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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
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    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, Decembrie.
    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.
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    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

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