IDEAS home Printed from https://ideas.repec.org/p/zbw/bubdp1/201135.html
   My bibliography  Save this paper

U-MIDAS: MIDAS regressions with unrestricted lag polynomials

Author

Listed:
  • Foroni, Claudia
  • Marcellino, Massimiliano
  • Schumacher, Christian

Abstract

Mixed-data sampling (MIDAS) regressions allow to estimate dynamic equations that explain a low-frequency variable by high-frequency variables and their lags. When the difference in sampling frequencies between the regressand and the regressors is large, distributed lag functions are typically employed to model dynamics avoiding parameter proliferation. In macroeconomic applications, however, differences in sampling frequencies are often small. In such a case, it might not be necessary to employ distributed lag functions. In this paper, we discuss the pros and cons of unrestricted lag polynomials in MIDAS regressions. We derive unrestricted MIDAS regressions (U-MIDAS) from linear high-frequency models, discuss identification issues, and show that their parameters can be estimated by OLS. In Monte Carlo experiments, we compare U-MIDAS to MIDAS with functional distributed lags estimated by NLS. We show that U-MIDAS generally performs better than MIDAS when mixing quarterly and monthly data. On the other hand, with larger differences in sampling frequencies, distributed lag-functions outperform unrestricted polynomials. In an empirical application on out-of-sample nowcasting GDP in the US and the Euro area using monthly predictors, we find a good performance of U-MIDAS for a number of indicators, albeit the results depend on the evaluation sample. We suggest to consider U-MIDAS as a potential alternative to the existing MIDAS approach in particular for mixing monthly and quarterly variables. In practice, the choice between the two approaches should be made on a case-by-case basis, depending on their relative performance.

Suggested Citation

  • Foroni, Claudia & Marcellino, Massimiliano & Schumacher, Christian, 2011. "U-MIDAS: MIDAS regressions with unrestricted lag polynomials," Discussion Paper Series 1: Economic Studies 2011,35, Deutsche Bundesbank.
  • Handle: RePEc:zbw:bubdp1:201135
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/55529/1/685618153.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Roberto S. Mariano & Yasutomo Murasawa, 2003. "A new coincident index of business cycles based on monthly and quarterly series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(4), pages 427-443.
    2. Claudia FORONI & Massimiliano MARCELLINO, 2012. "A Comparison of Mixed Frequency Approaches for Modelling Euro Area Macroeconomic Variables," Economics Working Papers ECO2012/07, European University Institute.
    3. Evan F. Koenig & Sheila Dolmas & Jeremy Piger, 2003. "The Use and Abuse of Real-Time Data in Economic Forecasting," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 618-628, August.
    4. Giannone, Domenico & Reichlin, Lucrezia & Small, David, 2008. "Nowcasting: The real-time informational content of macroeconomic data," Journal of Monetary Economics, Elsevier, vol. 55(4), pages 665-676, May.
    5. Rodriguez, Abel & Puggioni, Gavino, 2010. "Mixed frequency models: Bayesian approaches to estimation and prediction," International Journal of Forecasting, Elsevier, vol. 26(2), pages 293-311, April.
    6. Massimiliano Marcellino, 2007. "Pooling-Based Data Interpolation and Backdating," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(1), pages 53-71, January.
    7. Marcellino, Massimiliano & Stock, James H. & Watson, Mark W., 2006. "A comparison of direct and iterated multistep AR methods for forecasting macroeconomic time series," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 499-526.
    8. Kuzin, Vladimir & Marcellino, Massimiliano & Schumacher, Christian, 2011. "MIDAS vs. mixed-frequency VAR: Nowcasting GDP in the euro area," International Journal of Forecasting, Elsevier, vol. 27(2), pages 529-542.
    9. Massimiliano Marcellino & Christian Schumacher, 2010. "Factor MIDAS for Nowcasting and Forecasting with Ragged-Edge Data: A Model Comparison for German GDP," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 72(4), pages 518-550, August.
    10. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2005. "There is a risk-return trade-off after all," Journal of Financial Economics, Elsevier, vol. 76(3), pages 509-548, June.
    11. Virmantas Kvedaras & Alfredas Račkauskas, 2010. "Regression Models with Variables of Different Frequencies: The Case of a Fixed Frequency Ratio," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 72(5), pages 600-620, October.
    12. Andreou, Elena & Ghysels, Eric & Kourtellos, Andros, 2010. "Regression models with mixed sampling frequencies," Journal of Econometrics, Elsevier, vol. 158(2), pages 246-261, October.
    13. James H. Stock & Mark W. Watson, 2003. "How did leading indicator forecasts perform during the 2001 recession?," Economic Quarterly, Federal Reserve Bank of Richmond, issue Sum, pages 71-90.
    14. Domenico Giannone & Lucrezia Reichlin & David H. Small, 2005. "Nowcasting GDP and inflation: the real-time informational content of macroeconomic data releases," Finance and Economics Discussion Series 2005-42, Board of Governors of the Federal Reserve System (U.S.).
    15. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2006. "Predicting volatility: getting the most out of return data sampled at different frequencies," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 59-95.
    16. Angelini, Elena & Henry, Jerome & Marcellino, Massimiliano, 2006. "Interpolation and backdating with a large information set," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2693-2724, December.
    17. Eric Ghysels & Arthur Sinko & Rossen Valkanov, 2007. "MIDAS Regressions: Further Results and New Directions," Econometric Reviews, Taylor & Francis Journals, vol. 26(1), pages 53-90.
    18. Weiss, Andrew A., 1984. "Systematic sampling and temporal aggregation in time series models," Journal of Econometrics, Elsevier, vol. 26(3), pages 271-281, December.
    19. Tommaso Proietti & Filippo Moauro, 2006. "Dynamic factor analysis with non-linear temporal aggregation constraints," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(2), pages 281-300.
    20. Lutkepohl, Helmut, 1981. "A model for non-negative and non-positive distributed lag functions," Journal of Econometrics, Elsevier, vol. 16(2), pages 211-219, June.
    21. Michael P. Clements & Ana Beatriz Galvao, 2009. "Forecasting US output growth using leading indicators: an appraisal using MIDAS models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(7), pages 1187-1206.
    22. Marie Diron, 2008. "Short-term forecasts of euro area real GDP growth: an assessment of real-time performance based on vintage data," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(5), pages 371-390.
    23. Marcellino, Massimiliano, 1999. "Some Consequences of Temporal Aggregation in Empirical Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 129-136, January.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    mixed data sampling; distributed lag polynomals; time aggregation; now-casting;

    JEL classification:

    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zbw:bubdp1:201135. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (ZBW - German National Library of Economics). General contact details of provider: http://edirc.repec.org/data/dbbgvde.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.