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Fractional integration versus trend stationary in time series analysis

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  • Marmol, Francesc

Abstract

The objective of this paper is to study the effects of spurious detrending of a nonstationary fractionally integrated process (NFI(d), d ~5) on the performance of the traditional least squares estimators and tests. We extend previous work on the subject undertaken by Durlauf and Phillips (1988) which considered only the leading difference stationary (d = 1) case. Moreover, we also consider the possibility of a double misspecification both in the stochastic and in the nonstochastic trends. Standard t-Student tests are shown to diverge in distribution invalidating any inference concerning the presence of time trends. On the other hand, we prove that, even under this double misspecification, the Durbin-Watson statistic remains to be a useful misspecification test,

Suggested Citation

  • Marmol, Francesc, 1997. "Fractional integration versus trend stationary in time series analysis," DES - Working Papers. Statistics and Econometrics. WS 10498, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:10498
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    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. Francesc Marmol, 1995. "SPURIOUS REGRESSIONS BETWEEN I(d) PROCESSES," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(3), pages 313-321, May.
    3. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    4. Chambers, Marcus J., 1996. "Fractional integration, trend stationarity and difference stationarity Evidence from some U.K. macroeconomic time series," Economics Letters, Elsevier, vol. 50(1), pages 19-24, January.
    5. Durlauf, Steven N & Phillips, Peter C B, 1988. "Trends versus Random Walks in Time Series Analysis," Econometrica, Econometric Society, vol. 56(6), pages 1333-1354, November.
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    1. Hassler, Uwe & Marmol, Francesc, 1998. "Fractional cointegrating regressions in the presence of linear time trends," DES - Working Papers. Statistics and Econometrics. WS 9794, Universidad Carlos III de Madrid. Departamento de Estadística.

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