Abstract
Testing procedures for the null hypothesis of short memory against long memory alternatives are investigated. Our new test statistic is constructed using penalized splines method and Fan’s (1996) canonical multivariate normal hypothesis testing procedure. Using penalized splines method, we are able to eliminate the effects of nuisance parameters typically induced by short memory autocorrelation. Therefore, under the null hypothesis of any short memory processes, our new test statistic has a known asymptotic distribution. The proposed test statistic is completely data-driven or adaptive, which avoids the need to select any smoothing parameters. Since the convergence of our test statistic toward its asymptotic distribution is relatively slow, Monte Carlo methods are investigated to determine the corresponding critical value. The finite-sample properties of our procedure are compared to other well-known tests in the literature. These show that the empirical size properties of the new statistic can be very robust compared to existing tests and also that it competes well in terms of power.
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Acknowledgement
The first author of this chapter would like to express his sincere gratitude to his advisor, Prof. Hira L. Koul for his constant guidance, heart-warming encouragement, and generous support throughout author’s doctoral study at Michigan State University and years later. Prof. Koul’s extensive knowledge, insight, and dedication to statistics have been author’s source of inspiration to work harder and make the best effort possible. Both authors of this chapter are grateful to one referee for his/her very helpful suggestions, which greatly improved the presentation and the content of the chapter.
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Li, L., Lu, K. (2014). Testing for Long Memory Using Penalized Splines and Adaptive Neyman Methods. In: Lahiri, S., Schick, A., SenGupta, A., Sriram, T. (eds) Contemporary Developments in Statistical Theory. Springer Proceedings in Mathematics & Statistics, vol 68. Springer, Cham. https://doi.org/10.1007/978-3-319-02651-0_16
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DOI: https://doi.org/10.1007/978-3-319-02651-0_16
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