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Temporal aggregation and bandwidth selection in estimating long memory

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  • Souza, Leonardo Rocha

Abstract

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.

Suggested Citation

  • Souza, Leonardo Rocha, 2003. "Temporal aggregation and bandwidth selection in estimating long memory," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 478, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  • Handle: RePEc:fgv:epgewp:478
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    1. 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.
    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 da Rocha de, 2003. "The aliasing effect, the Fejer Kernel and temporally aggregated long memory processes," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 470, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    4. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    5. 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.
    6. 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.
    7. Chambers, Marcus J, 1998. "Long Memory and Aggregation in Macroeconomic Time Series," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1053-1072, November.
    8. 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.
    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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    Cited by:

    1. 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.
    2. repec:hal:journl:peer-00815563 is not listed on IDEAS
    3. Ye, Xunyu & Gao, Ping & Li, Handong, 2015. "Improving estimation of the fractionally differencing parameter in the SARFIMA model using tapered periodogram," Economic Modelling, Elsevier, vol. 46(C), pages 167-179.
    4. 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, vol. 29(C), pages 1-9.
    5. 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.
    6. Sun, Jingwei & Shi, Wendong, 2014. "Aggregation of the generalized fractional processes," Economics Letters, Elsevier, vol. 124(2), pages 258-262.
    7. Guglielmo Caporale & Luis Gil-Alana, 2013. "Long memory in US real output per capita," Empirical Economics, Springer, vol. 44(2), pages 591-611, April.
    8. 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.
    9. Hassler, Uwe, 2011. "Estimation of fractional integration under temporal aggregation," Journal of Econometrics, Elsevier, vol. 162(2), pages 240-247, June.
    10. Per Frederiksen & Frank S. Nielsen, 2008. "Estimation of Dynamic Models with Nonparametric Simulated Maximum Likelihood," CREATES Research Papers 2008-59, Department of Economics and Business Economics, Aarhus University.
    11. Pierre Perron & Wendong Shi, 2014. "Temporal Aggregation, Bandwidth Selection and Long Memory for Volatility Models," Boston University - Department of Economics - Working Papers Series wp2014-009, Boston University - Department of Economics.
    12. Giorgio Canarella & Stephen M. Miller, 2016. "Inflation Targeting: New Evidence from Fractional Integration and Cointegration," Working papers 2016-08, University of Connecticut, Department of Economics.
    13. 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.
    14. Uwe Hassler, 2013. "Effect of temporal aggregation on multiple time series in the frequency domain," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(5), pages 562-573, September.

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