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

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  • Wildi, Marc
  • McElroy, Tucker S.

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.

Suggested Citation

  • Wildi, Marc & McElroy, Tucker S., 2019. "The trilemma between accuracy, timeliness and smoothness in real-time signal extraction," International Journal of Forecasting, Elsevier, vol. 35(3), pages 1072-1084.
    • Handle: RePEc:eee:intfor:v:35:y:2019:i:3:p:1072-1084
    DOI: 10.1016/j.ijforecast.2019.03.008
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    1. Lawrence J. Christiano & Terry J. Fitzgerald, 2003. "The Band Pass Filter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(2), pages 435-465, May.
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    4. William R. Bell & Donald E. K. Martin, 2004. "Computation of asymmetric signal extraction filters and mean squared error for ARIMA component models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 603-623, July.
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    Cited by:

    1. Webel, Karsten, 2022. "A review of some recent developments in the modelling and seasonal adjustment of infra-monthly time series," Discussion Papers 31/2022, Deutsche Bundesbank.
    2. McElroy, Tucker S. & Wildi, Marc, 2020. "The Multivariate Linear Prediction Problem: Model-Based and Direct Filtering Solutions," Econometrics and Statistics, Elsevier, vol. 14(C), pages 112-130.

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