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Simple Robust Tests for the Specification of High-Frequency Predictors of a Low-Frequency Series

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Abstract

I propose two variable addition test statistics aimed at the specification of a high-frequency predictor of a series observed at a lower frequency. Under the null, the high-frequency predictor is aggregated to the low frequency versus mixed-frequency alternatives. The first test statistic is similar to those in the extant literature, but I show its robustness to conditionally biased forecast error and cointegrated and deterministically trending covariates. It is feasible and consistent even if estimation is not feasible under the alternative. However, its size is not robust to nuisance parameters when the high-frequency predictor is stochastically trending, and size distortion may be severe. The second test statistic is a simple modification of the first that sacrifices power in order to correct this distortion. An application to forecasting and nowcasting monthly state-level retail gasoline prices illustrates how the test statistics may be utilized when the presence of nuisance parameters and orders of integration are unknown.

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  • J. Isaac Miller, 2014. "Simple Robust Tests for the Specification of High-Frequency Predictors of a Low-Frequency Series," Working Papers 1412, Department of Economics, University of Missouri.
    • Handle: RePEc:umc:wpaper:1412
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    1. Wu, De-Min, 1973. "Alternative Tests of Independence Between Stochastic Regressors and Disturbances," Econometrica, Econometric Society, vol. 41(4), pages 733-750, July.
    2. Eric Ghysels & J. Isaac Miller, 2015. "Testing for Cointegration with Temporally Aggregated and Mixed-Frequency Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(6), pages 797-816, November.
    3. Francis X. Diebold, 2015. "Comparing Predictive Accuracy, Twenty Years Later: A Personal Perspective on the Use and Abuse of Diebold-Mariano Tests," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 1-1, January.
    4. Anthony S. Tay, 2007. "Financial Variables as Predictors of Real Output Growth," Development Economics Working Papers 22482, East Asian Bureau of Economic Research.
    5. 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.
    6. Clark, Todd E. & McCracken, Michael W., 2001. "Tests of equal forecast accuracy and encompassing for nested models," Journal of Econometrics, Elsevier, vol. 105(1), pages 85-110, November.
    7. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-1084, September.
    8. Thomas B. Götz & Alain Hecq & Jean‐Pierre Urbain, 2014. "Forecasting Mixed‐Frequency Time Series with ECM‐MIDAS Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(3), pages 198-213, April.
    9. Michelle T. Armesto & Kristie M. Engemann & Michael T. Owyang, 2010. "Forecasting with mixed frequencies," Review, Federal Reserve Bank of St. Louis, vol. 92(Nov), pages 521-536.
    10. 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.
    11. 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.
    12. Schumacher, Christian & Breitung, Jörg, 2008. "Real-time forecasting of German GDP based on a large factor model with monthly and quarterly data," International Journal of Forecasting, Elsevier, vol. 24(3), pages 386-398.
    13. J. Isaac Miller, 2014. "Mixed-frequency Cointegrating Regressions with Parsimonious Distributed Lag Structures," Journal of Financial Econometrics, Oxford University Press, vol. 12(3), pages 584-614.
    14. Elena Andreou & Eric Ghysels & Andros Kourtellos, 2013. "Should Macroeconomic Forecasters Use Daily Financial Data and How?," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(2), pages 240-251, April.
    15. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    16. 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.
    17. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2004. "The MIDAS Touch: Mixed Data Sampling Regression Models," University of California at Los Angeles, Anderson Graduate School of Management qt9mf223rs, Anderson Graduate School of Management, UCLA.
    18. Andreou, Elena & Ghysels, Eric & Kourtellos, Andros, 2010. "Regression models with mixed sampling frequencies," Journal of Econometrics, Elsevier, vol. 158(2), pages 246-261, October.
    19. Phillips, P C B, 1991. "Error Correction and Long-Run Equilibrium in Continuous Time," Econometrica, Econometric Society, vol. 59(4), pages 967-980, July.
    20. J. Isaac Miller, 2016. "Conditionally Efficient Estimation of Long-Run Relationships Using Mixed-Frequency Time Series," Econometric Reviews, Taylor & Francis Journals, vol. 35(6), pages 1142-1171, June.
    21. Kvedaras, Virmantas & Zemlys, Vaidotas, 2012. "Testing the functional constraints on parameters in regressions with variables of different frequency," Economics Letters, Elsevier, vol. 116(2), pages 250-254.
    22. 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.
    23. J. Isaac Miller & Xi Wang, 2016. "Implementing Residual-Based KPSS Tests for Cointegration with Data Subject to Temporal Aggregation and Mixed Sampling Frequencies," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(6), pages 810-824, November.
    24. Elliott, Graham, 2006. "Forecasting with Trending Data," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 11, pages 555-604, Elsevier.
    25. JÖrg Breitung & Christoph Roling, 2015. "Forecasting Inflation Rates Using Daily Data: A Nonparametric MIDAS Approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 34(7), pages 588-603, November.
    26. Neil Kellard & Denise Osborn & Jerry Coakley & Marcus J. Chambers, 2015. "Testing for a Unit Root in a Near-Integrated Model with Skip-Sampled Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(5), pages 630-649, September.
    27. Clements, Michael P & Galvão, Ana Beatriz, 2008. "Macroeconomic Forecasting With Mixed-Frequency Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 546-554.
    28. Anthony Tay, 2007. "Financial Variables as Predictors of Real Output Growth," Working Papers 14-2007, Singapore Management University, School of Economics.
    29. Jens Hogrefe, 2008. "Forecasting data revisions of GDP: a mixed frequency approach," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(3), pages 271-296, August.
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    Cited by:

    1. Yun Liu & Yeonwoo Rho, 2018. "On the Choice of Instruments in Mixed Frequency Specification Tests," Papers 1809.05503, arXiv.org.
    2. Khalaf, Lynda & Kichian, Maral & Saunders, Charles J. & Voia, Marcel, 2021. "Dynamic panels with MIDAS covariates: Nonlinearity, estimation and fit," Journal of Econometrics, Elsevier, vol. 220(2), pages 589-605.

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    More about this item

    Keywords

    temporal aggregation; mixed-frequency model; MIDAS; variable addition test; forecasting model comparison; retail gasoline prices;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • Q41 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Demand and Supply; Prices

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