IDEAS home Printed from https://ideas.repec.org/p/umc/wpaper/1809.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://drive.google.com/file/d/1Ncxr9KU_5XQaRrUVyFjpo3clRlglKgYA/view?usp=sharing
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Marcus J. Chambers, 2011. "Cointegration and sampling frequency," Econometrics Journal, Royal Economic Society, vol. 14(2), pages 156-185, July.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Phillips, P C B, 1991. "Error Correction and Long-Run Equilibrium in Continuous Time," Econometrica, Econometric Society, vol. 59(4), pages 967-980, July.
    11. 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.
    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. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    14. Heino Bohn Nielsen, 2004. "Cointegration analysis in the presence of outliers," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 249-271, June.
    15. Corradi, Valentina, 1997. "Comovements Between Diffusion Processes," Econometric Theory, Cambridge University Press, vol. 13(5), pages 646-666, October.
    16. 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.
    17. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Proietti, Tommaso & Maddanu, Federico, 2024. "Modelling cycles in climate series: The fractional sinusoidal waveform process," Journal of Econometrics, Elsevier, vol. 239(1).
    2. Vasco J.Gabriel & Luis F. Martins & Anthoulla Phella, 2021. "Modelling Low-Frequency Covariability of Paleoclimatic Data," Working Papers 2022_17, Business School - Economics, University of Glasgow.
    3. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chambers, Marcus J., 2016. "The estimation of continuous time models with mixed frequency data," Journal of Econometrics, Elsevier, vol. 193(2), pages 390-404.
    2. 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.
    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. 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.
    5. 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.
    6. Eleni Constantinou & Avo Kazandjian & Georgios P. Kouretas & Vera Tahmazian, 2008. "Common Stochastic Trends Among The Cyprus Stock Exchange And The Ase, Lse And Nyse," Bulletin of Economic Research, Wiley Blackwell, vol. 60(4), pages 327-349, October.
    7. Giorgio Canarella & Stephen M. Miller & Stephen K. Pollard, 2012. "Purchasing Power Parity between the UK and the Euro Area," Working Papers 1208, University of Nevada, Las Vegas , Department of Economics.
    8. Podivinsky, Jan M., 1998. "Testing misspecified cointegrating relationships," Economics Letters, Elsevier, vol. 60(1), pages 1-9, July.
    9. Levent, Korap, 2007. "Modeling purchasing power parity using co-integration: evidence from Turkey," MPRA Paper 19584, University Library of Munich, Germany.
    10. Tor Jacobson & Johan Lyhagen & Rolf Larsson & Marianne Nessén, 2008. "Inflation, exchange rates and PPP in a multivariate panel cointegration model," Econometrics Journal, Royal Economic Society, vol. 11(1), pages 58-79, March.
    11. Levent KORAP, 2008. "Exchange Rate Determination Of Tl/Us$:A Co-Integration Approach," Istanbul University Econometrics and Statistics e-Journal, Department of Econometrics, Faculty of Economics, Istanbul University, vol. 7(1), pages 24-50, May.
    12. Perles-Ribes, José Francisco & Ramón-Rodríguez, Ana Belén & Rubia, Antonio & Moreno-Izquierdo, Luis, 2017. "Is the tourism-led growth hypothesis valid after the global economic and financial crisis? The case of Spain 1957–2014," Tourism Management, Elsevier, vol. 61(C), pages 96-109.
    13. Pedro Hugo Clavijo Cortes, 2017. "Balance comercial y volatilidad del tipo de cambio nominal: Un estudio de series de tiempo para Colombia," Revista Economía y Región, Universidad Tecnológica de Bolívar, vol. 11(1), pages 37-58, June.
    14. Jeremy B. Rudd & Karl Whelan, 2002. "A note on the cointegration of consumption, income, and wealth," Finance and Economics Discussion Series 2002-53, Board of Governors of the Federal Reserve System (U.S.).
    15. Alfred A. Haug, 2002. "Temporal Aggregation and the Power of Cointegration Tests: a Monte Carlo Study," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 64(4), pages 399-412, September.
    16. repec:kap:iaecre:v:15:y:2009:i:4:p:470-482 is not listed on IDEAS
    17. 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.
    18. MacDonald, Ronald & Marsh, Ian W., 2004. "Currency spillovers and tri-polarity: a simultaneous model of the US dollar, German mark and Japanese yen," Journal of International Money and Finance, Elsevier, vol. 23(1), pages 99-111, February.
    19. Mayes, David G. & Vilmunen, Jouko, 1999. "Unemployment in a small open economy: Finland and New Zealand," Bank of Finland Research Discussion Papers 10/1999, Bank of Finland.
    20. Alexander Schätz, 2010. "Macroeconomic Effects on Emerging Market Sector Indices," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 9(2), pages 131-169, August.
    21. 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.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:umc:wpaper:1809. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chao Gu (email available below). General contact details of provider: https://edirc.repec.org/data/edumous.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.