ARIMA Model

The ARIMA (autoregressive integrated moving average) is a model describing time series
yt = 1,2…= {y1,y2,…}.


The full (p,d,q)(P,D,Q)s notation is given in the form of backshift polynomials. It encompasses set of simpler models:


The differencing model DIFF(d) of order d:

The seasonal differencing model DIFF(D)s of order D and seasonality lag s:

The autoregressive model AR(p) of order p:

The seasonal autoregressive model AR(P)s of order P and seasonality lag s:

The moving average model MA(q) of order q:

The seasonal moving average model MA(Q)s of order Q and seasonality lag s:

The εt is white noise (with properties: zero mean, constant variance, independence and normality):