Probabilistic modeling

The current section is dedicated to probabilistic methods and concepts.

• Standard parametric models
• Copulas
• Affine combination of independent univariate random variables

Stochastic process

• Stochastic process definitions
  • Notations
  • Spatial (temporal) and Stochastic Mean
  • Normal process
  • Weak stationarity (second order stationarity)
  • Stationarity
  • Spectral density function

Transformation of fields

• Trend computation
• Box Cox transformation

ARMA stochastic process

• ARMA stochastic process
• ARMA process estimation

Normal processes

• Covariance models
• Parametric stationary covariance models
• Estimation of a stationary covariance model
• Estimation of a non stationary cov. model
• Estimation of a spectral density function
• Parametric spectral density functions

Process transformation

• Field functions
• Process transformation

Stationarity tests

• Dickey-Fuller stationarity test