mean is the model mean (i.e. mu) or the long-run mean of the differenced time series.

sigma is the standard deviation of the model's residuals/innovations.

s is the length of seasonality (expressed in steps, where s>1).

theta is the coefficient of the non-seasonal MA component (see model description).

theta2 is the coefficient of the seasonal MA component (see model description).

1. The underlying model is described here.
2. The long-run mean argument (mean) can take any value or be omitted, in this case a zero value is assumed.
3. The value of the residuals/innovations standard deviation (sigma) must be positive.
4. The season length must be greater than one.
5. The input argument for the non-seasonal MA parameter - theta - is optional and can be omitted, in which case no non-seasonal MA component is included.
6. The input argument for the seasonal MA parameter - theta2 - is optional and can be omitted, in which case no seasonal MA component is included.
7. The function was added in version 1.63 SHAMROCK.

Files Examples

Related Links

• Wikipedia - Akaike's Information Criterion (AIC)
• Wikipedia - Autoregressive moving average model

References

• Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
• Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740