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

  • Anurag Banerjee

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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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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  1. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-313, September.
  2. Christian Kleiber & Walter Kr�mer, 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
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