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Temporal Aggregation and Bandwidth Selection in Estimating Long Memory

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  • Souza, Leonardo Rocha

Abstract

This article aims at showing that a temporal aggregation and a specific bandwidth reduction lead to the same asymptotic properties in estimating long memory by Geweke and Porter-Hudak's [Journal of Time Series Analysis (1983) vol. 4, pp. 221-237] and Robinson's [Annals of Statistics (1995b) vol. 23, pp. 1630-1661] estimators. In other words, irrespective of the level of temporal aggregation, the asymptotic properties of the estimator are uniquely determined by the number of periodogram ordinates used in the estimation, provided some mild additional assumptions are imposed. Monte Carlo simulations show that this result is a good approximation in finite samples. A real example with the daily US Dollar/French Franc exchange rate series is also provided. Copyright 2007 The Author Journal compilation 2007 Blackwell Publishing Ltd.

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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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References

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  1. 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.
  2. Marcus J. Chambers, . "Long Memory and Aggregation in Macroeconomic Time Series," Economics Discussion Papers 437, University of Essex, 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. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. Souza, Leonardo Rocha, 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).
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Cited by:
  1. Leonardo Souza & Jeremy Smith & Reinaldo Souza, 2006. "Convex combinations of long memory estimates from different sampling rates," Computational Statistics, Springer, vol. 21(3), pages 399-413, December.
  2. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2009. "Long Memory in US Real Output per Capita," Discussion Papers of DIW Berlin 891, DIW Berlin, German Institute for Economic Research.
  3. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2013. "Long Memory and Fractional Integration in High Frequency Data on the US Dollar / British Pound Spot Exchange Rate," CESifo Working Paper Series 4224, CESifo Group Munich.
  4. Kuswanto, Heri, 2009. "A New Simple Test Against Spurious Long Memory Using Temporal Aggregation," Hannover Economic Papers (HEP) dp-425, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  5. Kang, Sang Hoon & Cheong, Chongcheul & Yoon, Seong-Min, 2010. "Contemporaneous aggregation and long-memory property of returns and volatility in the Korean stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4844-4854.
  6. Per Frederiksen & Frank S. Nielsen, 2008. "Estimation of Dynamic Models with Nonparametric Simulated Maximum Likelihood," CREATES Research Papers 2008-59, School of Economics and Management, University of Aarhus.
  7. Hassler, Uwe, 2011. "Estimation of fractional integration under temporal aggregation," Journal of Econometrics, Elsevier, vol. 162(2), pages 240-247, June.
  8. M. Ali Khan & Tapan Mitra, 2005. "On choice of technique in the Robinson-Solow-Srinivasan model," International Journal of Economic Theory, The International Society for Economic Theory, vol. 1(2), pages 83-110.

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