On the Model-based Interpretation of Trend-cycle Filters

• Activity Number: 214
• Type: Topic Contributed
• Date/Time: Tuesday, August 10, 2004 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economics Statistics Section
• Author(s): Tommaso Proietti*+
• Companies: Dipartimento di Scienze Statistiche
• Keywords: signal extraction ; Kalman filter and smoother ; revisions ; reliability

Abstract

The paper is concerned with a class of trend cycle filters, encompassing the Hodrick-Prescott and rational square wave filters, that are derived using the Wiener-Kolmogorov signal extraction theory under maintained models that prove unrealistic in applied time series analysis. As the maintained model is misspecified, inference about the unobserved components, and in particular their posterior mean and variance, are not delivered by the Kalman filter and smoother or the Wiener-Kolmogorov filter for the maintained model. The paper proposes a model-based framework according to which the same class of filters is adapted to the particular time series under investigation; the idea rests on an "embedding principle" by which any linear time series can be decomposed into orthogonal components with a given representation; the resulting decomposition "objectifies" the filters, giving them autonomous justification; nevertheless, it is the interaction with the series and its time series properties than enables the components to be estimated and their uncertainty assessed. This embedding principle guarantees that correct inferences are standard and are provided in finite samples.