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Adapting to Unknown Disturbance Autocorrelation in Regression with Long Memory

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  • Javier Hidalgo

    (London School of Economics, U.K)

  • Peter M. Robinson

    (London School of Economics, U.K)

Abstract

We show that it is possible to adapt to nonparametric disturbance autocorrelation in time series regression in the presence of long memory in both regressors and disturbances by using a smoothed nonparametric spectrum estimate in frequency-domain generalized least squares. When the collective memory in regressors and disturbances is sufficiently strong, ordinary least squares is not only asymptotically inefficient but asymptotically non-normal and has a slow rate of convergence, whereas generalized least squares is asymptotically normal and Gauss-Markov efficient with standard convergence rate. Despite the anomalous behavior of nonparametric spectrum estimates near a spectral pole, we are able to justify a standard construction of frequency-domain generalized least squares, earlier considered in case of short memory disturbances. A small Monte Carlo study of finite sample performance is included. Copyright The Econometric Society 2002.

Suggested Citation

  • 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.
    • Handle: RePEc:ecm:emetrp:v:70:y:2002:i:4:p:1545-1581
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    Citations

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    Cited by:

    1. Javier Hidalgo, 2007. "Specification Testing Forregression Models Withdependent Data," STICERD - Econometrics Paper Series 518, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. Hidalgo, Javier, 2005. "Semiparametric estimation for stationary processes whose spectra have an unknown pole," LSE Research Online Documents on Economics 6842, London School of Economics and Political Science, LSE Library.
    3. Javier Hidalgo, 2005. "Semiparametric Estimation for Stationary Processes whose Spectra have an Unknown Pole," STICERD - Econometrics Paper Series 481, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    4. Hira L. Koul & Fang Li, 2020. "Comparing two nonparametric regression curves in the presence of long memory in covariates and errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(4), pages 499-517, May.
    5. Morten Ørregaard 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.
    6. Marcel Aloy & Gilles de Truchis, 2012. "Estimation and Testing for Fractional Cointegration," Working Papers halshs-00793206, HAL.
    7. 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.
    8. Hidalgo, Javier, 2007. "Specification testing for regression models with dependent data," LSE Research Online Documents on Economics 6799, London School of Economics and Political Science, LSE Library.
    9. 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.
    10. Peter M Robinson, 2009. "Developments in the Analysis of Spatial Data," STICERD - Econometrics Paper Series 531, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    11. Hidalgo, Javier, 2002. "Consistent order selection with strongly dependent data and its application to efficient estimation," Journal of Econometrics, Elsevier, vol. 110(2), pages 213-239, October.
    12. Gilles de Truchis & Elena Ivona Dumitrescu, 2019. "Narrow-band Weighted Nonlinear Least Squares Estimation of Unbalanced Cointegration Systems," Working Papers hal-04141871, HAL.
    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. 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.
    15. George Kapetanios & Zacharias Psaradakis, 2016. "Semiparametric Sieve-Type Generalized Least Squares Inference," Econometric Reviews, Taylor & Francis Journals, vol. 35(6), pages 951-985, June.
    16. Robinson, Peter, 2008. "Developments in the analysis of spatial data," LSE Research Online Documents on Economics 25473, London School of Economics and Political Science, LSE Library.

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