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Biometrika 1987 74(1):95-101; doi:10.1093/biomet/74.1.95
© 1987 by Biometrika Trust
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Tests for Hurst effect

R. B. DAVIES and D. S. HARTE

Applied Mathematics Division, D.S.I.R. Wellington, New Zealand
Biometrics Section, Ministry of Agriculture and Fisheries Wellington, New Zealand

We consider the power of tests for distinguishing between fractional Gaussian noise and white noise of a first-order autoregressive process. Our tests are based on the beta-optimal principle (Davies, 1969), local optimality and the rescaled range test.

Key Words: Autoregressive process • Beta-optimal test • Fractional Gaussian noise • Hydrological series • Locally optimal test • Long-term dependence • Rescaled range • Self-similar process • Simulation


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