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Sensitivity of OLS estimates against ARFIMA error process as small sample Test for long memory

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  • Anurag Banerjee

Abstract

Recently there have been much discussion of the theory and applications of long memory processes. In this paper we consider the standard linear model y=X*b+u and assume that the variance covariance matrix of the errors being generated from an ARFIMA(0,d,0) model. Following Banerjee and Magnus (1999) we investigate the sensitivity of the standard OLS slope (B_{L}) and sensitivity of variance estimates (D_{L}) of the linear model near =0. We also investigate the behavior of B_{L} and D_{L} under different short memory specifications (for example AR(1) and MA(1) processes) of u. Recalling the Durbin-Watson statistic (DW or D1) was related to the sensitivity measure for the OLS variance estimate against ARMA(p,q) errors ( Banerjee and Magnus (1999)).This gives us a method to discriminate between long memory and short memory processes, by constructing statistics B_{L/1} and D_{L/1}. In this we interpret D_{L/1} as test for long memory process without the short-memory effects

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  • Anurag Banerjee, 2004. "Sensitivity of OLS estimates against ARFIMA error process as small sample Test for long memory," Econometric Society 2004 Australasian Meetings 159, Econometric Society.
    • Handle: RePEc:ecm:ausm04:159
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    1. Banerjee, Anurag N. & Magnus, Jan R., 1999. "The sensitivity of OLS when the variance matrix is (partially) unknown," Journal of Econometrics, Elsevier, vol. 92(2), pages 295-323, October.
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    4. Christian Kleiber & Walter Krämer, 2005. "Finite-sample power of the Durbin--Watson test against fractionally integrated disturbances," Econometrics Journal, Royal Economic Society, vol. 8(3), pages 406-417, December.
    5. King, Maxwell L. & Evans, Merran A., 1988. "Locally Optimal Properties of the Durbin-Watson Test," Econometric Theory, Cambridge University Press, vol. 4(3), pages 509-516, December.
    6. Hisamatsu, Hiroyuki & Maekawa, Koichi, 1994. "The distribution of the Durbin-Watson statistic in integrated and near-integrated models," Journal of Econometrics, Elsevier, vol. 61(2), pages 367-382, April.
    7. Nakamura, Shisei & Taniguchi, Masanobu, 1999. "Asymptotic Theory For The Durbin–Watson Statistic Under Long-Memory Dependence," Econometric Theory, Cambridge University Press, vol. 15(6), pages 847-866, December.
    8. Kleiber, Christian & Krämer, Walter, 2004. "Finite sample of the Durbin-Watson test against fractionally integrated disturbances," Technical Reports 2004,15, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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    More about this item

    Keywords

    Sensitivity; long memory time series;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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