IDEAS home Printed from https://ideas.repec.org/p/umc/wpaper/1905.html
   My bibliography  Save this paper

Time-Varying Cointegration and the Kalman Filter

Author

Listed:
  • Burak Alparslan Eroglu
  • J. Isaac Miller

    (Department of Economics, University of Missouri)

  • Taner Yigit

Abstract

Published in Econometric Reviews (https://doi.org/10.1080/07474938.2020.1861776) We show that time-varying parameter state-space models estimated using the Kalman filter are particularly vulnerable to the problem of spurious regression, because the integrated error is transferred to the estimated state equation. We offer a simple yet effective methodology to reliably recover the instability in cointegrating vectors. In the process, the proposed methodology successfully distinguishes between the cases of no cointegration, fixed cointegration, and time-varying cointegration. We apply these proposed tests to elucidate the relationship between concentrations of greenhouse gases and global temperatures, an important relationship to both climate scientists and economists.

Suggested Citation

  • Burak Alparslan Eroglu & J. Isaac Miller & Taner Yigit, 2019. "Time-Varying Cointegration and the Kalman Filter," Working Papers 1905, Department of Economics, University of Missouri.
    • Handle: RePEc:umc:wpaper:1905
    as

    Download full text from publisher

    File URL: https://drive.google.com/file/d/1JLxA-OcS_cN5VQVWrEEgjWkSmljlc-3T/view?usp=sharing
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Honohan, Patrick, 1993. "Cointegration and time-varying parameters : A comment," European Economic Review, Elsevier, vol. 37(6), pages 1279-1281, August.
    2. Seo, Byeongseon, 1998. "Tests For Structural Change In Cointegrated Systems," Econometric Theory, Cambridge University Press, vol. 14(2), pages 222-259, April.
    3. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(3), pages 269-298, June.
    4. 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.
    5. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    6. Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 379-400, July.
    7. Park, Joon Y. & Hahn, Sang B., 1999. "Cointegrating Regressions With Time Varying Coefficients," Econometric Theory, Cambridge University Press, vol. 15(5), pages 664-703, October.
    8. Henrik Hansen & Søren Johansen, 1999. "Some tests for parameter constancy in cointegrated VAR-models," Econometrics Journal, Royal Economic Society, vol. 2(2), pages 306-333.
    9. Evans, Martin, 1991. "Discovering the Link between Inflation Rates and Inflation Uncertainty," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 23(2), pages 169-184, May.
    10. Yoosoon Chang & Joon Y. Park & Peter C. B. Phillips, 2001. "Nonlinear econometric models with cointegrated and deterministically trending regressors," Econometrics Journal, Royal Economic Society, vol. 4(1), pages 1-36.
    11. Cooley, Thomas F & Prescott, Edward C, 1976. "Estimation in the Presence of Stochastic Parameter Variation," Econometrica, Econometric Society, vol. 44(1), pages 167-184, January.
    12. Robert Kaufmann & Heikki Kauppi & Michael Mann & James Stock, 2013. "Does temperature contain a stochastic trend: linking statistical results to physical mechanisms," Climatic Change, Springer, vol. 118(3), pages 729-743, June.
    13. Davidson, Russell & MacKinnon, James G., 2007. "Improving the reliability of bootstrap tests with the fast double bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3259-3281, April.
    14. Francisco Estrada & Pierre Perron & Benjamin Martinez-Lopez, 2013. "Statistically-derived contributions of diverse human influences to 20th century temperature changes," Boston University - Department of Economics - Working Papers Series 2013-017, Boston University - Department of Economics.
    15. Kim, Chang-Jin, 2006. "Time-varying parameter models with endogenous regressors," Economics Letters, Elsevier, vol. 91(1), pages 21-26, April.
    16. Hansen, Bruce E., 1992. "Heteroskedastic cointegration," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 139-158.
    17. Kim, Chang-Jin, 1993. "Unobserved-Component Time Series Models with Markov-Switching Heteroscedasticity: Changes in Regime and the Link between Inflation Rates and Inflation Uncertainty," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(3), pages 341-349, July.
    18. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-161, January.
    19. Felix Pretis & Michael Mann & Robert Kaufmann, 2015. "Testing competing models of the temperature hiatus: assessing the effects of conditioning variables and temporal uncertainties through sample-wide break detection," Climatic Change, Springer, vol. 131(4), pages 705-718, August.
    20. de Jong, Robert M., 1997. "Central Limit Theorems for Dependent Heterogeneous Random Variables," Econometric Theory, Cambridge University Press, vol. 13(3), pages 353-367, June.
    21. Canarellsal, Giorgio & Pollard, Stephen K. & Lai, Kon S., 1990. "Cointegration between exchange rates and relative prices: another view," European Economic Review, Elsevier, vol. 34(7), pages 1303-1322, November.
    22. de Jong, Robert & Wang, Chien-Ho, 2005. "Further Results On The Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 21(2), pages 413-430, April.
    23. Martin Leduc & H. Damon Matthews & Ramón de Elía, 2016. "Regional estimates of the transient climate response to cumulative CO2 emissions," Nature Climate Change, Nature, vol. 6(5), pages 474-478, May.
    24. Mirza Trokić, 2019. "Wavelet energy ratio unit root tests," Econometric Reviews, Taylor & Francis Journals, vol. 38(1), pages 69-94, January.
    25. Bierens, Herman J. & Martins, Luis F., 2010. "Time-Varying Cointegration," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1453-1490, October.
    26. McCabe, Brendan & Leybourne, Stephen & Harris, David, 2006. "A Residual-Based Test For Stochastic Cointegration," Econometric Theory, Cambridge University Press, vol. 22(3), pages 429-456, June.
    27. Harris, David & McCabe, Brendan & Leybourne, Stephen, 2002. "Stochastic cointegration: estimation and inference," Journal of Econometrics, Elsevier, vol. 111(2), pages 363-384, December.
    Full references (including those not matched with items on IDEAS)

    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. Miller, Stephen M. & Martins, Luis Filipe & Gupta, Rangan, 2019. "A Time-Varying Approach Of The Us Welfare Cost Of Inflation," Macroeconomic Dynamics, Cambridge University Press, vol. 23(2), pages 775-797, March.
    2. repec:wyi:journl:002195 is not listed on IDEAS
    3. Rickard Sandberg, 2017. "Sample Moments and Weak Convergence to Multivariate Stochastic Power Integrals," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 1000-1009, November.
    4. repec:ipg:wpaper:2014-474 is not listed on IDEAS
    5. Miller J. Isaac, 2010. "A Nonlinear IV Likelihood-Based Rank Test for Multivariate Time Series and Long Panels," Journal of Time Series Econometrics, De Gruyter, vol. 2(1), pages 1-38, September.
    6. Chen, Haiqiang & Fang, Ying & Li, Yingxing, 2015. "Estimation And Inference For Varying-Coefficient Models With Nonstationary Regressors Using Penalized Splines," Econometric Theory, Cambridge University Press, vol. 31(4), pages 753-777, August.
    7. Martins, Luis F. & Gabriel, Vasco J., 2014. "Modelling long run comovements in equity markets: A flexible approach," Journal of Banking & Finance, Elsevier, vol. 47(C), pages 288-295.
    8. Marmer, Vadim, 2008. "Nonlinearity, nonstationarity, and spurious forecasts," Journal of Econometrics, Elsevier, vol. 142(1), pages 1-27, January.
    9. Matei Demetrescu & Christoph Hanck & Adina I. Tarcolea, 2014. "Iv-Based Cointegration Testing In Dependent Panels With Time-Varying Variance," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(5), pages 393-406, August.
    10. Stypka, Oliver & Wagner, Martin & Grabarczyk, Peter & Kawka, Rafael, 2017. "The Asymptotic Validity of "Standard" Fully Modified OLS Estimation and Inference in Cointegrating Polynomial Regressions," Economics Series 333, Institute for Advanced Studies.
    11. Yicong Lin & Hanno Reuvers, 2019. "Efficient Estimation by Fully Modified GLS with an Application to the Environmental Kuznets Curve," Papers 1908.02552, arXiv.org, revised Aug 2020.
    12. Kasparis, Ioannis, 2010. "The Bierens test for certain nonstationary models," Journal of Econometrics, Elsevier, vol. 158(2), pages 221-230, October.
    13. Dong, Chaohua & Linton, Oliver & Peng, Bin, 2021. "A weighted sieve estimator for nonparametric time series models with nonstationary variables," Journal of Econometrics, Elsevier, vol. 222(2), pages 909-932.
    14. David E. Allen & Michael McAleer, 2020. "A Nonlinear Autoregressive Distributed Lag (NARDL) Analysis of West Texas Intermediate Oil Prices and the DOW JONES Index," Energies, MDPI, vol. 13(15), pages 1-11, August.
    15. Dong, Chaohua & Linton, Oliver, 2018. "Additive nonparametric models with time variable and both stationary and nonstationary regressors," Journal of Econometrics, Elsevier, vol. 207(1), pages 212-236.
    16. Demetrescu Matei, 2009. "Panel Unit Root Testing with Nonlinear Instruments for Infinite-Order Autoregressive Processes," Journal of Time Series Econometrics, De Gruyter, vol. 1(2), pages 1-30, December.
    17. Tu, Yundong & Liang, Han-Ying & Wang, Qiying, 2022. "Nonparametric inference for quantile cointegrations with stationary covariates," Journal of Econometrics, Elsevier, vol. 230(2), pages 453-482.
    18. Biqing Cai & Jiti Gao & Dag Tjøstheim, 2017. "A New Class of Bivariate Threshold Cointegration Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 288-305, April.
    19. Hong, Seung Hyun & Phillips, Peter C. B., 2010. "Testing Linearity in Cointegrating Relations With an Application to Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 96-114.
    20. repec:zbw:bofitp:2011_027 is not listed on IDEAS
    21. Arai, Yoichi, 2016. "Testing For Linearity In Regressions With I(1) Processes," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 57(1), pages 111-138, June.
    22. Chen, Li & Gao, Jiti & Vahid, Farshid, 2022. "Global temperatures and greenhouse gases: A common features approach," Journal of Econometrics, Elsevier, vol. 230(2), pages 240-254.
    23. Lee, Jungick & de Jong, Robert M., 2008. "Exponential functionals of integrated processes," Economics Letters, Elsevier, vol. 100(2), pages 181-184, August.

    More about this item

    Keywords

    : time-varying cointegration; Kalman filter; spurious regression;
    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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • 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:1905. 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.