Nonparametric Tests for Serial Independence Based on Quadratic Forms

Cees Diks () and Valentyn Panchenko
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Cees Diks: CeNDEF, Faculty of Economics, University of Amsterdam

No 05-076/1, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: See also C. Diks: 'Nonparametric tests for independence' . In R. Meyers (Ed.), Encyclopedia of Complexity and Systems Science. Berlin: Springer Verlag, 2009.

Tests for serial independence and goodness-of-fit based on divergence notions between probability distributions, such as the Kullback-Leibler divergence or Hellinger distance, have recently received much interest in time series analysis. The aim of this paper is to introduce tests for serial independence using kernel-based quadratic forms. This separates the problem of consistently estimating the divergence measure from that of consistently estimating the underlying joint densities, the existence of which is no longer required. Exact level tests are obtained by implementing a Monte Carlo procedure using permutations of the original observations. The bandwidth selection problem is addressed by introducing a multiple bandwidth procedure based on a range of different bandwidth values. After numerically establishing that the tests perform well compared to existing nonparametric tests, applications to estimated time series residuals are considered. The approach is illustrated with an application to financial returns data.

Keywords: Bandwidth selection; Nonparametric tests; Serial independence; Quadratic forms (search for similar items in EconPapers)
JEL-codes: C14 C15 (search for similar items in EconPapers)
Date: 2005-08-02
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Working Paper: Nonparametric Tests for Serial Independence Based on Quadratic Forms (2005)
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