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Temporal aggregation and bandwidth selection in estimating long memory

  • Souza, Leonardo Rocha

This paper reinterprets results of Ohanissian et al (2003) to show the asymptotic equivalence of temporally aggregating series and using less bandwidth in estimating long memory by Geweke and Porter-Hudak’s (1983) estimator, provided that the same number of periodogram ordinates is used in both cases. This equivalence is in the sense that their joint distribution is asymptotically normal with common mean and variance and unity correlation. Furthermore, I prove that the same applies to the estimator of Robinson (1995). Monte Carlo simulations show that this asymptotic equivalence is a good approximation in finite samples. Moreover, a real example with the daily US Dollar/French Franc exchange rate series is provided.

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Paper provided by FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil) in its series Economics Working Papers (Ensaios Economicos da EPGE) with number 478.

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Date of creation: 30 Mar 2003
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Handle: RePEc:fgv:epgewp:478
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  1. Chambers, Marcus J, 1995. "Long Memory and Aggregation in Macroeconomic Time Series," Economics Discussion Papers 2766, University of Essex, Department of Economics.
  2. Smith, Jeremy & Taylor, Nick & Yadav, Sanjay, 1995. "Comparing the Bias and Misspecification in Arfima Models," The Warwick Economics Research Paper Series (TWERPS) 442, University of Warwick, Department of Economics.
  3. Souza, Leonardo R. & Smith, Jeremy, 2004. "Effects of temporal aggregation on estimates and forecasts of fractionally integrated processes: a Monte-Carlo study," International Journal of Forecasting, Elsevier, vol. 20(3), pages 487-502.
  4. Bisaglia, Luisa & Guegan, Dominique, 1998. "A comparison of techniques of estimation in long-memory processes," Computational Statistics & Data Analysis, Elsevier, vol. 27(1), pages 61-81, March.
  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. Diebold, Francis X. & Rudebusch, Glenn D., 1989. "Long memory and persistence in aggregate output," Journal of Monetary Economics, Elsevier, vol. 24(2), pages 189-209, September.
  7. Souza, Leonardo da Rocha de, 2003. "The aliasing effect, the Fejer Kernel and temporally aggregated long memory processes," Economics Working Papers (Ensaios Economicos da EPGE) 470, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  8. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
  9. Souza, Leonardo R. & Smith, Jeremy, 2002. "Bias in the memory parameter for different sampling rates," International Journal of Forecasting, Elsevier, vol. 18(2), pages 299-313.
  10. Hosking, Jonathan R. M., 1996. "Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series," Journal of Econometrics, Elsevier, vol. 73(1), pages 261-284, July.
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