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Time Series
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  • Stationary time series models: AR, MA, ARMA
  • Nonstationary time series models: ARIMA, SARIMA
  • Univariate and multivariate time series models
  • Covariance, correlation, and partial correlation functions
  • Structural models: state-space form and the Kalman filter
  • ARCH and GARCH models

Model Identification

  • Estimation of sample covariance, correlation, and partial correlation functions
  • Akaike's Information Criterion (AIC)
  • Bayesian Information Criterion (BIC)

Parameter Estimation

  • Yule-Walker, Levinson-Durbin, Burg's, innovations, and long autoregression algorithms
  • Hannan-Rissanen procedure
  • Maximum likelihood method
  • Conditional maximum likelihood method

Diagnostic Checking

  • Residuals
  • Portmanteau, turning points, and difference-sign tests
  • Information matrix


  • Exact and approximate best linear predictors
  • Updating the prediction

Spectral Analysis

  • Spectra of ARMA models
  • Spectrum estimation
  • Smoothing spectrum
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