Is Brownian motion necessary to model high-frequency data?

By Yacine Aït-Sahalia, Jean Jacod. 2010

113 citations recorded by the source corpus.

This paper considers the problem of testing for the presence of a continuous part in a semimartingale sampled at high frequency. We provide two tests, one where the null hypothesis is that a continuous component is present, the other where the continuous component is absent, and the model is then driven by a pure jump process. When applied to high-frequency individual stock data, both tests point toward the need to include a continuous component in the model.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/81964995d345b76ef192f1346c85ec610d3dead4

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Citations in the corpus

MODELING HIGH-FREQUENCY FINANCIAL DATA BY PURE JUMP PROCESSES (2012, methodology): “In that aspect, our proposed test works more generally than those proposed earlier by Cont and Mancini (2007) and Aı̈t-Sahalia and Jacod (2010).”
Limit theorems for moving averages of discretized processes plus noise (2010, methodology): “ the noise-free framework are (i) estimation of the quadratic variation (see [8, 13]), (ii) tests for the presence of jumps (see [4, 9]), (iii) tests for the presence of the continuous component (see [3, 10]) or (iv) estimation of the “activity index” of the jump part (see [2, 20]). The aim of this ”
Econometrics of co-jumps in high-frequency data with noise (2015, background): “24 related to the strategy of proof pursued for truncated power variations in Aı̈t-Sahalia and Jacod (2010).”