Autoregressive Models

Autoregressive Models
  • An autoregressive model is a regression where that a value from a time series is regressed on previous values from that same time series.
  • The order of an autoregression is the number of immediately preceding values in the series that are used to predict the value at the present time.
    • A first-order autoregression[=autoregressive model] is represented as AR(1).
      • The value at time t is predicted from the value at time t-1
      • e.g.) y_t=\beta_0+\beta_1 y_{t-1}+\epsilon
    • A second-order autoregression is represented as AR(2).
      • The value at time t is predicted from the values at time t-1 and time t-2.
      • e.g.) y_t=\beta_0+\beta_1 y_{t-1}+\beta_2 y_{t-2}+\epsilon

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