Fourier methods for analyzing piecewise constant volatilities
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We develop procedures for testing whether a sequence of independent random variables has constant variance. If this is fulfilled, the modulus of a Fourier-type transformation of the volatility process is identically equal to one. Our approach takes advantage of this property considering a canonical estimator for the modulus under the assumption of piecewise identically distributed zero mean observations. Using blockwise variance estimation, we introduce several test statistics resulting from different weight functions. All of them are given by simple explicit formulae. We prove the consistency of the corresponding tests and compare them to alternative procedures on extensive Monte Carlo experiments. According to the results, our proposals offer fairly high power, particularly in the case of multiple structural breaks. They also allow for an adequate estimation of the change point positions. We apply our procedure to gold mining data and also briefly discuss how it can be modified to test for the stationarity of other distributional parameters.
KeywordsChange point analysis Variance Piecewise identical distribution Independence Weight function
The work was supported in part by the Collaborative Research Center 823, Project C3 (Analysis of Structural Change in Dynamic Processes), of the German Research Foundation and by Grant No.11699 of the Special Account for Research Grants (ELKE) of the National and Kapodistrian University of Athens. We also thank the anonymous referees for their valuable remarks which helped us to improve this work.
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