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U-MIDAS: MIDAS regressions with unrestricted lag polynomials

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

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.

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Paper provided by Deutsche Bundesbank, Research Centre in its series Discussion Paper Series 1: Economic Studies with number 2011,35.

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Date of creation: 2011
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Handle: RePEc:zbw:bubdp1:201135
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  1. Andreou, Elena & Ghysels, Eric & Kourtellos, Andros, 2010. "Regression models with mixed sampling frequencies," Journal of Econometrics, Elsevier, vol. 158(2), pages 246-261, October.
  2. Kuzin, Vladimir & Marcellino, Massimiliano & Schumacher, Christian, 2009. "MIDAS vs. mixed-frequency VAR: Nowcasting GDP in the Euro Area," CEPR Discussion Papers 7445, C.E.P.R. Discussion Papers.
  3. Diron, Marie, 2006. "Short-term forecasts of euro area real GDP growth: an assessment of real-time performance based on vintage data," Working Paper Series 0622, European Central Bank.
  4. Giannone, Domenico & Reichlin, Lucrezia & Small, David H., 2006. "Nowcasting GDP and inflation: the real-time informational content of macroeconomic data releases," Working Paper Series 0633, European Central Bank.
  5. 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.
  6. 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.
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