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Conditional-Sum-of-Squares Estimation ofModels for Stationary Time Series with Long Memory

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  • Peter M Robinson

Abstract

Employing recent results of Robinson (2005) we consider the asymptotic properties ofconditional-sum-of-squares (CSS) estimates of parametric models for stationary timeseries with long memory. CSS estimation has been considered as a rival to Gaussianmaximum likelihood and Whittle estimation of time series models. The latter kinds ofestimate have been rigorously shown to be asymptotically normally distributed in case oflong memory. However, CSS estimates, which should have the same asymptoticdistributional properties under similar conditions, have not received comparabletreatment: the truncation of the infinite autoregressive representation inherent in CSSestimation has been essentially ignored in proofs of asymptotic normality. Unlike in shortmemory models it is not straightforward to show the truncation has negligible effect.

Suggested Citation

  • Peter M Robinson, 2006. "Conditional-Sum-of-Squares Estimation ofModels for Stationary Time Series with Long Memory," STICERD - Econometrics Paper Series 505, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:505
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    Cited by:

    1. Alonso Fernández, Andrés Modesto & Bastos, Guadalupe & García-Martos, Carolina, 2017. "BIAS correction for dynamic factor models," DES - Working Papers. Statistics and Econometrics. WS 24029, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Martin, Gael M. & Nadarajah, K. & Poskitt, D.S., 2020. "Issues in the estimation of mis-specified models of fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 215(2), pages 559-573.
    3. Tobias Hartl & Rolf Tschernig & Enzo Weber, 2020. "Fractional trends in unobserved components models," Papers 2005.03988, arXiv.org, revised May 2020.
    4. Javier Hualde & Morten {O}rregaard Nielsen, 2022. "Fractional integration and cointegration," Papers 2211.10235, arXiv.org.
    5. Papailias, Fotis & Fruet Dias, Gustavo, 2015. "Forecasting long memory series subject to structural change: A two-stage approach," International Journal of Forecasting, Elsevier, vol. 31(4), pages 1056-1066.
    6. Tobias Hartl, 2021. "Monitoring the pandemic: A fractional filter for the COVID-19 contact rate," Papers 2102.10067, arXiv.org.
    7. Morten Ørregaard Nielsen, 2015. "Asymptotics for the Conditional-Sum-of-Squares Estimator in Multivariate Fractional Time-Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 154-188, March.
    8. Samir Amine & Wilner Predelus, 2019. "The Persistence of the 2008-2009 Recession and Insolvency Filings in Canada," Economics Bulletin, AccessEcon, vol. 39(1), pages 84-93.
    9. Baillie, Richard T. & Kapetanios, George, 2008. "Nonlinear models for strongly dependent processes with financial applications," Journal of Econometrics, Elsevier, vol. 147(1), pages 60-71, November.
    10. Hartl, Tobias, 2021. "Monitoring the pandemic: A fractional filter for the COVID-19 contact rate," VfS Annual Conference 2021 (Virtual Conference): Climate Economics 242380, Verein für Socialpolitik / German Economic Association.
    11. Baillie, Richard T. & Kongcharoen, Chaleampong & Kapetanios, George, 2012. "Prediction from ARFIMA models: Comparisons between MLE and semiparametric estimation procedures," International Journal of Forecasting, Elsevier, vol. 28(1), pages 46-53.
    12. Richard Hunt & Shelton Peiris & Neville Weber, 2022. "Estimation methods for stationary Gegenbauer processes," Statistical Papers, Springer, vol. 63(6), pages 1707-1741, December.

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