# Nonseasonal ARIMA Model - Aster Analytics

## Teradata Aster® Analytics Foundation User GuideUpdate 2

Product
Aster Analytics
Release Number
7.00.02
Published
September 2017
Language
English (United States)
Last Update
2018-04-17
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uce1497542673292.ditamap
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dita:id
B700-1022
lifecycle
previous
Product Category
Software

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

where:

• 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 .