Uncertainty in Model-Based Seasonal Adjustment Procedures and Construction of Minimax Filters

Abstract

Unobserved component autoregressive integrated moving average models are often the cornerstone of model-based seasonal adjustment procedures. Unfortunately these models are inherently underidentified and ad hoc assumptions must be made prior to the analysis. This article investigates the effect of seasonal adjustment filters on a class of observationally equivalent models. Bounds on the mean squared error (MSE) associated with arbitrary linear filters are derived. The article also derives robust seasonal adjustment filters. The filters are robust in the sense that they minimize the maximum MSE from the set of observationally equivalent models. The article shows that the minimax and minimum extraction filters are equivalent for a certain class of models. Empirical results for a number of economic time series are presented.

Key Words:

• Signal extraction
• Unobserved components model
• Minimax estimates