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Testing for Cointegration with Temporally Aggregated and Mixed-frequency Time Series

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Abstract

We examine the effects of mixed sampling frequencies and temporal aggregation on standard tests for cointegration. While it is well known that aggregation and sampling frequency do not affect the long-run properties of time series, we find that the effects of aggregation on the size of commonly used tests may be severe. Matching sampling schemes of all series generally reduces size, and the nominal size is obtained when all series are skip-sampled in the same way -- e.g., end-of-period sampling. When matching is not feasible, the size of the likelihood-based trace test may be improved by using a mixed-frequency model rather than an aggregated model. However, a mixed-frequency strategy may not improve the size distortion of residual-based cointegration tests compared to aggregated series. We test stock prices and dividends for cointegration as an empirical demonstration of the size distortion.

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  • Eric Ghysels & J. Isaac Miller, 2013. "Testing for Cointegration with Temporally Aggregated and Mixed-frequency Time Series," Working Papers 1307, Department of Economics, University of Missouri, revised 07 May 2014.
  • Handle: RePEc:umc:wpaper:1307
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    Cited by:

    1. Chambers, Marcus J., 2020. "Frequency domain estimation of cointegrating vectors with mixed frequency and mixed sample data," Journal of Econometrics, Elsevier, vol. 217(1), pages 140-160.
    2. Thomas B. Götz & Alain W. Hecq, 2019. "Granger Causality Testing in Mixed‐Frequency VARs with Possibly (Co)Integrated Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 40(6), pages 914-935, November.
    3. Lixiong Yang, 2022. "Threshold mixed data sampling (TMIDAS) regression models with an application to GDP forecast errors," Empirical Economics, Springer, vol. 62(2), pages 533-551, February.
    4. Marçal, Emerson Fernandes & Zimmermann, Beatrice & de Prince, Diogo & Merlin, Giovanni, 2018. "Assessing interdependence among countries' fundamentals and its implications for exchange rate misalignment estimates: An empirical exercise based on GVAR," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 72(4), December.
    5. Götz, Thomas B. & Hecq, Alain & Smeekes, Stephan, 2016. "Testing for Granger causality in large mixed-frequency VARs," Journal of Econometrics, Elsevier, vol. 193(2), pages 418-432.
    6. 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.
    7. Cláudia Duarte, 2015. "Covariate-augmented unit root tests with mixed-frequency data," Working Papers w201507, Banco de Portugal, Economics and Research Department.
    8. Götz, Thomas B. & Hecq, Alain, 2014. "Nowcasting causality in mixed frequency vector autoregressive models," Economics Letters, Elsevier, vol. 122(1), pages 74-78.
    9. Mamingi Nlandu, 2017. "Beauty and Ugliness of Aggregation over Time: A Survey," Review of Economics, De Gruyter, vol. 68(3), pages 205-227, December.
    10. Ghysels, Eric & Hill, Jonathan B. & Motegi, Kaiji, 2016. "Testing for Granger causality with mixed frequency data," Journal of Econometrics, Elsevier, vol. 192(1), pages 207-230.
    11. Marçal, Emerson Fernandes & Zimmermann, Beatrice Aline & Mendonça, Diogo de Prince & Merlin, Giovanni Tondin, 2015. "Does mixed frequency vector error correction model add relevant information to exchange misalignment calculus? Evidence for United States," Textos para discussão 385, FGV EESP - Escola de Economia de São Paulo, Fundação Getulio Vargas (Brazil).
    12. Chang, Yoosoon & Kim, Chang Sik & Miller, J. Isaac & Park, Joon Y. & Park, Sungkeun, 2014. "Time-varying Long-run Income and Output Elasticities of Electricity Demand with an Application to Korea," Energy Economics, Elsevier, vol. 46(C), pages 334-347.
    13. Chambers, Marcus J., 2016. "The estimation of continuous time models with mixed frequency data," Journal of Econometrics, Elsevier, vol. 193(2), pages 390-404.
    14. J. Isaac Miller, 2019. "Testing Cointegrating Relationships Using Irregular and Non‐Contemporaneous Series with an Application to Paleoclimate Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 40(6), pages 936-950, November.
    15. Miller, J. Isaac, 2018. "Simple robust tests for the specification of high-frequency predictors of a low-frequency series," Econometrics and Statistics, Elsevier, vol. 5(C), pages 45-66.
    16. 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.
    17. John Cotter & Mark Hallam & Kamil Yilmaz, 2017. "Mixed-frequency macro-financial spillovers," Working Papers 201704, Geary Institute, University College Dublin.
    18. Eric Ghysels & J. Isaac Miller, 2014. "On the Size Distortion from Linearly Interpolating Low-frequency Series for Cointegration Tests," Advances in Econometrics, in: Essays in Honor of Peter C. B. Phillips, volume 14, pages 93-122, Emerald Group Publishing Limited.
    19. Yoosoon Chang & Chang Sik Kim & J. Isaac Miller & Joon Y. Park & Sungkeun Park, 2014. "Time-varying Long-run Income and Output Elasticities of Electricity Demand," Working Papers 1409, Department of Economics, University of Missouri.

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    More about this item

    Keywords

    temporal aggregation; mixed sampling frequencies; cointegration; trace test; residual-based cointegration test;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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