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Official Journal of the Asia Oceania Geosciences Society (AOGS)

Table 4 Groups of six parameters, the sample length n, the mean value \(\overline{u}\) and the variation coefficient Cvu of the stochastic component, the half-amplitude B, the periodicity length T and the initial phase t0 of the periodic component, used in statistical tests for investigating their influences on the identification of periodicities

From: Correlation-aided method for identification and gradation of periodicities in hydrologic time series

Test N \(\overline{u}\) Cvu B T t0
1 100, 150, 200, 250, 300, 350, 400, 450, 500 100 0.2 30 25 0
2 200 100, 150, 200, 250, 300, 350, 400, 450, 500 0.2 30 25 0
3 200 100 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45 30 25 0
4 200 100 0.2 1.0, 1.5, 2.0, 2.5, 3.0a 25 0
5 200 100 0.2 30 5, 10, 15, 20, 25, 30 0
6 200 100 0.2 30 300 0, ± 0.25π, ± 0.5π, ± 0.75π, πb
  1. aThe half-amplitude should be comparable with the stochastic fluctuation. Therefore, let B = A × M, where A = |quantile (x(t), 3/4) − quantile (x(t), 1/4)|. The quantile (x(t), 1/4) and quantile (x(t), 3/4) here are the upper and lower quartiles of time series x(t), respectively. M is a coefficient representing multiple relation between B and A
  2. bAs t0 = π and t0 = − π represent the same phase for the sinusoidal function, only t0 = π is tested