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Semiparametric Estimation in Time-Series Regression with Long-Range Dependence

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  • Morten Orregaard Nielsen

Abstract

We consider semiparametric estimation in time-series regression in the presence of long-range dependence in both the errors and the stochastic regressors. A central limit theorem is established for a class of semiparametric frequency domain-weighted least squares estimates, which includes both narrow-band ordinary least squares and narrow-band generalized least squares as special cases. The estimates are semiparametric in the sense that focus is on the neighbourhood of the origin, and only periodogram ordinates in a degenerating band around the origin are used. This setting differs from earlier studies on time-series regression with long-range dependence, where a fully parametric approach has been employed. The generalized least squares estimate is infeasible when the degree of long-range dependence is unknown and must be estimated in an initial step. In that case, we show that a feasible estimate which has the same asymptotic properties as the infeasible estimate, exists. By Monte Carlo simulation, we evaluate the finite-sample performance of the generalized least squares estimate and the feasible estimate. Copyright 2005 Blackwell Publishing Ltd.

Suggested Citation

  • Morten Orregaard Nielsen, 2005. "Semiparametric Estimation in Time-Series Regression with Long-Range Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(2), pages 279-304, March.
  • Handle: RePEc:bla:jtsera:v:26:y:2005:i:2:p:279-304
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    References listed on IDEAS

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    1. Lobato, I. & Robinson, P. M., 1996. "Averaged periodogram estimation of long memory," Journal of Econometrics, Elsevier, vol. 73(1), pages 303-324, July.
    2. Lobato, Ignacio N., 1999. "A semiparametric two-step estimator in a multivariate long memory model," Journal of Econometrics, Elsevier, vol. 90(1), pages 129-153, May.
    3. Hassler, U. & Marmol, F. & Velasco, C., 2006. "Residual log-periodogram inference for long-run relationships," Journal of Econometrics, Elsevier, vol. 130(1), pages 165-207, January.
    4. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    5. Tsay, Wen-Jen & Chung, Ching-Fan, 2000. "The spurious regression of fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 96(1), pages 155-182, May.
    6. Hannan, E. J., 1979. "The central limit theorem for time series regression," Stochastic Processes and their Applications, Elsevier, vol. 9(3), pages 281-289, December.
    7. Carlos Velasco, 2003. "Gaussian Semi-parametric Estimation of Fractional Cointegration," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(3), pages 345-378, May.
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    Citations

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    Cited by:

    1. Peter M Robinson, 2007. "Multiple Local Whittle Estimation in StationarySystems," STICERD - Econometrics Paper Series 525, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. Robinson, Peter M., 2007. "Multiple local whittle estimation in stationary systems," LSE Research Online Documents on Economics 4436, London School of Economics and Political Science, LSE Library.
    3. Morten Ørregaard Nielsen & Per Frederiksen, 2011. "Fully modified narrow‐band least squares estimation of weak fractional cointegration," Econometrics Journal, Royal Economic Society, vol. 14, pages 77-120, February.
    4. Afonso da Silva & Peter Robinson, 2008. "Finite Sample Performance in Cointegration Analysis of Nonlinear Time Series with Long Memory," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 268-297.
    5. George Kapetanios & Zacharias Psaradakis, 2007. "Semiparametric Sieve-Type GLS Inference in Regressions with Long-Range Dependence," Working Papers 587, Queen Mary University of London, School of Economics and Finance.
    6. Torben G. Andersen & Rasmus T. Varneskov, 2702. "Consistent Inference for Predictive Regressions in Persistent VAR Economies," CREATES Research Papers 2018-09, Department of Economics and Business Economics, Aarhus University.
    7. Do, Hung Xuan & Brooks, Robert Darren & Treepongkaruna, Sirimon, 2013. "Generalized impulse response analysis in a fractionally integrated vector autoregressive model," Economics Letters, Elsevier, vol. 118(3), pages 462-465.
    8. Ørregaard Nielsen, Morten, 2004. "Local empirical spectral measure of multivariate processes with long range dependence," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 145-166, January.
    9. George Kapetanios & Zacharias Psaradakis, 2007. "Semiparametric Sieve-Type GLS Inference in Regressions with Long-Range Dependence," Working Papers 587, Queen Mary University of London, School of Economics and Finance.
    10. Morten Ørregaard Nielsen & Per Frederiksen, 2008. "Fully Modified Narrow-Band Least Squares Estimation of Stationary Fractional Cointegration," Working Papers 1171, Queen's University, Department of Economics.

    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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