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

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  • Eric Ghysels
  • J. Isaac Miller

Abstract

type="main" xml:id="jtsa12129-abs-0001"> We examine the effects of mixed sampling frequencies and temporal aggregation on the size of commonly used tests for cointegration, and we find that these effects may be severe. Matching sampling schemes of all series generally reduces size distortion, and the nominal size is obtained asymptotically only when all series are skip sampled in the same way – for example, end-of-period sampling. We propose and analyse mixed-frequency versions of the cointegration tests in order to control the size when some high-frequency data are available. Otherwise, when no high-frequency data are available, we discuss controlling size using bootstrapped critical values. We test stock prices and dividends for cointegration as an empirical demonstration.

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  • 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.
    • Handle: RePEc:bla:jtsera:v:36:y:2015:i:6:p:797-816
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    Cited by:

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    2. 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.
    3. 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.
    4. Götz, Thomas B. & Hecq, Alain, 2014. "Nowcasting causality in mixed frequency vector autoregressive models," Economics Letters, Elsevier, vol. 122(1), pages 74-78.
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    6. 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.
    7. 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.
    8. John Cotter & Mark Hallam & Kamil Yilmaz, 2017. "Mixed-frequency macro-financial spillovers," Working Papers 201704, Geary Institute, University College Dublin.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Cláudia Duarte, 2015. "Covariate-augmented unit root tests with mixed-frequency data," Working Papers w201507, Banco de Portugal, Economics and Research Department.
    16. Chambers, Marcus J., 2016. "The estimation of continuous time models with mixed frequency data," Journal of Econometrics, Elsevier, vol. 193(2), pages 390-404.
    17. Mamingi Nlandu, 2017. "Beauty and Ugliness of Aggregation over Time: A Survey," Review of Economics, De Gruyter, vol. 68(3), pages 205-227, December.
    18. 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).
    19. 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.

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    • 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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