Fourier methods for analysing piecewise constant volatilities
Loading...
Date
2016
Journal Title
Journal ISSN
Volume Title
Publisher
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.
Description
Table of contents
Keywords
change point analysis, weight function, independence, piecewise identical distribution, variance