Conference Agenda
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Statistics for Stochastic Processes Location: 0.002 Session Chair: Fabian Mies | |
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Sharp adaptive nonparametric testing for a constant volatility Albert-Ludwigs-Universität Freiburg, Germany Based on discrete observations within the nonparametric Gaussian white noise model $dY_t = sigma(t)dW_t$, we develop a test to infer if the volatility function $sigma(cdot)$ is constant. In particular, at prescribed significance, we simultaneously identify those time intervals where a violation of the constancy hypothesis occurs without a priori knowledge of their number and size. The testing procedure is shown to be minimax-optimal and adaptive for infill asymptotics and these results entail that a deviation from the null hypothesis of constancy is best measured in terms of $sup_{tin [0,1]}|sigma(t)^2 /|sigma|_{L^2}^2 - 1|$. The derivation of the optimal constants requires to build hypotheses with height solving $F_n(x)=0$ for given functions $F_n$ and to understand the asymptotic behavior of their solution, which is done using the implicit function theorem. | |
