springer.
  • Gajic, Z. (2003). Linear dynamic systems and signals. Prentice Hall/Pearson Education.
  • Chatfield, C. (2003). The analysis of time series: an introduction. 6th Ed. CRC press.
  • Harrison, J., & West, M. (1999). Bayesian Forecasting & Dynamic Models. Springer.
  • Chen, C. T. (1998). Linear system theory and design. Oxford University Press.
  • Rugh, W. J. (1996). Linear system theory. Prentice Hall.
  • Hamilton, J. D. (1994). Time series analysis. Princeton University Press.
  • Callier, F. M., & Desoer, C. A. (1991). Linear System Theory. Springer New York.
  • Harvey, A. C. (1990). Forecasting, structural time series models and the Kalman filter. Cambridge university press.
  • Harvey, A. C. (1993). Time series models. 2nd Ed. The MIT Press.
  • Delchamps, D. F. (1988). State space and input-output linear systems. Springer Science & Business Media.
  • Cryer, J. D. (1986). Time series analysis. Duxbury Press.
  • Kailath, T. (1980). Linear systems. Prentice-Hall.
  • Luenberger, D. G. (1979). Introduction to dynamic systems. John Wiley & Sons.

Scholarly Articles[edit]

  • Archer, E., Park, I. M., Buesing, L., Cunningham, J., & Paninski, L. (2015). Black box variational inference for state space models. arXiv preprint arXiv:1511.07367.
  • Taieb, S. B., Bontempi, G., Atiya, A. F., & Sorjamaa, A. (2012). A review and comparison of strategies for multi-step ahead time series forecasting based on the NN5 forecasting competition. Expert systems with applications, 39(8), 7067-7083.
  • Petris, G., & Petrone, S. (2011). State space models in R. Journal of Statistical Software41(4), 1-25.
  • Taieb, S. B., Sorjamaa, A., & Bontempi, G. (2010). Multiple-output modeling for multi-step-ahead time series forecasting. Neurocomputing, 73(10-12), 1950-1957.
  • Vishwanathan, S. V. N., Smola, A. J., & Vidal, R. (2007). Binet-Cauchy kernels on dynamical systems and its application to the analysis of dynamic scenes. International Journal of Computer Vision, 73(1), 95-119.
  • Chan, A. B., & Vasconcelos, N. (2007). Classifying video with kernel dynamic textures. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (pp. 1-6).
  • Cheng, H., Tan, P. N., Gao, J., & Scripps, J. (2006). Multistep-ahead time series prediction. In Pacific-Asia Conference on Knowledge Discovery and Data Mining (pp. 765-774). Springer.
  • Rudary, M., Singh, S., & Wingate, D. (2005). Predictive linear-Gaussian models of stochastic dynamical systems. Conference on Uncertainty in Artificial Intelligence.
  • Doretto, G., Chiuso, A., Wu, Y. N., & Soatto, S. (2003). Dynamic textures. International Journal of Computer Vision, 51(2), 91-109.
  • Martin, R. J. (2000). A metric for ARMA processes. IEEE Transactions on Signal Processing, 48(4), 1164-1170.
  • Minka, T. (1999). From hidden markov models to linear dynamical systems. Technical Report, MIT.
  • Kim, C. J. (1994). Dynamic linear models with Markov-switching. Journal of Econometrics60(1-2), 1-22.
  • Ghahramani, Z., & Hinton, G. E. (1996). Parameter estimation for linear dynamical systems. Technical Report CRG-TR-96-2, University of Toronto, Dept. of Computer Science.
  • Kalman, R. E. (1963). Mathematical description of linear dynamical systems. Journal of the Society for Industrial and Applied Mathematics, Series A: Control1(2), 152-192.


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Other Resources[edit]