Seasonal generalized AR models

Abstract

This paper looks at a novel type of seasonality labeled as a seasonal Generalized auto-regressive (GAR) model. The seasonal GAR models are found to be short-memory models, and expressions for the autocorrelation function and large sample results for the parameter estimates are established. Traditional Box-Jenkins seasonality models and Gegenbauer seasonality models are compared with the seasonal GAR model. Finally, the three methods are compared in the analysis of a specific process - the Mauna Loa CO₂ data - showing that in this case, the seasonal GAR model provides forecasts with a lower mean squared error.

KEYWORDS:

• Seasonality
• Box-Jenkins
• Gegenbauer
• GAR

Mathematics Subject Classification::

• 62M10

Disclosure statement

No potential conflict of interest was reported by the authors.

Availability of data and material

Where a source of data is not specifically indicated in the paper, all data may be obtained from the authors.

Code availability

All code may be obtained from the corresponding author.