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Nonparametric Tests for Independence

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Complex Systems in Finance and Econometrics

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Article Outline

Glossary

Definition of the Subject

Introduction

Invariant Tests

Tests Based on Divergence Measures

Tests Based on Other Measures of Dependence

Bootstrap and Permutation Tests

Future Directions

Bibliography

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Notes

  1. 1.

    It is exactly degenerate for i.i.d. data from the uniform distribution on the circle, i. e. the interval \({[0,a]}\) with the endpoints identified [16]. Theiler [102] simulated variance of \( S=C_{m,n}(\varepsilon)-(C_{i,n}(\varepsilon))^m \) in the degenerate case, and found that it converges to 0 at the rate \({n^{-2}}\) instead of the usual rate \({n^{-1}}\).

Abbreviations

Hypothesis :

A hypothesis is a statement concerning the (joint) distribution underlying the observed data.

Nonparametric test :

In contrast to a parametric test, a nonparametric test does not presume a particular parametric structure concerning the data generating process.

Serial dependence :

Statistical dependence among time series observations.

Time series :

A sequence of observed values of some variable over time, such as a historical temperature record, a sequence of closing prices of a stock, etc.

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  1. University of Amsterdam, Amsterdam, The Netherlands

    Cees Diks

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  1. Cees Diks
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  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Diks, C. (2009). Nonparametric Tests for Independence. In: Meyers, R. (eds) Complex Systems in Finance and Econometrics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7701-4_35

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