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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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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 Australasian Meetings with number 159.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:ausm04:159

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Keywords: Sensitivity; long memory time series;

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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.
  2. 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.
  3. Prof. Dr. Walter Krämer & Christian Kleiber, . "Finite-Sample Power of the Durbin-Watson Test Against Fractionally Integrated Disturbances," Working Papers 10, Business and Social Statistics Department, Technische Universität Dortmund.
  4. King, Maxwell L. & Evans, Merran A., 1988. "Locally Optimal Properties of the Durbin-Watson Test," Econometric Theory, Cambridge University Press, vol. 4(03), pages 509-516, December.
  5. Lo, Andrew W. (Andrew Wen-Chuan), 1989. "Long-term memory in stock market prices," Working papers 3014-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  6. Nakamura, Shisei & Taniguchi, Masanobu, 1999. "Asymptotic Theory For The Durbin Watson Statistic Under Long-Memory Dependence," Econometric Theory, Cambridge University Press, vol. 15(06), pages 847-866, December.
  7. 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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