Authors: Wornowizki, Max
Fried, Roland
Meintanis, Simos G.
Title: Fourier methods for analysing piecewise constant volatilities
Language (ISO): en
Abstract: We develop procedures for testing the hypothesis that a parameter of a distribution is constant throughout a sequence of independent random variables. Our proposals are illustrated considering the variance and the kurtosis. Under the null hypothesis of constant variance, the modulus of a Fourier type transformation of the volatility process is identically equal to one. The approach proposed utilizes this property considering a canonical estimator for this modulus under the assumption of indepen- dent and piecewise identically distributed observations with zero mean. Using blockwise estimators we introduce several test statistics resulting from different weight functions which are all given by simple explicit for- mulae. The methods are compared to other tests for constant volatility in extensive Monte Carlo experiments. Our proposals offer comparatively good power particularly in the case of multiple structural breaks and allow adequate estimation of the positions of the structural breaks. An appli- cation to process control data is given, and it is shown how the methods can be adapted to test for constancy of other quantities like the kurtosis.
Subject Headings: change point analysis
weight function
piecewise identical distribution
Issue Date: 2016
Appears in Collections:Sonderforschungsbereich (SFB) 823

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