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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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  • Christian de Peretti, 2003. "Bilateral Bootstrap Tests for Long Memory: An Application to the Silver Market," Computational Economics, Springer;Society for Computational Economics, vol. 22(2), pages 187-212, October.
    • Handle: RePEc:kap:compec:v:22:y:2003:i:2:p:187-212
    DOI: 10.1023/A:1026129729224
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    3. 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.
    4. 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.
    5. repec:lan:wpaper:3051 is not listed on IDEAS
    6. Christian Peretti, 2007. "Long Memory and Hysteresis," Springer Books, in: Gilles Teyssière & Alan P. Kirman (ed.), Long Memory in Economics, pages 363-389, Springer.
    7. Araichi, Sawssen & Peretti, Christian de & Belkacem, Lotfi, 2016. "Solvency capital requirement for a temporal dependent losses in insurance," Economic Modelling, Elsevier, vol. 58(C), pages 588-598.
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