Autoregression

Autoregression

• Definition: A time series model that predicts the current value as a linear combination of its past values.

• Mathematical form (AR(p)):

  $$X_t=c+{\varphi }_1{X}_{t-1}+{\varphi }_2{X}_{t-2}+\cdots +{\varphi }_p{X}_{t-p}+{ϵ}_t$$

  where ${ϵ}_t$ is white noise.

• Purpose: Forecasting future values from historical dependencies.

• Use cases:

  • ARIMA modeling.
  • Capturing short-term dependencies.