| # Auto-regressive models for time series prediction A popular model for the prediction of time series is based on the so-called auto-regressive (AR) model where ’s are constant coefficients, and is the memory length of the model. The interpretation of the model is that the next output is a linear function of the past. Elaborate variants of auto-regressive models are widely used for prediction of time series arising in finance and economics. To find the coefficient vector theta in , we collect observations (with ) of the time series, and try to minimize the total squared error in the above equation: This can be expressed as a linear least-squares problem, with appropriate data . See also: Linear regression via Least-Squares.