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Spurius regression theory with nonstationary fractionally integrated processes

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  • Marmol, Francesc

Abstract

This paper develops an analytical study of the asymptotic distributions obtained when we run linear regressions in the levels of nonstationary fractionally integrated FI(d) processes, that are spuriously related in a multivariate single-equation setting which aIIows for the existence of co integrating relationships and quite general deterministic components. In doing this, the analytical studies of PhiIIips (1986), haldrup (1994) and Marmol (1995, 1996) are embedded in our results.

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  • Marmol, Francesc, 1997. "Spurius regression theory with nonstationary fractionally integrated processes," DES - Working Papers. Statistics and Econometrics. WS 10733, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:10733
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    1. Marmol, Francesc, 1996. "Nonsense Regressions between Integrated Processes of Different Orders," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(3), pages 525-536, August.
    2. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
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    6. Haldrup, Niels, 1994. "The asymptotics of single-equation cointegration regressions with I(1) and I(2) variables," Journal of Econometrics, Elsevier, vol. 63(1), pages 153-181, July.
    7. repec:crs:wpaper:8913 is not listed on IDEAS
    8. Hassler, Uwe, 1996. "Spurious regressions when stationary regressors are included," Economics Letters, Elsevier, vol. 50(1), pages 25-31, January.
    9. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
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    11. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
    12. Juan J. Dolado & Francisco Mármol, 1996. "Efficient Estimation of Cointegrating Relationships Among Higher Order and Fractionally Integrated Processes," Working Papers 9617, Banco de España.
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    Cited by:

    1. D. Ventosa-Santaulària, 2009. "Spurious Regression," Journal of Probability and Statistics, Hindawi, vol. 2009, pages 1-27, August.
    2. Aparicio, Felipe M. & Escribano, Álvaro & Mármol, Francesc, 1999. "A new instrumental variable approach for estimation and testing in fractional cointegrating regressions," DES - Working Papers. Statistics and Econometrics. WS 6298, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Noriega Antonio E. & Ventosa-Santaulària Daniel, 2006. "Spurious Regression and Econometric Trends," Working Papers 2006-05, Banco de México.
    4. Phillips, Peter C.B., 2005. "Challenges of trending time series econometrics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(5), pages 401-416.
    5. McHale, I.G. & Peel, D.A., 2010. "Habit and long memory in UK lottery sales," Economics Letters, Elsevier, vol. 109(1), pages 7-10, October.
    6. Sun, Yixiao, 2006. "Spurious regressions between stationary generalized long memory processes," Economics Letters, Elsevier, vol. 90(3), pages 446-454, March.
    7. Antonio E. Noriega & Daniel Ventosa‐Santaulària, 2006. "Spurious Regression Under Broken‐Trend Stationarity," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(5), pages 671-684, September.
    8. Zhang, Lingxiang, 2013. "Partial unit root and linear spurious regression: A Monte Carlo simulation study," Economics Letters, Elsevier, vol. 118(1), pages 189-191.
    9. Mármol, Francesc, 1999. "How spurious features arise in case of fractional cointegration," DES - Working Papers. Statistics and Econometrics. WS 6349, Universidad Carlos III de Madrid. Departamento de Estadística.
    10. Francesc Marmol & Juan C. Reboredo, 1999. "Near Observational Equivalence and Fractionally Integrated Processes," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(2), pages 283-290, May.
    11. Kruse Robinson & Ventosa-Santaulària Daniel & Noriega Antonio E., 2017. "Changes in persistence, spurious regressions and the Fisher hypothesis," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(3), pages 1-28, June.
    12. Antonio E. Noriega & Daniel Ventosa‐Santaulària, 2007. "Spurious Regression and Trending Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 69(3), pages 439-444, June.
    13. Ferson, Wayne E. & Sarkissian, Sergei & Simin, Timothy, 2008. "Asset Pricing Models with Conditional Betas and Alphas: The Effects of Data Snooping and Spurious Regression," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 43(2), pages 331-353, June.
    14. Lee, Young-Sook & Kim, Tae-Hwan & Newbold, Paul, 2005. "Spurious nonlinear regressions in econometrics," Economics Letters, Elsevier, vol. 87(3), pages 301-306, June.
    15. Mármol, Francesc, 1998. "FM-OLS estimation of cointegrating relationships among nonstationary fractionally integrated processes," DES - Working Papers. Statistics and Econometrics. WS 4672, Universidad Carlos III de Madrid. Departamento de Estadística.
    16. Antonio E. Noriega & Daniel Ventosa-Santaularia, 2005. "Spurious regression under deterministic and stochastic trends," Department of Economics and Finance Working Papers EM200503, Universidad de Guanajuato, Department of Economics and Finance.
    17. Hao Jin & Si Zhang & Jinsuo Zhang, 2017. "Spurious regression due to neglected of non-stationary volatility," Computational Statistics, Springer, vol. 32(3), pages 1065-1081, September.
    18. Noriega Antonio E. & Ventosa-Santaulària Daniel, 2011. "A Simple Test for Spurious Regressions," Working Papers 2011-05, Banco de México.
    19. Wayne E. Ferson & Sergei Sarkissian & Timothy T. Simin, 2003. "Spurious Regressions in Financial Economics?," Journal of Finance, American Finance Association, vol. 58(4), pages 1393-1413, August.
    20. Jin, Hao & Zhang, Jinsuo & Zhang, Si & Yu, Cong, 2013. "The spurious regression of AR(p) infinite-variance sequence in the presence of structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 25-40.
    21. Hualde, Javier, 2006. "Unbalanced Cointegration," Econometric Theory, Cambridge University Press, vol. 22(5), pages 765-814, October.
    22. Chris Stewart, 2011. "A note on spurious significance in regressions involving I(0) and I(1) variables," Empirical Economics, Springer, vol. 41(3), pages 565-571, December.
    23. Stewart, Chris, 2006. "Spurious correlation of I(0) regressors in models with an I(1) dependent variable," Economics Letters, Elsevier, vol. 91(2), pages 184-189, May.
    24. Marmol, Francesc & Velasco, Carlos, 2002. "Trend stationarity versus long-range dependence in time series analysis," Journal of Econometrics, Elsevier, vol. 108(1), pages 25-42, May.
    25. Davidson, James, 2002. "A model of fractional cointegration, and tests for cointegration using the bootstrap," Journal of Econometrics, Elsevier, vol. 110(2), pages 187-212, October.

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