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Nevertheless, the Pettitt test does not detect a change in distribution if there is no change of location. In his article of 1979 Pettitt describes the null hypothesis as being that the T variables follow the same distribution F, and the alternative hypothesis as being that at a time t there is a change of distribution. The Pettitt's test is an adaptation of the tank-based Mann-Whitney test that allows identifying the time at which the shift occurs. The Pettitt's test is a nonparametric test that requires no assumption about the distribution of data. Before applying these tests, you need to be sure you want to identify a time at which there is a shift between two homogeneous series. Note 2: The tests presented below are sensitive to a trend (for example a linear trend). If one believes that the variance changes, you can use a comparison test of variances (F-test in the normal case, for example, or Kolmogorov-Smirnov in a more general case). For example, assuming that the variables follow normal distributions, one can use the test z (known variance) or the Student t test (estimated variance) to test the presence of a change at time t. Note 1: If you have a clear idea of the time when the shift occurs, one can use the tests available in the parametric or nonparametric tests sections. Exact calculations are either impossible or too costly in computing time. For all tests, XLSTAT provides p-values using Monte Carlo resamplings. The tests presented in this tool correspond to the alternative hypothesis of a single shift. The variety of the tests comes from the fact that there are many possible alternative hypotheses: changes in distribution, changes in average (one or more times) or presence of trend.
TESTS FOR HOMOSCEDASTICITY IN XLSTAT SERIES
Homogeneity tests involve a large number of tests, XLSTAT offer four tests ( Pettitt, Buishand, SNHT, or von Neumann), for which the null hypothesis is that a time series is homogenous between two given times. Homogeneity tests enables you to determine if a series may be considered as homogeneous over time, or if there is a time at which a change occurs. The results show that in this particular study area, Level 1 models, even BDF, are quite accurate, but the above modelling strategy maximises the extracted information from the local data and BMA reveals that the higher uncertainties occur at areas with higher vulnerability whereas lower uncertainties are observed at areas with lower vulnerabilities.What are homogeneity tests for time series The model performance is tested by using the nitrate-N concentrations measured for the aquifer. BMA is naturally an Inclusive Multiple Modelling (IMM) strategy at two levels at Level 1 multiple models are constructed and the paper constructs three AI (Artificial Intelligence) models, which comprise ANN (Artificial Neural Network), GEP (Gene Expression Programming), and SVM (Support Vector Machines) but their outputs are fed to the next level model at Level 2, BMA combines ANN, GEP and SVM (the Level 1 models) to quantify their inherent uncertainty in terms of within and in-between model errors. Bayesian Model Averaging (BMA) is used to study inherent uncertainties using the Basic DRASTIC Framework (BDF) for assessing the groundwater vulnerability in a study area related to Lake Urmia.