Abstract We propose a novel test to determine, given a time series, if the dynamics are generated by a deterministic (including low dimensional chaos), rather than a stochastic, process. In addition, we introduce a new nonparametric bootstrap test for independence which is consistent against a...

The BDS test is the best-known correlation integral–based test, and it is now an important part of most standard econometric data analysis software packages. This test depends on the proximity (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\varepsilon )$$</EquationSource> </InlineEquation> and the embedding dimension (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$m)$$</EquationSource> </InlineEquation> parameters both of which are chosen by the...</equationsource></inlineequation></equationsource></inlineequation>

In this article we introduce a test for independence between two processes &lcub;X_t&rcub; and &lcub;Y_t&rcub;. To this end we rely on symbolic dynamics and permutation entropy as a measure of dependence. As a result, a nonparametric (model-free) test for either linear or nonlinear processes is presented. The test...

In the present paper, we construct a new, simple, consistent and powerful test for spatial independence, called the SG test, by using the new concept of symbolic entropy as a measure of spatial dependence. The standard asymptotic distribution of the test is an affine transformation of the...