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Testing Cointegrating Relationships Using Irregular and Non-Contemporaneous Series with an Application to Paleoclimate Data

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  • J. Isaac Miller

    (Department of Economics, University of Missouri, Columbia, Missouri, USA)

Abstract

Published in the Journal of Time Series Analysis (https://doi.org/10.1111/jtsa.12469) Time series that are observed neither regularly nor contemporaneously pose problems for most multivariate analyses. Common and intuitive solutions to these problems include linear and step interpolation or other types of imputation to a higher, regular frequency. However, interpolation is known to cause serious problems with the size and power of statistical tests. Due to the difficulty in measuring stochastically varying paleoclimate phenomena such as CO2 concentrations and surface temperatures, time series of such measurements are observed neither regularly nor contemporaneously. This paper presents large- and small-sample analyses of the size and power of cointegration tests of time series with these features and confirms the robustness of cointegration of these two series found in the extant literature. Step interpolation is preferred over linear interpolation.

Suggested Citation

  • J. Isaac Miller, 2018. "Testing Cointegrating Relationships Using Irregular and Non-Contemporaneous Series with an Application to Paleoclimate Data," Working Papers 1809, Department of Economics, University of Missouri.
    • Handle: RePEc:umc:wpaper:1809
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    1. 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.
    2. Marcus J. Chambers, 2011. "Cointegration and sampling frequency," Econometrics Journal, Royal Economic Society, vol. 14(2), pages 156-185, July.
    3. Johansen, Soren & Juselius, Katarina, 1990. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 52(2), pages 169-210, May.
    4. Heino Bohn Nielsen, 2004. "Cointegration analysis in the presence of outliers," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 249-271, June.
    5. Franses, Philip Hans & Haldrup, Niels, 1994. "The Effects of Additive Outliers on Tests for Unit Roots and Cointegration," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 471-478, October.
    6. Dieter Lüthi & Martine Le Floch & Bernhard Bereiter & Thomas Blunier & Jean-Marc Barnola & Urs Siegenthaler & Dominique Raynaud & Jean Jouzel & Hubertus Fischer & Kenji Kawamura & Thomas F. Stocker, 2008. "High-resolution carbon dioxide concentration record 650,000–800,000 years before present," Nature, Nature, vol. 453(7193), pages 379-382, May.
    7. J. Isaac Miller, 2010. "Cointegrating regressions with messy regressors and an application to mixed‐frequency series," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(4), pages 255-277, July.
    8. Phillips, P C B, 1991. "Error Correction and Long-Run Equilibrium in Continuous Time," Econometrica, Econometric Society, vol. 59(4), pages 967-980, July.
    9. Corradi, Valentina, 1997. "Comovements Between Diffusion Processes," Econometric Theory, Cambridge University Press, vol. 13(5), pages 646-666, October.
    10. Chambers, Marcus J., 2003. "The Asymptotic Efficiency Of Cointegration Estimators Under Temporal Aggregation," Econometric Theory, Cambridge University Press, vol. 19(1), pages 49-77, February.
    11. Busetti, Fabio & Taylor, A.M. Robert, 2005. "Stationarity Tests For Irregularly Spaced Observations And The Effects Of Sampling Frequency On Power," Econometric Theory, Cambridge University Press, vol. 21(4), pages 757-794, August.
    12. 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.
    13. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-193, January.
    14. Johansen, Søren & Juselius, Katarina, 1992. "Testing structural hypotheses in a multivariate cointegration analysis of the PPP and the UIP for UK," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 211-244.
    15. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    16. 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.
    17. James E. H. Davidson & David B. Stephenson & Alemtsehai A. Turasie, 2016. "Time series modeling of paleoclimate data," Environmetrics, John Wiley & Sons, Ltd., vol. 27(1), pages 55-65, February.
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    Cited by:

    1. Burak Alparslan Eroğlu & J. Isaac Miller & Taner Yiğit, 2022. "Time-varying cointegration and the Kalman filter," Econometric Reviews, Taylor & Francis Journals, vol. 41(1), pages 1-21, January.

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    More about this item

    Keywords

    cointegration; irregularly time series; non-contemporaneous time series; misaligned time series; paleoclimate data;
    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
    • 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
    • Q54 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Climate; Natural Disasters and their Management; Global Warming

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