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Optimal Residual Based Tests for Fractional Cointegration and Exchange Rate Dynamics

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  • Morten Oerregaard Nielsen

    (Department of Economics, University of Aarhus, Denmark)

Abstract

We propose a Lagrange Multiplier (LM) test of the null hypothesis of cointegration in fractionally cointegrated models. The test statistic utilizes fully modified residuals to cancel the endogeneity and serial correlation biases, and we show that standard asymptotics apply. With i.i.d. Gaussian errors the asymptotic Gaussian power envelope of all invariant (invariant and unbiased) tests is achieved by the one-sided (two-sided) test. The finite sample properties are illustrated by a Monte Carlo study. In an application to the dynamics among exchange rates for seven major currencies against the US dollar some evidence of the existence of a cointegrating relation is found.

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  • Morten Oerregaard Nielsen, "undated". "Optimal Residual Based Tests for Fractional Cointegration and Exchange Rate Dynamics," Economics Working Papers 2002-7, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:aarhec:2002-7
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    References listed on IDEAS

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    1. Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 165-188.
    2. repec:cup:etheor:v:7:y:1991:i:1:p:1-21 is not listed on IDEAS
    3. 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.
    4. Nielsen, Morten Ørregaard, 2004. "Efficient Likelihood Inference In Nonstationary Univariate Models," Econometric Theory, Cambridge University Press, vol. 20(1), pages 116-146, February.
    5. Diebold, Francis X & Gardeazabal, Javier & Yilmaz, Kamil, 1994. "On Cointegration and Exchange Rate Dynamics," Journal of Finance, American Finance Association, vol. 49(2), pages 727-735, June.
    6. 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.
    7. Marinucci, D & Robinson, Peter M., 2001. "Semiparametric fractional cointegration analysis," LSE Research Online Documents on Economics 2269, London School of Economics and Political Science, LSE Library.
    8. Baillie, Richard T & Bollerslev, Tim, 1989. " Common Stochastic Trends in a System of Exchange Rates," Journal of Finance, American Finance Association, vol. 44(1), pages 167-181, March.
    9. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    10. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
    11. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(1), pages 1-21, March.
    12. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(1), pages 99-125.
    13. Diebold, Francis X. & Rudebusch, Glenn D., 1989. "Long memory and persistence in aggregate output," Journal of Monetary Economics, Elsevier, vol. 24(2), pages 189-209, September.
    14. Cheung, Yin-Wong & Lai, Kon S, 1993. "A Fractional Cointegration Analysis of Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 103-112, January.
    15. Lobato, Ignacio N & Velasco, Carlos, 2000. "Long Memory in Stock-Market Trading Volume," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(4), pages 410-427, October.
    16. Michael Dueker & Richard Startz, 1998. "Maximum-Likelihood Estimation Of Fractional Cointegration With An Application To U.S. And Canadian Bond Rates," The Review of Economics and Statistics, MIT Press, vol. 80(3), pages 420-426, August.
    17. Peter C. B. Phillips & Mico Loretan, 1991. "Estimating Long-run Economic Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(3), pages 407-436.
    18. Jeganathan, P., 1999. "On Asymptotic Inference In Cointegrated Time Series With Fractionally Integrated Errors," Econometric Theory, Cambridge University Press, vol. 15(4), pages 583-621, August.
    19. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(4), pages 549-582, August.
    20. Marinucci, D. & Robinson, P. M., 2001. "Semiparametric fractional cointegration analysis," Journal of Econometrics, Elsevier, vol. 105(1), pages 225-247, November.
    21. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    22. D Marinucci & Peter M Robinson, 2001. "Semiparametric Fractional Cointegration Analysis," STICERD - Econometrics Paper Series 420, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    23. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January.
    24. Baillie, Richard T & Bollerslev, Tim, 1994. "Cointegration, Fractional Cointegration, and Exchange Rate Dynamics," Journal of Finance, American Finance Association, vol. 49(2), pages 737-745, June.
    25. Jansson, Michael, 2005. "Point optimal tests of the null hypothesis of cointegration," Journal of Econometrics, Elsevier, vol. 124(1), pages 187-201, January.
    26. Christos Agiakloglou & Paul Newbold, 1994. "Lagrange Multiplier Tests For Fractional Difference," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(3), pages 253-262, May.
    27. Shin, Yongcheol, 1994. "A Residual-Based Test of the Null of Cointegration Against the Alternative of No Cointegration," Econometric Theory, Cambridge University Press, vol. 10(1), pages 91-115, March.
    28. Jansson, Michael & Haldrup, Niels, 2002. "Regression Theory For Nearly Cointegrated Time Series," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1309-1335, December.
    29. Peter C.B. Phillips & Bruce E. Hansen, 1988. "Statistical Inference in Instrumental Variables," Cowles Foundation Discussion Papers 869R, Cowles Foundation for Research in Economics, Yale University, revised Apr 1989.
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    Cited by:

    1. de Truchis, Gilles & Dell’Eva, Cyril & Keddad, Benjamin, 2017. "On exchange rate comovements: New evidence from a Taylor rule fundamentals model with adaptive learning," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 48(C), pages 82-98.
    2. de Truchis, Gilles & Keddad, Benjamin, 2016. "On the risk comovements between the crude oil market and U.S. dollar exchange rates," Economic Modelling, Elsevier, vol. 52(PA), pages 206-215.
    3. Bent Jesper Christensen & Robinson Kruse & Philipp Sibbertsen, 2013. "A unified framework for testing in the linear regression model under unknown order of fractional integration," CREATES Research Papers 2013-35, Department of Economics and Business Economics, Aarhus University.
    4. Cheng, Xu & Phillips, Peter C.B., 2012. "Cointegrating rank selection in models with time-varying variance," Journal of Econometrics, Elsevier, vol. 169(2), pages 155-165.
    5. Marcel Aloy & Gilles de Truchis, 2012. "Estimation and Testing for Fractional Cointegration," Working Papers halshs-00793206, HAL.
    6. Katarzyna Łasak & Carlos Velasco, 2015. "Fractional Cointegration Rank Estimation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 241-254, April.
    7. Demetrescu, Matei & Kusin, Vladimir & Salish, Nazarii, 2022. "Testing for no cointegration in vector autoregressions with estimated degree of fractional integration," Economic Modelling, Elsevier, vol. 108(C).
    8. Luis A. Gil-Alana & Christophe André & Rangan Gupta & Tsangyao Chang & Omid Ranjbar, 2016. "The Feldstein--Horioka puzzle in South Africa: A fractional cointegration approach," The Journal of International Trade & Economic Development, Taylor & Francis Journals, vol. 25(7), pages 978-991, October.
    9. Morten Orregaard Nielsen, 2004. "Efficient inference in multivariate fractionally integrated time series models," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 63-97, June.
    10. Nielsen, Morten Orregaard & Shimotsu, Katsumi, 2007. "Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach," Journal of Econometrics, Elsevier, vol. 141(2), pages 574-596, December.
    11. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    12. Mauro Costantini & Roy Cerqueti, 2007. "Non parametric Fractional Cointegration Analysis," ISAE Working Papers 78, ISTAT - Italian National Institute of Statistics - (Rome, ITALY).
    13. Frank S. Nielsen, 2009. "Local Whittle estimation of multivariate fractionally integrated processes," CREATES Research Papers 2009-38, Department of Economics and Business Economics, Aarhus University.
    14. Banerjee, Anindya & Urga, Giovanni, 2005. "Modelling structural breaks, long memory and stock market volatility: an overview," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 1-34.
    15. Avarucci, Marco & Velasco, Carlos, 2009. "A Wald test for the cointegration rank in nonstationary fractional systems," Journal of Econometrics, Elsevier, vol. 151(2), pages 178-189, August.
    16. Aaron D. Smallwood & Stefan C. Norrbin, 2006. "Generalized long memory processes, failure of cointegration tests and exchange rate dynamics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(4), pages 409-417, May.
    17. Frank S. Nielsen, 2011. "Local Whittle estimation of multi‐variate fractionally integrated processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(3), pages 317-335, May.
    18. Gil-Alana, Luis A. & Carcel, Hector, 2020. "A fractional cointegration var analysis of exchange rate dynamics," The North American Journal of Economics and Finance, Elsevier, vol. 51(C).

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    More about this item

    Keywords

    Cointegration Test; Fully Modified Estimation; Nonstationarity; Optimal Test; Power Envelope;
    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

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