7.00.02 - Nonseasonal ARIMA Model - Aster Analytics

Teradata Aster® Analytics Foundation User GuideUpdate 2

Aster Analytics
Release Number
Release Date
September 2017
Content Type
Programming Reference
User Guide
Publication ID
English (United States)

In a nonseasonal ARIMA model, ARIMA(p, d, q):

  • p is the order of the autoregressive part
  • d is the degree of first differencing
  • q is the order of the moving average part

To calculate the coefficients of the input parameters, the Arima function uses this formula:

AR(p) * d_differences = MA(q) + c


  • AR(p) = 1 - φ 1 B - … - φ p B p
  • d_differences = (1 - B) d y t
  • MA(q) = (1 + θ 1 B + … + θ q B q )e t

The φ values are nonseasonal autoregressive parameters and the θ values are nonseasonal moving average parameters.

The value B is the backshift operator, which is defined as follows:

By t = y t-1

B n y t = y t-n

e t is the residual error, the difference between the actual and predicted values of y t .