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U-MIDAS : MIDAS regressions with unrestricted lag polynomials
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Deutsche Bundesbank; Series 1 : Economic Studies Discussion Paper; 2011/35
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FORONI, Claudia, MARCELLINO, Massimiliano, SCHUMACHER, Christian, U-MIDAS : MIDAS regressions with unrestricted lag polynomials, Deutsche Bundesbank, Series 1 : Economic Studies Discussion Paper, 2011/35 - https://hdl.handle.net/1814/40284
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 di§erence 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, di§erences 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 identiÖcation issues, and show that their parameters can be estimated by OLS. In Monte Carlo experiments, we compare UMIDAS 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 di§erences in sampling frequencies, distributed lag-functions outperform unrestricted polynomials. In an empirical application on outof-sample nowcasting GDP in the US and the Euro area using monthly predictors, we Önd 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.