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Illuminating Model-Based Seasonal Adjustment with the First Order Seasonal Autoregressive and Airline Models
Illuminating Model-Based Seasonal Adjustment with the First Order Seasonal Autoregressive and Airline Models
RRS2015-02
Abstract
Stationary first order seasonal autoregressive series are shown to have a canonical model-based decomposition whose estimates have simple formulas from linear regression. The formulas are used to reveal many features of ARMA and ARIMA model-based seasonal adjustment. Our tutorial focus also yields new results, including relative smoothness results based on autocorrelation comparisons of same-calendar-month subseries before and after seasonal adjustment. For a deeper analysis of the SAR(1) decomposition and for generalizations to ARIMA model-based decompositions, the Wiener-Kolmogorov signal extraction filter formulas are developed. These formulas and their ARIMA generalizations by Bell (1984) are applied in several ways. For example, Bell's formulas easily reveal how the seasonal moving average coefficient controls the responsiveness or resistance of ARIMA model-based seasonal adjustments to short term movements in the time series.
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Page Last Revised - October 28, 2021
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