时间序列¶

24Spring DATA620005，时间序列与空间统计，陈钊

Hilbert空间视角下的时间序列。

主要内容¶

• Hilbert Spaces
  • Inner-product spaces
  • Projection theorem
  • Orthogonality
• Stationary ARMA
  • Causal and Invertible ARMA
  • MA of infinite order
  • ACF of ARMA
  • PACF
  • ACF generating function
• Spectral Representation
  • Complex valued stationary time series
  • Spectral distribution
  • Herglotz's theorem
  • Spectral density
• Prediction
  • Prediction in time domain
  • Recrusive methods
    • DL algorithm
    • Innovation algorithm
• Estimation
  • Mean
  • ACF
  • Yule-Walker estimation
  • Preliminary Estimation for AR Using the DL Algorithm
  • Preliminary Estimation for MA Using the Innovations Algorithm
• Model Building
  • ARIMA
  • Identification
  • Order selection
  • Diagnose
  • Forecasting
  • SARIMA
• Inference for the Spectrum
  • Periodogram
• State-Space Models
  • Kalman Recursions
  • Controllability and Observability

参考书¶

Time Series: Theory and Methods, Peter J. Brockwell, Richard A. Davis

体会¶

万物基于投影，投影定理真是太好用啦！学好线性代数，这门课完全不用怕～