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Semiparametric Estimation in Time Series Regression with Long Range Dependence

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Author Info
Nielsen, Morten Oe. () (Department of Economics, University of Aarhus, Denmark)

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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.

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Paper provided by School of Economics and Management, University of Aarhus in its series Economics Working Papers with number 2002-17.

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Handle: RePEc:aah:aarhec:2002-17

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Related research
Keywords: Fractional integration; generalized least squares; linear regression; long range dependence; semiparametric estimation; Whittle likelihood;

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Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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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. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December. [Downloadable!] (restricted)
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  5. Carlos Velasco, 2003. "Gaussian Semi-parametric Estimation of Fractional Cointegration," Journal of Time Series Analysis, Blackwell Publishing, vol. 24(3), pages 345-378, 05. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
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Cited by:
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  1. 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. [Downloadable!]
  2. Peter M Robinson, 2007. "Multiple Local Whittle Estimation in StationarySystems," STICERD - Econometrics Paper Series /2007/525, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  3. Afonso Gonçalves da Silva & Peter M Robinson, 2006. "Finite Sample Performance in CointegrationAnalysis of Nonlinear Time Series with LongMemory," STICERD - Econometrics Paper Series /2006/501, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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