Open Access
June 2017 Semimartingale detection and goodness-of-fit tests
Adam D. Bull
Ann. Statist. 45(3): 1254-1283 (June 2017). DOI: 10.1214/16-AOS1484


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.


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Adam D. Bull. "Semimartingale detection and goodness-of-fit tests." Ann. Statist. 45 (3) 1254 - 1283, June 2017.


Received: 1 September 2015; Revised: 1 June 2016; Published: June 2017
First available in Project Euclid: 13 June 2017

zbMATH: 06756080
MathSciNet: MR3662454
Digital Object Identifier: 10.1214/16-AOS1484

Primary: 62M02
Secondary: 60J60 , 60J75 , 62G10 , 65T60

Keywords: diffusion , Goodness-of-fit , jump process , Semimartingale , Wavelets

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.45 • No. 3 • June 2017
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