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Semiparametric Estimation in Time Series Regression with Long Range Dependence

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  • Nielsen, Morten Oe.

    (Department of Economics, University of Aarhus, Denmark)

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 neighborhood of the origin, and only periodogram ordinates in a degenerating band around the origin are used. This setting differs from earlier work 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 exists, which has the same asymptotic properties as the infeasible estimate. By Monte Carlo simulation, we evaluate the finite-sample performance of the generalized least squares estimate and the feasible estimate.

Suggested Citation

  • Nielsen, Morten Oe., "undated". "Semiparametric Estimation in Time Series Regression with Long Range Dependence," Economics Working Papers 2002-17, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:aarhec:2002-17
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    References listed on IDEAS

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    1. Javier Hidalgo & Peter M Robinson, 1997. "Time Series Regression with Long Range Dependence - (Now published in 'Annals of Statistics', 25, (1997)pp.2054-2083.)," STICERD - Econometrics Paper Series 318, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
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    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. Lobato, I. & Robinson, P. M., 1996. "Averaged periodogram estimation of long memory," Journal of Econometrics, Elsevier, vol. 73(1), pages 303-324, July.
    7. 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.
    8. 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.
    9. Javier Hidalgo & Peter M. Robinson, 2002. "Adapting to Unknown Disturbance Autocorrelation in Regression with Long Memory," Econometrica, Econometric Society, vol. 70(4), pages 1545-1581, July.
    10. 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.
    11. 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. 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.
    2. Gilles de Truchis & Elena Ivona Dumitrescu & Florent Dubois, 2019. "Local Whittle Analysis of Stationary Unbalanced Fractional Cointegration Systems," EconomiX Working Papers 2019-15, University of Paris Nanterre, EconomiX.
    3. Morten Ø. Nielsen & Per Houmann Frederiksen, 2008. "Fully Modified Narrow-band Least Squares Estimation Of Stationary Fractional Cointegration," Working Paper 1171, Economics Department, Queen's University.
    4. Christian Leschinski & Michelle Voges & Philipp Sibbertsen, 2021. "A comparison of semiparametric tests for fractional cointegration," Statistical Papers, Springer, vol. 62(4), pages 1997-2030, August.
    5. Javier Hualde & Morten {O}rregaard Nielsen, 2022. "Fractional integration and cointegration," Papers 2211.10235, arXiv.org.
    6. George Kapetanios & Zacharias Psaradakis, 2016. "Semiparametric Sieve-Type Generalized Least Squares Inference," Econometric Reviews, Taylor & Francis Journals, vol. 35(6), pages 951-985, June.
    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. 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.
    10. Torben G. Andersen & Rasmus T. Varneskov, 2018. "Consistent Inference for Predictive Regressions in Persistent VAR Economies," CREATES Research Papers 2018-09, Department of Economics and Business Economics, Aarhus University.
    11. Afonso Goncalves 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.
    12. Andersen, Torben G. & Varneskov, Rasmus T., 2021. "Consistent inference for predictive regressions in persistent economic systems," Journal of Econometrics, Elsevier, vol. 224(1), pages 215-244.
    13. 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.
    14. Gilles de Truchis & Elena Ivona Dumitrescu, 2019. "Narrow-band Weighted Nonlinear Least Squares Estimation of Unbalanced Cointegration Systems," EconomiX Working Papers 2019-14, University of Paris Nanterre, EconomiX.

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    More about this item

    Keywords

    Fractional integration; generalized least squares; linear regression; long range dependence; semiparametric estimation; Whittle likelihood;
    All these keywords.

    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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