Statistical Properties of Model-Based Signal Extraction Diagnostic Tests

Abstract

A model-based diagnostic test for signal extraction was first described in Maravall (2003), and this basic idea was modified and studied in Findley et al. (2004). This paper improves on the latter work in two ways: central limit theorems for the diagnostics are developed, and two hypothesis-testing paradigms for practical use are explicitly described. A further modified diagnostic provides an interpretation of one-sided rejection of the null hypothesis, yielding general notions of “over-modeling” and “under-modeling.” The new diagnostics are demonstrated on two U.S. Census Bureau time series exhibiting seasonality.

Keywords:

• ARIMA model
• Central limit theorem
• Filtering; Seasonal adjustment

Mathematics Subject Classification:

• Primary 62M10
• Secondary 62M15

Acknowledgments

This paper is released to inform interested parties of ongoing research and to encourage discussion of work in progress. The views expressed are those of the author and not necessarily those of the U.S. Census Bureau.