MA 364: Linear and Non-linear Time Series Analysis

Credits: 3:0


 

Linear time series analysis - modelling time series using stochastic processes, stationarity, autocovariance, auto correlation, multivariate analysis - AR, MA, ARMA, AIC criterion for order selection;

Spectral analysis - deterministic processes, concentration problem, stochastic spectral analysis, nonparametric spectral estimation (periodogram, tapering, windowing), multitaper spectral estimation; parametric spectral estimation (Yule-Walker equations, Levinson Durbin)(recursions);

Multivariate analysis - coherence, causality relations; bootstrap techniques for estimation of parameters;

Nonlinear time series analysis - Lyapunov exponents, correlation dimension, embedding methods, surrogate data analysis.     


Suggested books and references:

  1. Box, G. E. P. and jenkins, G. M., Time series analysis, Holden-Day, 1976.
  2. Jenkins, G. M. and Watts, D. G., Spectral analysis and its applications, Holden-Day, 1986.
  3. Efron, B., The Jackknife, the bootstrap and other resampling plans, SIAM, 1982.
  4. Parker, T. S. and Chua, L. O., Practical numerical algorithms for chaotic systems, Springer-Verlag, 1989.

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Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 31 Jan 2025