IDEAS home Printed from https://ideas.repec.org/p/aah/create/2010-69.html
   My bibliography  Save this paper

The analysis of nonstationary time series using regression, correlation and cointegration with an application to annual mean temperature and sea level

Author

Listed:
  • Søren Johansen

    (Department of Economics, University of Copenhagen and CREATES, University of Aarhus)

Abstract

There are simple well-known conditions for the validity of regression and correlation as statistical tools. We analyse by examples the effect of nonstationarity on inference using these methods and compare them to model based inference. Finally we analyse some data on annual mean temperature and sea level, by applying the cointegrated vector autoregressive model, which explicitly takes into account the nonstationarity of the variables.

Suggested Citation

  • Søren Johansen, 2010. "The analysis of nonstationary time series using regression, correlation and cointegration with an application to annual mean temperature and sea level," CREATES Research Papers 2010-69, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2010-69
    as

    Download full text from publisher

    File URL: https://repec.econ.au.dk/repec/creates/rp/10/rp10_69.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    2. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    3. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
    4. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
    5. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    6. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    7. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    8. Juselius, Katarina, 2006. "The Cointegrated VAR Model: Methodology and Applications," OUP Catalogue, Oxford University Press, number 9780199285679.
    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. Søren Johansen, 2010. "An Extension of Cointegration to Fractional Autoregressive Processes," Discussion Papers 10-28, University of Copenhagen. Department of Economics.
    2. Matthew T. Holt & Timo Teräsvirta, 2012. "Global Hemispheric Temperature Trends and Co–Shifting: A Shifting Mean Vector Autoregressive Analysis," CREATES Research Papers 2012-54, Department of Economics and Business Economics, Aarhus University.
    3. Laila Taskeen Qazi & Atta Ur Rahman & Saleem Gul, 2015. "Which Pairs of Stocks should we Trade? Selection of Pairs for Statistical Arbitrage and Pairs Trading in Karachi Stock Exchange," The Pakistan Development Review, Pakistan Institute of Development Economics, vol. 54(3), pages 215-244.
    4. Jean Chung & Guanchao Tong & Jiayou Chao & Wei Zhu, 2021. "Path Analysis of Sea-Level Rise and Its Impact," Stats, MDPI, vol. 5(1), pages 1-14, December.
    5. Holt, Matthew T. & Teräsvirta, Timo, 2020. "Global hemispheric temperatures and co-shifting: A vector shifting-mean autoregressive analysis," Journal of Econometrics, Elsevier, vol. 214(1), pages 198-215.

    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. Esther Stroe-Kunold & Joachim Werner, 2009. "A drunk and her dog: a spurious relation? Cointegration tests as instruments to detect spurious correlations between integrated time series," Quality & Quantity: International Journal of Methodology, Springer, vol. 43(6), pages 913-940, November.
    2. Goldberg, Michael D. & Frydman, Roman, 1996. "Empirical exchange rate models and shifts in the co-integrating vector," Structural Change and Economic Dynamics, Elsevier, vol. 7(1), pages 55-78, March.
    3. John Y. Campbell & Pierre Perron, 1991. "Pitfalls and Opportunities: What Macroeconomists Should Know about Unit Roots," NBER Chapters, in: NBER Macroeconomics Annual 1991, Volume 6, pages 141-220, National Bureau of Economic Research, Inc.
    4. Österholm, Pär, 2003. "Testing for Cointegration in Misspecified Systems –A Monte Carlo Study of Size Distortions," Working Paper Series 2003:21, Uppsala University, Department of Economics.
    5. Kerry Patterson & Michael A. Thornton, 2013. "A review of econometric concepts and methods for empirical macroeconomics," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 2, pages 4-42, Edward Elgar Publishing.
    6. Committee, Nobel Prize, 2003. "Time-series Econometrics: Cointegration and Autoregressive Conditional Heteroskedasticity," Nobel Prize in Economics documents 2003-1, Nobel Prize Committee.
    7. Yap, Wei Yim & Lam, Jasmine S.L., 2006. "Competition dynamics between container ports in East Asia," Transportation Research Part A: Policy and Practice, Elsevier, vol. 40(1), pages 35-51, January.
    8. 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.
    9. David F. Hendry & Grayham E. Mizon, 2016. "Improving the teaching of econometrics," Cogent Economics & Finance, Taylor & Francis Journals, vol. 4(1), pages 1170096-117, December.
    10. Geweke, J. & Joel Horowitz & Pesaran, M.H., 2006. "Econometrics: A Bird’s Eye View," Cambridge Working Papers in Economics 0655, Faculty of Economics, University of Cambridge.
    11. Campos, Julia & Ericsson, Neil R. & Hendry, David F., 1996. "Cointegration tests in the presence of structural breaks," Journal of Econometrics, Elsevier, vol. 70(1), pages 187-220, January.
    12. Usman Qamar Sheikh & Muhammad Zafar Iqbal & Hafiz Khalil Ahmad, 2016. "The Impact of Foreign Aid, Energy Production and Human Capital on Income Inequality: A Case Study of Pakistan," Bulletin of Business and Economics (BBE), Research Foundation for Humanity (RFH), vol. 5(1), pages 1-9, March.
    13. Kaminski, Jermain & Hopp, Christian & Tykvová, Tereza, 2019. "New technology assessment in entrepreneurial financing – Does crowdfunding predict venture capital investments?," Technological Forecasting and Social Change, Elsevier, vol. 139(C), pages 287-302.
    14. N. Vijayamohanan Pillai, 2010. "Electricity Demand Analysis and Forecasting- The Tradition is Questioned," Working Papers id:2966, eSocialSciences.
    15. Herzer, Dierk, 2013. "Cross-Country Heterogeneity and the Trade-Income Relationship," World Development, Elsevier, vol. 44(C), pages 194-211.
    16. Masoud Moghaddam, 1997. "Financial innovations and the interest elasticity of money demand: Evidence from an error correction model," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 25(2), pages 155-163, June.
    17. Tang, Chor-Foon & Lau, Evan, 2011. "The Behaviour of Disaggregated Public Expenditures and Income in Malaysia," Review of Applied Economics, Lincoln University, Department of Financial and Business Systems, vol. 7(1-2), pages 1-13, March.
    18. Ericsson, Neil R., 1992. "Cointegration, exogeneity, and policy analysis: An overview," Journal of Policy Modeling, Elsevier, vol. 14(3), pages 251-280, June.
    19. Abhijit Sharma & Theodore Panagiotidis, 2003. "An Analysis of Exports and Growth in India: Some Empirical Evidence (1971-2001)," Working Papers 2003004, The University of Sheffield, Department of Economics, revised Nov 2003.
    20. Ma, Tao & Zhou, Zhou & Abdulhai, Baher, 2015. "Nonlinear multivariate time–space threshold vector error correction model for short term traffic state prediction," Transportation Research Part B: Methodological, Elsevier, vol. 76(C), pages 27-47.

    More about this item

    Keywords

    Regression correlation cointegration; model based inference; likelihood inference; annual mean temperature; sea level;
    All these keywords.

    JEL classification:

    • 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

    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:aah:create:2010-69. 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: the person in charge (email available below). General contact details of provider: http://www.econ.au.dk/afn/ .

    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.