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Signal Extraction Revision Variances as a Goodness-of-Fit Measure

Author

Listed:
  • McElroy Tucker

    (U.S. Census Bureau)

  • Wildi Marc

    (Institute of Data Analysis and Process Design)

Abstract

Typically, model misspecification is addressed by statistics relying on model-residuals, i.e., on one-step ahead forecasting errors. In practice, however, users are often also interested in problems involving multi-step ahead forecasting performances, which are not explicitly addressed by traditional diagnostics. In this article, we consider the topic of misspecification from the perspective of signal extraction. More precisely, we emphasize the connection between models and real-time (concurrent) filter performances by analyzing revision errors instead of one-step ahead forecasting errors. In applications, real-time filters are important for computing trends, for performing seasonal adjustment or for inferring turning-points towards the current boundary of time series. Since revision errors of real-time filters generally rely on particular linear combinations of one- and multi-step ahead forecasts, we here address a generalization of traditional diagnostics. Formally, a hypothesis testing paradigm for the empirical revision measure is developed through theoretical calculations of the asymptotic distribution under the null hypothesis, and the method is assessed through real data studies as well as simulations. In particular, we analyze the effect of model misspecification with respect to unit roots, which are likely to determine multi-step ahead forecasting performances. We also show that this framework can be extended to general forecasting problems by defining suitable artificial signals.

Suggested Citation

  • McElroy Tucker & Wildi Marc, 2010. "Signal Extraction Revision Variances as a Goodness-of-Fit Measure," Journal of Time Series Econometrics, De Gruyter, vol. 2(1), pages 1-32, June.
    • Handle: RePEc:bpj:jtsmet:v:2:y:2010:i:1:n:4
    DOI: 10.2202/1941-1928.1012
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    References listed on IDEAS

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    1. Pierce, David A., 1980. "Data revisions with moving average seasonal adjustment procedures," Journal of Econometrics, Elsevier, vol. 14(1), pages 95-114, September.
    2. Marc Wildi & Bernd Schips, 2004. "Signal Extraction: How (In)efficient Are Model-Based Approaches? An Empirical Study Based on TRAMO/SEATS and Census X-12-ARIMA," KOF Working papers 04-96, KOF Swiss Economic Institute, ETH Zurich.
    3. McElroy, Tucker, 2008. "Matrix Formulas For Nonstationary Arima Signal Extraction," Econometric Theory, Cambridge University Press, vol. 24(4), pages 988-1009, August.
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    Cited by:

    1. 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.
    2. Wildi Marc & McElroy Tucker, 2016. "Optimal Real-Time Filters for Linear Prediction Problems," Journal of Time Series Econometrics, De Gruyter, vol. 8(2), pages 155-192, July.
    3. Agustín Maravall Herrero & Domingo Pérez Cañete, 2011. "Applying and interpreting model-based seasonal adjustment. The euro-area industrial production series," Working Papers 1116, Banco de España.

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