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Abstract:
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Several new statistical procedures for high frequency financial data analysis have been developed for estimating risk quantities and testing the presence of jump in the underlying continuous-time financial processes. Although the role of micro-market noise is important in high frequency financial data, there are basic questions on the effects of presence of noise and jump in the underlying stochastic processes. When there can be jump and (micro-market) noise at the same time, it is not obvious whether the existing statistical methods are reliable or not for the applications in actual data analysis. We investigate the misspecification effects of jump and noise on some basic statistics and the testing procedures for jumps proposed by Ait-Sahalia and Jacod (2009, Annals of Statistics). We have found that their first test is asymptotically robust in the small-noise asymptotic sense against possible misspecification while their second test is quite sensitive to the presence of noise.
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