Autoregression (AR)

Autoregression is a time series model used in statistical analysis, which uses past observations as input to predict future values.

An AR(p) model is an autoregressive model where specific lagged values of yt are used as predictor variables. The value of p is called the order. AR1 is the first order process, meaning that future value depends upon immediately preceding value. Similarly, AR2 is the second order process, meaning that future value depends upon the previous two values.

The AR(p) model is defined as:

yt = δ + θ1yt-1 +θ2yt-2 + … + θpyt-1 + εt

Where,

             yt-1, yt-2…yt-p are the past series values

             εt is white noise  (randomness)

            and δ is constant