Permutation tests for serial independence using three different statistics based on empirical distributions are proposed. These tests are shown to be consistent under the alternative of m-dependence and are all simple to perform in practice. A small simulation study demonstrates that the proposed tests have good power in small samples. The tests are then applied to Canadian gross domestic product (GDP data), corroborating the random-walk hypothesis of GDP growth.

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Keywords m-dependence, Permutation test, Serial independence, The blum-kiefer-rosenblatt statistic, The cramer-von mises statistic, The kolmogorov-smirnov statistic
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Journal Statistica Neerlandica
Tran, L. (Lanh), Chu, B, Huang, C. (Chunfeng), & Huynh, K.P. (Kim P.). (2014). Adaptive permutation tests for serial independence. Statistica Neerlandica, 68(3), 183–208. doi:10.1111/stan.12028