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Common price and volatility jumps in noisy high-frequency data. (English) Zbl 1398.62281
This paper deals with testing high-frequency financial data for simultaneous jumps in price and volatility. The investigated data model is of the form $Y_{i} = X_{i/n} + \epsilon_i$ with the latent log-price process $$X$$ satisfying $X_t = X_0 + \int_0^t b_s d s + \int_0^t \sigma_s d W_s + P(t),$ where $$P$$ is another specific random process generating jumps. To test for simultaneous jumps in price and volatility, first price jumps are localized via thresholding, and afterwards local tests for volatility jumps based on self-scaling test statistics are performed. The asymptotic distribution of this test statistic is analyzed, such that the testing procedure can be properly calibrated.
Details on a possible implementation are provided, as well as a simulation study which reveals the investigated procedure to be robust w.r.t. the microstructure noise $$\epsilon_i$$. The procedure is furthermore applied to real NASDAQ data.

##### MSC:
 62P05 Applications of statistics to actuarial sciences and financial mathematics 62M09 Non-Markovian processes: estimation 62G10 Nonparametric hypothesis testing 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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