Linear Dynamical System

From Ioannis Kourouklides
Jump to navigation Jump to search

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.

Software[edit]

See also[edit]

Other Resources[edit]