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Semimartingale detection and goodness-of-fit tests. (English) Zbl 1426.62307
Summary: In quantitative finance, we often fit a parametric semimartingale model to asset prices. To ensure our model is correct, we must then perform goodness-of-fit tests. In this paper, we give a new goodness-of-fit test for volatility-like processes, which is easily applied to a variety of semimartingale models. In each case, we reduce the problem to the detection of a semimartingale observed under noise. In this setting, we then describe a wavelet-thresholding test, which obtains adaptive and near-optimal detection rates.

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
62M02 Markov processes: hypothesis testing
60J60 Diffusion processes
62G10 Nonparametric hypothesis testing
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