A non-parametric test for independence based on symbolic dynamics. (English) Zbl 1163.62324
Summary: We propose a powerful, yet simple, nonparametric test for independence based on symbolic dynamic analysis. The absence of dependences in the unknown underlying data generating process is studied via symbolic dynamics. This is possible due to the ordering property of real numbers on an interval. Interestingly, the test is closely related to entropy concepts. Apart from being correctly sized, the new test is powerful for realistic finite data sets, and it is easy to use as one does not need to select any free parameter, which sharply contrasts with other tests of independence. In addition, the test is robust in the presence of noise which is one of the most typical cases when dealing with economic time series.
MSC:
| 62G10 | Nonparametric hypothesis testing |
| 37B10 | Symbolic dynamics |
| 62B10 | Statistical aspects of information-theoretic topics |
| 62G35 | Nonparametric robustness |
| 65C60 | Computational problems in statistics (MSC2010) |
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