The First-Order Seasonal Autoregressive Model as a Fundamental Model for Moving Seasonality and Model-Based Seasonal Adjustment

• Activity Number: 675
• Type: Topic Contributed
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): David Findley*+ and Demetra Lytras
• Companies: US Census Bureau and US Census Bureau
• Keywords: Seasonality detection ; Model-based seasonal adjustment ; Moving seasonality

Abstract

We demonstrate how the stationary first-order seasonal autoregressive model, or (1,0,0)12 model in the case of monthly data, provides the simplest insight-bringing model for seasonal adjusters of a time series with moving seasonality. It has the pedagogical advantage that simple algebraic formulas describe its canonical finite-sample model-based seasonal adjustment filters and the mean square errors of the estimates they produce. These formulas clearly express some properties of model-based adjustments otherwise known only abstractly or empirically. Also, SAR(1) series reveal important features, including weaknesses, of the main diagnostics in use for detecting seasonality, both stable seasonality and residual seasonality.