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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.

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  • Leonardo Rocha Souza, 2007. "Temporal Aggregation and Bandwidth selection in estimating long memory," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(5), pages 701-722, September.
    • Handle: RePEc:bla:jtsera:v:28:y:2007:i:5:p:701-722
    DOI: 10.1111/j.1467-9892.2007.00533.x
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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.
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    7. Souza, Leonardo Rocha, 2003. "The aliasing effect, the Fejer Kernel and temporally aggregated long memory processes," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 470, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    8. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    9. 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.
    10. 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.
    11. 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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    4. 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.
    5. 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.
    6. 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.
    7. Pierre Perron & Wendong Shi, 2020. "Temporal Aggregation and Long Memory for Asset Price Volatility," JRFM, MDPI, vol. 13(8), pages 1-18, August.
    8. Sun, Jingwei & Shi, Wendong, 2014. "Aggregation of the generalized fractional processes," Economics Letters, Elsevier, vol. 124(2), pages 258-262.
    9. Guglielmo Caporale & Luis Gil-Alana, 2013. "Long memory in US real output per capita," Empirical Economics, Springer, vol. 44(2), pages 591-611, April.
    10. 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.
    11. Hassler, Uwe, 2011. "Estimation of fractional integration under temporal aggregation," Journal of Econometrics, Elsevier, vol. 162(2), pages 240-247, June.
    12. 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.
    13. Avishek Bhandari & Bandi Kamaiah, 2021. "Long Memory and Fractality Among Global Equity Markets: a Multivariate Wavelet Approach," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 23-37, March.
    14. 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.
    15. 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.
    16. 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.
    17. Bhandari, Avishek, 2020. "Long memory and fractality among global equity markets: A multivariate wavelet approach," MPRA Paper 99653, University Library of Munich, Germany.
    18. 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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