Auto-Regressive (AR) Time Series Models

  • Auto-Regressive (AR) Time Series Models
  • This type of time series model utilizes a time period lagged observation as the independent variable to predict the dependent variable, which is the value in the next time period.

xt = b0 + b1xt-1 + εt

  • There can be more than one time period lag independent variable.
  • Valid statistical inferences from AR time series models only if the time series is covariance stationary; a time series with growth over time or seasonality is not covariance stationary.
  • It is critical to test your AR time series model for serial correlation and the Durbin-Watson test cannot be used for this model.
  • An AR time series model that is covariance stationary will exhibit mean reversion – it will tend to fall after going above the mean and rise after going below the mean.
  • Root Mean Square Error (RMSE) = a method of assessing the out of sample accuracy of a time series model’s forecast.  If comparing multiple models, the model will the lowest RMSE is considered to have the best forecasting capabilities.