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Bilateral Bootstrap Tests for Long Memory: An Application to the Silver Market

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  • Christian de Peretti

Abstract

Many time series in diverse fields of application may exhibit long-memory.The class of fractionally integrated (FI) processes can be used to try to model this strong data dependence. Asymptotic tests for FI include the re-scaled range statistic test and its modified form, the frequency-domain regression-based procedure, the modified Higuchi's test and Jensen's test. De Peretti and Marimoutou (2002) finds that proper finite-sample inferences are not possible using these techniques without correcting for size distortions. Some attempt this correction through `bootstrapping', but this method is not perfect and needs more study and improvements. In this paper, I examine and compare the finite-sample properties of parametric andnonparametric bootstrap tests by using graphical techniques of Davidson and MacKinnon (1998a) for showing whether they properly correct the distortions while retaining their power relative to the corresponding asymptotic tests.One of the tests uses a double bootstrap that provide better true power and size properties. I use a bilateral P value that permits the true power of the tests to grow when the size distortions are asymmetric. We then apply these procedures to a realtime series to investigate its long memory properties. Copyright Kluwer Academic Publishers 2003

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Bibliographic Info

Article provided by Society for Computational Economics in its journal Computational Economics.

Volume (Year): 22 (2003)
Issue (Month): 2 (October)
Pages: 187-212

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Handle: RePEc:kap:compec:v:22:y:2003:i:2:p:187-212

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Keywords: parametric and nonparametric bootstrap; long memory; tests; P value plots; corrected size-power curves;

References

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  1. Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, University of Manchester, vol. 66(1), pages 1-26, January.
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  12. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
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  16. Andersson, Michael K. & Gredenhoff, Mikael P., 1998. "Robust Testing for Fractional Integration Using the Bootstrap," Working Paper Series in Economics and Finance 218, Stockholm School of Economics.
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Cited by:
  1. Banerjee, Anindya & Urga, Giovanni, 2005. "Modelling structural breaks, long memory and stock market volatility: an overview," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 1-34.
  2. Murphy, A. & Izzeldin, M., 2009. "Bootstrapping long memory tests: Some Monte Carlo results," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2325-2334, April.

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