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Temporal Aggregation and Bandwidth selection in estimating long memory

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  • Leonardo Rocha Souza

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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Bibliographic Info

Article provided by Wiley Blackwell in its journal Journal of Time Series Analysis.

Volume (Year): 28 (2007)
Issue (Month): 5 (09)
Pages: 701-722

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Handle: RePEc:bla:jtsera:v:28:y:2007:i:5:p:701-722

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  1. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, Elsevier, vol. 83(1-2), pages 325-348.
  2. Bisaglia, Luisa & Guegan, Dominique, 1998. "A comparison of techniques of estimation in long-memory processes," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 27(1), pages 61-81, March.
  3. Marcus J. Chambers, . "Long Memory and Aggregation in Macroeconomic Time Series," Economics Discussion Papers, University of Essex, Department of Economics 437, University of Essex, Department of Economics.
  4. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, Econometric Society, vol. 59(5), pages 1279-313, September.
  5. 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, Elsevier, vol. 20(3), pages 487-502.
  6. Diebold, Francis X. & Rudebusch, Glenn D., 1989. "Long memory and persistence in aggregate output," Journal of Monetary Economics, Elsevier, Elsevier, vol. 24(2), pages 189-209, September.
  7. Souza, Leonardo R. & Smith, Jeremy, 2002. "Bias in the memory parameter for different sampling rates," International Journal of Forecasting, Elsevier, Elsevier, vol. 18(2), pages 299-313.
  8. 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).
  9. Hosking, Jonathan R. M., 1996. "Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series," Journal of Econometrics, Elsevier, Elsevier, vol. 73(1), pages 261-284, July.
  10. Smith, Jeremy & Taylor, Nick & Yadav, Sanjay, 1995. "Comparing the Bias and Misspecification in Arfima Models," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 442, University of Warwick, Department of Economics.
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Cited by:
  1. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2009. "Long Memory in US Real Output per Capita," CESifo Working Paper Series 2671, CESifo Group Munich.
  2. 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, Elsevier, vol. 389(21), pages 4844-4854.
  3. Khan, M. Ali, 2003. "On choice of technique in the Robinson-Solow-Srinivasan model," Economics Working Papers (Ensaios Economicos da EPGE) 504, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  4. Leonardo Souza & Jeremy Smith & Reinaldo Souza, 2006. "Convex combinations of long memory estimates from different sampling rates," Computational Statistics, Springer, Springer, vol. 21(3), pages 399-413, December.
  5. 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.
  6. Uwe Hassler, 2011. "Estimation of fractional integration under temporal aggregation," Post-Print, HAL hal-00815563, HAL.
  7. Kuswanto, Heri, 2009. "A New Simple Test Against Spurious Long Memory Using Temporal Aggregation," Hannover Economic Papers (HEP), Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät dp-425, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  8. Caporale, Guglielmo Maria & Gil-Alana, Luis A., 2013. "Long memory and fractional integration in high frequency data on the US dollar/British pound spot exchange rate," International Review of Financial Analysis, Elsevier, Elsevier, vol. 29(C), pages 1-9.

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