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State Space Models and MIDAS Regressions

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  • Jennie Bai
  • Eric Ghysels
  • Jonathan H. Wright

Abstract

We examine the relationship between Mi(xed) Da(ta) S(ampling) (MIDAS) regressions and the Kalman filter when forecasting with mixed frequency data. In general, state space models involve a system of equations, whereas MIDAS regressions involve a single equation. As a consequence, MIDAS regressions might be less efficient, but could also be less prone to parameter estimation error and/or specification errors. We examine how MIDAS regressions and Kalman filters match up under ideal circumstances, that is in population, and in cases where all the stochastic processes—low and high frequency—are correctly specified. We characterize cases where the MIDAS regression exactly replicates the steady state Kalman filter weights. We compare MIDAS and Kalman filter forecasts in population where the state space model is misspecified. We also compare MIDAS and Kalman filter forecasts in small samples. The paper concludes with an empirical application. Overall we find that the MIDAS and Kalman filter methods give similar forecasts. In most cases, the Kalman filter is a bit more accurate, but it is also computationally much more demanding.

Suggested Citation

  • Jennie Bai & Eric Ghysels & Jonathan H. Wright, 2013. "State Space Models and MIDAS Regressions," Econometric Reviews, Taylor & Francis Journals, vol. 32(7), pages 779-813, October.
    • Handle: RePEc:taf:emetrv:v:32:y:2013:i:7:p:779-813
    DOI: 10.1080/07474938.2012.690675
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    References listed on IDEAS

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    1. Alper, C. Emre & Fendoglu, Salih & Saltoglu, Burak, 2008. "Forecasting Stock Market Volatilities Using MIDAS Regressions: An Application to the Emerging Markets," MPRA Paper 7460, University Library of Munich, Germany.
    2. James H. Stock & Mark W. Watson, 1989. "New Indexes of Coincident and Leading Economic Indicators," NBER Chapters, in: NBER Macroeconomics Annual 1989, Volume 4, pages 351-409, National Bureau of Economic Research, Inc.
    3. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
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