The Estimation of a Changing Seasonal Pattern

Abstract A model is constructed for an economic time series with a changing seasonal pattern. This represents the seasonal component as itself a stationary time series with almost all of the spectral mass very near to the six (angular) frequencies, (πj/6). The problem of “predicting” this seasonal component at the time point n – μ (μ positive, zero or negative) is then solved on the basis of a reasonable model for this spectrum. The unspecified parameters are basically the signal to noise ratios and measures of the capacity of the seasonal to change through time. The estimation of this seasonal component can be regarded as a component in a servomechanism (the total mechanism being impossibly difficult to prescribe precisely) designed to control economic fluctuations. This component (a filter) can be adjusted by choice of the parameters so as to achieve some compromise between adequate damping and quick response.