The trilemma between accuracy, timeliness and smoothness in real-time signal extraction

Abstract

The evaluation of economic data and the monitoring of the economy is often concerned with an assessment of the mid- and long-term dynamics of time series (trend and/or cycle). Frequently, one is interested in the most recent estimate of a target signal, a so-called real-time estimate. Unfortunately, real-time signal extraction is a difficult estimation problem that involves linear combinations of possibly infinitely many multi-step ahead forecasts of a series. Here, we address the performances of real-time designs by proposing a generic direct filter approach. We decompose the ordinary mean squared error into accuracy, timeliness and smoothness error components, and we propose a new tradeoff between these competing terms, the so-called ATS-trilemma. This formalism enables us to derive a general class of optimization criteria that allow the user to address specific research priorities, in terms of the accuracy, timeliness and smoothness properties of the corresponding concurrent filter. We illustrate the new methods through simulations, and present an application to Indian industrial production data.