Seasonal Integration and the Evolving Seasonals Model

Abstract

In this paper it is argued that describing seasonal patterns as an evolving seasonals model in which the coefficients attached to seasonal trigonometric terms follow simple autoregressive processes can be very useful when one is faced with the task of extending well known results obtained for non-seasonal time series to the seasonal case. Such a perspective gains its utility from the fact that this evolving seasonal Model (ESM) can be decomposed into quantities that are non-seasonal and the behaviour of these variables can be examined with standard techniques. It emerges that this strategy will deliver methods currently in use for the analysis of seasonal series, and is also flexible enough to suggest some new alternatives.